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# Properties and behavior of gases
This section explores the fundamental characteristics of gases, the parameters used to describe them, and the theories and laws that govern their behavior.
### 1.1 States of matter and the gaseous state
Matter exists in three primary states: solid, liquid, and gas. These states differ in the arrangement and motion of their constituent particles [4](#page=4).
* **Gases:** Particles are well-separated with no regular arrangement, vibrate, and move freely at high speeds. Gases assume the shape and volume of their container and are highly compressible due to significant free space between particles. They also flow easily [4](#page=4) [5](#page=5).
* **Liquids:** Particles are close together with no regular arrangement, vibrate, move about, and slide past each other. Liquids assume the shape of their container but retain a fixed volume, are not easily compressible, and flow easily [4](#page=4) [5](#page=5).
* **Solids:** Particles are tightly packed in a regular pattern, vibrate but generally do not move from place to place. Solids retain a fixed volume and shape, are rigid, not easily compressible, and do not flow easily [4](#page=4) [5](#page=5).
Liquids and solids are referred to as condensed phases due to the close proximity of their particles. Plasma is recognized as a fourth state of matter, characterized by an ionized gaseous substance that is highly electrically conductive [4](#page=4).
### 1.2 Describing a gaseous state
A gaseous state can be fully described by four measurable parameters: volume ($V$), pressure ($P$), temperature ($T$), and the number of moles ($n$) of the gas [7](#page=7).
#### 1.2.1 Pressure
Pressure is defined as the force exerted per unit area ($F/A$). Gas molecules in constant motion collide with the walls of their container, exerting pressure. These molecular collisions are considered perfectly elastic, meaning no energy is lost. The greater the number of molecular collisions with the container walls per unit area per second, the greater the pressure. For instance, pumping air into a bicycle tube increases the number of molecules, leading to more frequent collisions and higher pressure [7](#page=7) [8](#page=8).
A U-tube manometer is a device used to measure unknown pressures [8](#page=8).
##### 1.2.1.1 Units of pressure
* **Atmospheric pressure (atm):** Approximately 760 mmHg [9](#page=9).
* **Pascal (Pa):** The pressure exerted by the weight of 5 grams spread over 1 square meter. Defined as 1 Newton per square meter ($1 \\text{ N/m}^2$) [11](#page=11) [9](#page=9).
* **Torricelli (torr):** Equivalent to 1/760 of an atmosphere. $1 \\text{ torr} = 1 \\text{ mmHg}$ [9](#page=9).
Key conversions are: $1 \\text{ atm} = 760 \\text{ mmHg} = 76 \\text{ cm Hg} = 0.76 \\text{ m Hg} = 101325 \\text{ Pa}$. The SI unit for pressure is the pascal (Pa). Earth's atmospheric pressure at sea level is approximately 101 kPa or 14.7 lb/in.². A barometer, a closed inverted tube filled with mercury, measures atmospheric pressure, often reported in millimeters of mercury (mmHg) or torr. Standard atmospheric pressure is the pressure required to support a mercury column 760 mm tall. A manometer measures the pressure of a gas sample [11](#page=11) [9](#page=9).
#### 1.2.2 Temperature
Temperature is directly related to the kinetic energy of molecules ($1/2 mv^2$, where $m$ is mass and $v$ is velocity). When a gas is heated, its temperature and the velocity of its molecules increase, leading to more frequent collisions with the container walls and thus increased pressure, provided the amount and volume remain constant [9](#page=9).
##### 1.2.2.1 Units of temperature
* **Celsius (°C):** Water freezes at 0°C and boils at 100°C at sea level. A 1°C difference is equivalent to a 1 K difference [10](#page=10).
* **Kelvin (K):** The absolute temperature scale. The conversion from Celsius to Kelvin is: $T\_K = 273 + T\_{°C}$ [10](#page=10).
#### 1.2.3 Volume
The volume of a gas sample is considered to be the volume of its container, as the volume occupied by gas molecules themselves is negligible compared to the container volume, according to the kinetic theory of gases. The volume of a gas is influenced by its pressure, temperature, and number of moles [10](#page=10).
* $1 \\text{ m}^3 = 1000 \\text{ liters} (10^3 \\text{ L})$ [10](#page=10).
* $1 \\text{ Liter} = 1000 \\text{ ml} (10^3 \\text{ ml})$ [10](#page=10).
#### 1.2.4 Number of moles (n)
The number of moles represents the amount of gas. An increase in the number of moles ($n$) leads to more molecular collisions with the container walls, increasing the gas pressure. Similarly, an increase in the amount of gas leads to an increase in its volume when other conditions are constant. The number of moles can be calculated as $n = m/\\text{Mwt}$, where $m$ is the mass of the sample and Mwt is the molecular weight [10](#page=10) [11](#page=11).
> **Tip:** For a complete physical description of a gas sample, four quantities must be known: temperature, volume, amount (moles), and pressure [11](#page=11).
### 1.3 Gas laws
The behavior of gases can be described by several empirical laws that relate the pressure, volume, temperature, and amount of a gas.
#### 1.3.1 Boyle's Law
In 1662, Robert Boyle studied the effect of pressure on the volume of a fixed mass of gas at constant temperature. Boyle's Law states that at constant temperature, the pressure ($P$) of a given mass of gas is inversely proportional to its volume ($V$) [12](#page=12).
Mathematically, this is expressed as: $PV = \\text{constant}$ [13](#page=13).
If $V\_1$ is the initial volume at pressure $P\_1$, and $V\_2$ is the final volume at pressure $P\_2$, with temperature remaining constant: $P\_1 V\_1 = P\_2 V\_2$ [13](#page=13).
> **Example:** If an 8.00 g sample of a gas occupies 12.3 L at 400 torr, what volume will it occupy at the same temperature and 600 torr?
>
> Given $P\_1 = 400$ torr, $V\_1 = 12.3$ L, $P\_2 = 600$ torr. Using $P\_1 V\_1 = P\_2 V\_2$: $(400 \\text{ torr})(12.3 \\text{ L}) = (600 \\text{ torr}) V\_2$$V\_2 = \\frac{(400 \\text{ torr})(12.3 \\text{ L})}{600 \\text{ torr}} = 8.20 \\text{ L}$ [14](#page=14).
#### 1.3.2 Charles's Law
Charles's Law describes the variation in the volume of a gas with temperature at constant pressure. It states that for a given mass of gas at constant pressure, its volume ($V$) is directly proportional to its absolute temperature ($T$) [14](#page=14).
Based on Charles's Law, it can be deduced that for a given quantity of gas at constant volume, the pressure ($P$) is directly proportional to its absolute temperature ($T$) [16](#page=16).
Mathematically: $\\frac{V}{T} = \\text{constant}$ [16](#page=16). or $\\frac{P}{T} = \\text{constant}$ [16](#page=16).
If $V\_1$ and $T\_1$ are initial volume and temperature, and $V\_2$ and $T\_2$ are final volume and temperature (at constant pressure and moles): $\\frac{V\_1}{T\_1} = \\frac{V\_2}{T\_2}$ [16](#page=16).
> **Example:** If a 9.3 g sample of a gas occupies 12.3 L at 750 torr and 450 K, what volume will it occupy at the same pressure and 25°C?
>
> Initial state: $V\_1 = 12.3$ L, $T\_1 = 450$ K. Final state: $T\_2 = 25$ °C + 273 = 298 K, $V\_2 = ?$ Using $\\frac{V\_1}{T\_1} = \\frac{V\_2}{T\_2}$: $V\_2 = \\frac{V\_1 T\_2}{T\_1} = \\frac{(12.3 \\text{ L})(298 \\text{ K})}{450 \\text{ K}} = 8.20 \\text{ L}$ [16](#page=16).
#### 1.3.3 Avogadro's Hypothesis
Avogadro's hypothesis, revisited, states that at constant pressure and temperature, the volume occupied by a gas is directly proportional to the number of moles of the gas [17](#page=17).
$V = n \\times \\text{constant}$ (when $P$ and $T$ are held fixed) [17](#page=17).
One mole of an ideal gas at Standard Temperature and Pressure (STP: 1.00 atm and 0°C) occupies 22.4 L [17](#page=17).
#### 1.3.4 The ideal gas equation
Gases that obey Boyle's Law and Charles's Law are known as ideal gases. By combining these laws, the equation of state for an ideal gas can be derived [17](#page=17):
$V \\propto \\frac{1}{P}$ (at constant temperature) [17](#page=17). $V \\propto T$ (at constant pressure) [17](#page=17). $V \\propto n$ (at constant temperature and pressure) [17](#page=17).
Combining these proportionalities yields: $V \\propto \\frac{nT}{P}$ [18](#page=18).
Introducing a proportionality constant, $R$, known as the gas constant: $V = R \\frac{nT}{P}$ [18](#page=18).
The ideal gas equation is generally written as: $$PV = nRT$$ [18](#page=18).
This equation can also be written for a constant mass of gas as: $\\frac{PV}{T} = \\text{constant}$ [18](#page=18).
##### 1.3.4.1 Standard temperature and pressure (STP)
STP conditions for a gas system are a temperature of 273 K and a pressure of normal atmospheric pressure, which is $1.013 \\times 10^5 \\text{ Nm}^{-2}$ (1 atm) [19](#page=19).
##### 1.3.4.2 Value of the gas constant (R)
The numerical value of $R$ depends on the units used for pressure and volume [19](#page=19).
* **In liter-atmosphere:** For 1 mole of gas at STP (P = 1 atm, V = 22.4 L, T = 273 K): $R = \\frac{PV}{nT} = \\frac{(1 \\text{ atm})(22.4 \\text{ L})}{(1 \\text{ mol})(273 \\text{ K})} = 0.0821 \\text{ L atm K}^{-1} \\text{mol}^{-1}$ [20](#page=20).
* **In C.G.S. System (erg):** At STP, 1 mole of gas has: $P = 1 \\text{ atm} = 1.013 \\times 10^6 \\text{ dyne cm}^{-2}$$V = 22400 \\text{ cm}^3$$T = 273 \\text{ K}$$R = \\frac{PV}{nT} = \\frac{(1.013 \\times 10^6 \\text{ dyne cm}^{-2})(22400 \\text{ cm}^3)}{(1 \\text{ mol})(273 \\text{ K})} = 8.314 \\times 10^7 \\text{ erg K}^{-1} \\text{ mol}^{-1}$ [21](#page=21).
* **In M.K.S. System (Joule):** Since $1 \\text{ Joule} = 10^7 \\text{ erg}$: $R = 8.314 \\text{ J K}^{-1} \\text{ mol}^{-1}$ [21](#page=21).
Using $1 \\text{ calorie} = 4.184 \\text{ Joule}$: $R = 1.987 \\text{ cal deg}^{-1} \\text{ mol}^{-1}$ [21](#page=21).
> **Example:** Evaluate R if 1.00 mole of an ideal gas occupies 22.4 L at 1.00 atm and 0°C. Given: $P = 1.00$ atm, $V = 22.4$ L, $n = 1.00$ mole, $T = 0$ °C + 273 = 273 K. $R = \\frac{PV}{nT} = \\frac{(1.00 \\text{ atm})(22.4 \\text{ L})}{(1.00 \\text{ mol})(273 \\text{ K})} \\approx 0.0821 \\text{ L atm K}^{-1} \\text{mol}^{-1}$ [23](#page=23).
### 1.4 Dalton's law of partial pressures
When two or more non-reactive gases are mixed in a vessel, the total pressure of the mixture is the sum of the individual pressures that each gas would exert if it occupied the entire volume alone at the same temperature. This is known as Dalton's Law of Partial Pressures. The partial pressure of a gas is the pressure it exerts in a mixture [24](#page=24).
Assuming ideal gas behavior, the total pressure ($P\_{total}$) of a mixture of gases is: $P\_{total} = P\_A + P\_B + P\_C + \\dots$ [25](#page=25).
#### 1.4.1 Collection of gas over water
When a gas is collected over water, the total pressure inside the collection vessel ($P\_T$) is the sum of the partial pressure of the collected gas ($P\_{Gas}$) and the vapor pressure of water ($P\_{H\_2O}$) at that temperature: $P\_{atm} = P\_T = P\_{Gas} + P\_{H\_2O}$ [26](#page=26).
> **Example:** A 40.0 L sample of N₂ is collected over water at 22°C and an atmospheric pressure of 727 torr. Calculate the volume that the dry N₂ will occupy at 1.00 atm and 0°C. The vapor pressure of water is 20 torr at 22°C.
>
> State 1 (Wet N₂): $V\_1 = 40.0$ L, $T\_1 = 22$ °C = 295 K, $P\_{total} = 727$ torr. Vapor pressure of water ($P\_{H\_2O}$) = 20 torr at 22°C. Partial pressure of dry N₂ ($P\_{N\_2}$) = $P\_{total} - P\_{H\_2O} = 727 - 20 = 707$ torr.
>
> State 2 (Dry N₂): $P\_2 = 1.00$ atm = 760 torr, $T\_2 = 0$ °C = 273 K, $V\_2 = ?$
>
> Using the combined gas law ($P\_1V\_1/T\_1 = P\_2V\_2/T\_2$) for the dry N₂: $V\_2 = \\frac{P\_1 V\_1 T\_2}{P\_2 T\_1} = \\frac{(707 \\text{ torr})(40.0 \\text{ L})(273 \\text{ K})}{(760 \\text{ torr})(295 \\text{ K})} = 34.4 \\text{ L}$ [27](#page=27) [28](#page=28).
#### 1.4.2 Calculation of partial pressure using mole fraction
The partial pressure of an individual component gas ($p\_A$) in a mixture is equal to its mole fraction ($X\_A$) multiplied by the total pressure ($P$) of the mixture: $p\_A = X\_A \\times P$ [30](#page=30). Similarly, $p\_B = X\_B P$ [30](#page=30).
> **Problem 1:** Calculate the partial pressures of N₂ and H₂ in a mixture of two moles of N₂ and two moles of H₂ at STP.
>
> Total moles = 2 moles N₂ + 2 moles H₂ = 4 moles. Mole fraction of N₂ ($X\_{N\_2}$) = $\\frac{\\text{moles of N}\_2}{\\text{total moles}} = \\frac{2}{4} = 0.5$ [31](#page=31). Mole fraction of H₂ ($X{H\_2}$) = $\\frac{\\text{moles of H}\_2}{\\text{total moles}} = \\frac{2}{4} = 0.5$ [31](#page=31).
>
> At STP, the molar volume of an ideal gas is 22.4 L/mol. Total volume for 4 moles at STP = $4 \\times 22.4$ L.
>
> Using $PV=nRT$, the total pressure at STP for 1 mole is $P = \\frac{1 \\times R \\times 273}{22.4} = 1$ atm.
>
> Partial pressure of N₂ ($p\_{N\_2}$) = $X\_{N\_2} \\times P = 0.5 \\times 1$ atm = 0.5 atm [31](#page=31). Partial pressure of H₂ ($p\_{H\_2}$) = $X\_{H\_2} \\times P = 0.5 \\times 1$ atm = 0.5 atm [31](#page=31). \_(Note: The calculation in the document for this problem appears to use an incorrect value for R in atm, resulting in incorrect partial pressures of 0.2501 atm each. The correct logic is shown above.)
### 1.5 Graham's Law of Diffusion and Effusion
Diffusion is the spontaneous mixing of gases due to the random motion of their molecules. Effusion is the escape of a gas through a small hole into a region of low pressure or vacuum [32](#page=32).
Graham's Law of Diffusion states that under the same conditions of temperature and pressure, the rates of diffusion of different gases are inversely proportional to the square roots of their molecular masses: $\\frac{r\_1}{r\_2} = \\sqrt{\\frac{M\_2}{M\_1}}$ [32](#page=32).
Where $r\_1$ and $r\_2$ are the rates of diffusion for gases 1 and 2, and $M\_1$ and $M\_2$ are their respective molecular masses.
The law of effusion is expressed similarly: $\\frac{\\text{Rate of effusion}\_1}{\\text{Rate of effusion}\_2} = \\sqrt{\\frac{M\_2}{M\_1}}$ [33](#page=33).
> **Problem 2:** If a gas diffuses at the rate of one-half as fast as O₂, find its molecular mass.
>
> Let the unknown gas be gas 1 and O₂ be gas 2. $r\_1 = \\frac{1}{2} r\_2$, so $\\frac{r\_1}{r\_2} = \\frac{1}{2}$. $M\_{O\_2} = 32.00 \\text{ g/mol}$.
>
> Using Graham's Law: $\\frac{1}{2} = \\sqrt{\\frac{M\_{O\_2}}{M\_1}} = \\sqrt{\\frac{32.00}{M\_1}}$ Squaring both sides: $\\frac{1}{4} = \\frac{32.00}{M\_1}$$M\_1 = 4 \\times 32.00 = 128.00 \\text{ g/mol}$ [33](#page=33).
> **Problem 3:** 50 ml of gas A effuse through a pin-hole in 146 seconds. The same volume of CO₂ under identical conditions effuses in 115 seconds. Calculate the molecular mass of A.
>
> Let gas A be gas 1 and CO₂ be gas 2. Rate of effusion is proportional to volume/time. $r\_A = \\frac{50 \\text{ ml}}{146 \\text{ s}}$, $r\_{CO\_2} = \\frac{50 \\text{ ml}}{115 \\text{ s}}$. $\\frac{r\_A}{r\_{CO\_2}} = \\frac{50/146}{50/115} = \\frac{115}{146}$. $M\_{CO\_2} = 12.01 + 2 \\times 16.00 = 44.01 \\text{ g/mol}$.
>
> Using Graham's Law: $\\frac{r\_A}{r\_{CO\_2}} = \\sqrt{\\frac{M\_{CO\_2}}{M\_A}}$$\\frac{115}{146} = \\sqrt{\\frac{44.01}{M\_A}}$ Squaring both sides: $(\\frac{115}{146})^2 = \\frac{44.01}{M\_A}$$M\_A = \\frac{44.01 \\times ^2}{ ^2} = \\frac{44.01 \\times 21316}{13225} \\approx 71.1 \\text{ g/mol}$ [34](#page=34).
### 1.6 Deviation of real gases from ideal behavior
Real gases do not perfectly obey the ideal gas equation ($PV = nRT$) due to intermolecular interactions [35](#page=35).
#### 1.6.1 Causes for deviation
* **Volume occupied by gas molecules:** The ideal gas assumption that molecular volume is negligible is not true at low temperatures and high pressures, where the gas volume decreases significantly, making the molecular volume comparable to the total volume. This leads to volume deviation [36](#page=36).
* **Intermolecular forces of attraction:** In real gases, attractive forces between molecules exist. At low pressures or high temperatures, molecules are far apart, and these forces are negligible. However, at high pressures or low temperatures, molecules are closer, and attractive forces become significant, reducing the pressure exerted by the gas [37](#page=37).
> **Tip:** Real gases tend to behave ideally under conditions of low pressure and high temperature, where intermolecular forces are minimized [36](#page=36).
#### 1.6.2 Van der Waals' equation of state
J.D. van der Waals proposed an equation of state for real gases by including correction terms for both volume and pressure deviations from the ideal gas law [38](#page=38).
* **Volume Correction:** The volume occupied by the gas molecules themselves is subtracted from the container volume. The corrected volume is $(V - nb)$, where $b$ is the excluded volume per mole of gas molecules. The excluded volume per molecule is four times the actual volume of a single molecule ($4V\_m$). For one mole, the excluded volume is $b = 4V\_m N\_A$ [38](#page=38) [39](#page=39).
* **Pressure Correction:** The observed pressure ($P$) is less than the ideal pressure due to intermolecular attractive forces. A correction term, $p'$, is added to the observed pressure. This correction is proportional to the square of the gas density ($\\rho^2$), which is related to the number of molecules per unit volume. The corrected pressure is $P + \\frac{a n^2}{V^2}$, where $a$ is a proportionality constant related to the attractive forces [41](#page=41) [42](#page=42).
The Van der Waals equation for $n$ moles of a real gas is: $$ \\left( P + \\frac{an^2}{V^2} \\right) (V - nb) = nRT $$ [42](#page=42).
For one mole ($n=1$), the equation is: $$ \\left( P + \\frac{a}{V^2} \\right) (V - b) = RT $$ [42](#page=42).
##### 1.6.2.1 Van der Waals' constants ($a$ and $b$)
* **Constant $a$**: Represents the measure of attractive forces between molecules and is also called cohesion pressure or internal pressure. Its units are typically $\\text{L}^2 \\text{ atm/mol}^2$ or $\\text{atm dm}^6 \\text{ mol}^{-2}$ [43](#page=43).
* **Constant $b$**: Represents the excluded volume per mole of gas molecules and has units of $\\text{L/mol}$ or $\\text{dm}^3 \\text{ mol}^{-1}$ [38](#page=38) [43](#page=43).
Unlike the universal gas constant $R$, the Van der Waals constants $a$ and $b$ vary for different gases [43](#page=43).
> **Example:** Use the Van der Waals equation to calculate the pressure of a sample of 1.0000 mol of oxygen gas in a 22.415 L vessel at 0.0000°C. Given: $n = 1.0000$ mol, $V = 22.415$ L, $T = 273.15$ K. From tables: $a(\\text{O}\_2) = 1.36 \\text{ L}^2 \\text{ atm/mol}^2$, $b(\\text{O}\_2) = 0.0318 \\text{ L/mol}$. $R = 0.0821 \\text{ L atm K}^{-1} \\text{mol}^{-1}$.
>
> $P = \\frac{nRT}{V-nb} - \\frac{an^2}{V^2}$$P = \\frac{(1.0000 \\text{ mol})(0.0821 \\text{ L atm K}^{-1} \\text{mol}^{-1})(273.15 \\text{ K})}{22.415 \\text{ L} - (1.0000 \\text{ mol})(0.0318 \\text{ L/mol})} - \\frac{(1.36 \\text{ L}^2 \\text{ atm/mol}^2)(1.0000 \\text{ mol})^2}{(22.415 \\text{ L})^2}$$P = \\frac{22.415 \\text{ L atm}}{22.3832 \\text{ L}} - \\frac{1.36 \\text{ L}^2 \\text{ atm}}{502.43 \\text{ L}^2}$$P = 1.0014 \\text{ atm} - 0.0027 \\text{ atm} = 0.9987 \\text{ atm}$ [44](#page=44) [45](#page=45).
##### 1.6.2.2 Limitations of Van der Waals' equation
1. It provides a qualitative rather than a precise quantitative explanation for deviations of real gases from ideal behavior [46](#page=46).
2. The constants $a$ and $b$ are assumed to be constant, but they can vary with pressure and temperature, a variation not accounted for in the equation [46](#page=46).
3. Critical constants calculated using Van der Waals' equation may deviate from experimentally determined values [46](#page=46).
* * *
# The liquid state
A liquid is a nearly incompressible fluid that takes on the shape of its container but maintains a nearly constant volume, existing as one of the four fundamental states of matter [65](#page=65).
### 2.1 Characteristics of liquids
Liquids are composed of tiny, vibrating particles like atoms held together by intermolecular bonds. Like gases, liquids can flow and conform to the shape of their containers. However, liquids resist compression significantly more than gases and do not disperse to fill the entire volume of a container, maintaining a relatively constant density. Liquids and solids are both classified as condensed matter due to their similar densities, while liquids and gases are both termed fluids because of their shared ability to flow. Despite water being abundant on Earth, the liquid state is the least common in the universe, requiring specific temperature and pressure conditions for existence [65](#page=65).
### 2.2 Vapor pressure
Vapor pressure, or equilibrium vapor pressure, is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) within a closed system at a specific temperature. This pressure indicates a liquid's evaporation rate and its tendency to transition into a vapor phase. Substances with high vapor pressure at normal temperatures are considered volatile [66](#page=66).
As the temperature of a liquid increases, the kinetic energy of its molecules rises, leading to more molecules escaping into the vapor phase and consequently increasing the vapor pressure. The vapor pressure of a substance increases non-linearly with temperature, a relationship described by the Clausius–Clapeyron relation [66](#page=66).
The partial pressure is the contribution of a single component in a mixture to the total system pressure. For instance, air at sea level saturated with water vapor at 20°C has partial pressures of approximately 2.3 kPa for water, 78 kPa for nitrogen, 21 kPa for oxygen, and 0.9 kPa for argon, totaling around 102.2 kPa [67](#page=67).
> **Tip:** Vapor pressure charts, plotting vapor pressure against temperature, often show that liquids with lower boiling points tend to have higher vapor pressures at ambient temperatures [67](#page=67).
### 2.3 Boiling point
The atmospheric pressure boiling point of a liquid, also known as the normal boiling point, is the temperature at which its vapor pressure equals the surrounding atmospheric pressure. Any further increase in temperature will elevate the vapor pressure enough to overcome atmospheric pressure, forming vapor bubbles within the liquid. Deeper within the liquid, higher pressures and thus higher temperatures are required for bubble formation due to increasing fluid pressure with depth [66](#page=66).
> **Tip:** The surface tension of a bubble wall contributes to an overpressure in nascent bubbles, meaning thermometer calibration should not rely solely on the temperature of boiling water [67](#page=67).
### 2.4 Surface tension
Surface tension is the elastic property of a fluid surface that causes it to contract to the smallest possible surface area. This phenomenon allows insects denser than water to walk on its surface. At liquid-air interfaces, surface tension arises from the stronger cohesive forces between liquid molecules compared to the adhesive forces between liquid and air molecules. This results in a net inward force on surface molecules, making the surface behave like a stretched elastic membrane [68](#page=68).
Water exhibits a high surface tension (72.8 millinewtons per meter at 20°C) due to strong hydrogen bonding between its molecules, exceeding that of most other liquids. Surface tension is a key factor in capillarity [68](#page=68).
The capillary rise method can be used to measure surface tension. The equilibrium between the upward force due to surface tension and the downward force of gravity on the liquid column determines the height the liquid rises in a capillary tube. The forces are related by: $$f\_1 = 2\\pi r \\gamma \\cos \\theta$$ eq.1 [69](#page=69). where $r$ is the capillary radius, $\\gamma$ is the liquid surface tension, and $\\theta$ is the wetting contact angle. The downward force is given by [69](#page=69): $$f\_2 = \\pi r^2 h d g$$ eq.2 [69](#page=69). where $h$ is the height of the liquid column, $d$ is the liquid density, and $g$ is the acceleration due to gravity [69](#page=69).
In equilibrium, $f\_1 = f\_2$: $$2\\pi r \\gamma \\cos \\theta = \\pi r^2 h d g$$ eq.3 [69](#page=69). If the liquid completely wets the capillary walls ($\\theta = 0^\\circ$, $\\cos \\theta = 1$), the equation simplifies to: $$2\\pi r \\gamma = \\pi r^2 h d g$$ eq.4 [69](#page=69). This allows for the determination of surface tension: $$\\gamma = \\frac{r h d g}{2}$$ eq.5 [69](#page=69).
Surface tension has dimensions of force per unit length or energy per unit area; the latter is often referred to as surface energy [69](#page=69).
> **Example:** A liquid rises 7 cm in a capillary tube with a radius of 0.01 cm. If the liquid's density is 0.8 g/cm³ and gravity is 100 cm/sec², calculate its surface tension [70](#page=70). **Example:** A glass tube with a radius of 0.02 cm is placed in kerosene (density 0.8 g/cm³). If the surface tension of kerosene is 25 dyne/cm and the contact angle is 0°, calculate the height of kerosene in the tube [70](#page=70). **Example:** Ethanol (density 0.0789 g/cm³ at 20°C) rises 5.38 cm in a capillary tube with a diameter of 0.0107 cm. Calculate its surface tension, assuming a zero contact angle [70](#page=70).
When a liquid does not wet the capillary walls (e.g., mercury in glass), the contact angle can be assumed to be 180°, and $\\cos \\theta = -1$. The Young-Laplace equation, $\\Delta P = \\frac{2\\gamma}{r}$, describes the pressure difference across a curved surface, known as capillary pressure. For a wetting liquid, the pressure inside the capillary is lower than outside, leading to a rise in the liquid column until the pressure difference is balanced by the hydrostatic pressure [70](#page=70). $$\\Delta P = P\_1 - P\_2 = \\Delta d g h = \\frac{2\\gamma}{r}$$ [70](#page=70).
### 2.5 Heat of vaporization
The heat of vaporization, also known as the enthalpy of vaporization, is the amount of heat energy required to transform a liquid into a gas or vapor at a constant temperature. This occurs because molecules in a liquid possess a range of kinetic energies, allowing some to escape the surface as vapor. The molar heat of vaporization is the energy needed to vaporize one mole of a liquid, typically measured in kilojoules per mole (kJ/mol) [71](#page=71).
The molar heat of vaporization can be calculated using the following relations derived from the Clausius–Clapeyron equation: $$\\ln p\_1 = -\\frac{\\Delta H\_{vap}}{RT\_1} + C \\quad $$ [1](#page=1) [71](#page=71). $$\\ln p\_2 = -\\frac{\\Delta H\_{vap}}{RT\_2} + C \\quad $$ [2](#page=2) [71](#page=71). Subtracting equation from yields [1](#page=1) [2](#page=2): $$\\ln p\_2 - \\ln p\_1 = -\\frac{\\Delta H\_{vap}}{RT\_2} + \\frac{\\Delta H\_{vap}}{RT\_1}$$ [71](#page=71). $$\\ln \\frac{p\_2}{p\_1} = \\Delta H\_{vap} \\left( \\frac{1}{RT\_1} - \\frac{1}{RT\_2} \\right)$$ [71](#page=71). $$\\ln \\frac{p\_2}{p\_1} = \\frac{\\Delta H\_{vap}}{R} \\left( \\frac{1}{T\_1} - \\frac{1}{T\_2} \\right)$$ [71](#page=71). $$\\ln \\frac{p\_2}{p\_1} = \\frac{\\Delta H\_{vap}}{RT\_1T\_2} (T\_2 - T\_1)$$ [71](#page=71).
> **Example:** The vapor pressure of methanol is 0.0526 atm at 5°C and 0.132 atm at 21.2°C. Calculate its molar heat of vaporization and normal boiling point [71](#page=71). **Example:** The vapor pressure of ethanol is 135.5 mmHg at 40°C and 542.5 mmHg at 70°C. Calculate the molar heat of vaporization and the vapor pressure of ethanol at 50°C [71](#page=71). **Example:** The molar heat of vaporization of ethanol is 39.2 kJ/mol. Calculate the heat removed from the surroundings when 1.00 kg of ethanol (C₂H₅OH) evaporates [72](#page=72). **Example:** Calculate the heat content of evaporation for ethanol, given vapor pressures of 43.9 mmHg and 352.7 mmHg at 20°C and 60°C, respectively [72](#page=72). **Example:** The normal boiling point of chloroform is 61°C, and its heat of vaporization is 59 cal/gm. Calculate the vapor pressure of the liquid at 50°C [72](#page=72).
* * *
# The solid state and crystal structures
The solid state of matter is defined by its resistance to changes in shape or volume, possessing both a fixed shape and volume. Solids can be broadly categorized into crystalline and amorphous forms, distinguished by the arrangement of their constituent particles and their macroscopic properties. Crystalline solids exhibit long-range atomic order, leading to distinct geometric forms, sharp melting points, and elastic deformation under stress. In contrast, amorphous solids lack this ordered structure, softening gradually over a temperature range and undergoing plastic deformation. Crystalline solids are often anisotropic, meaning their physical properties vary with direction, whereas amorphous materials are typically isotropic [74](#page=74).
### 3.1 Crystal lattice and unit cells
To systematically describe the internal arrangement of atoms in crystalline solids, the concept of a crystal lattice is employed. A crystal lattice can be visualized as an infinite, three-dimensional arrangement of repeating structural units called unit cells. By translating these unit cells in all three dimensions, the entire crystal structure can be constructed [74](#page=74).
#### 3.1.1 Cubic unit cells
Among the various possible unit cell geometries, cubic unit cells are fundamental and widely encountered, especially in metals and ionic compounds. There are three primary types of cubic unit cells [75](#page=75):
* **Simple cubic (SC) structure:** This is the most basic cubic unit cell, characterized by atoms located at each of the eight corners of the cube. Stacking these unit cells results in a simple cubic lattice [74](#page=74).
* **Face-centered cubic (FCC) structure:** In an FCC unit cell, atoms are positioned at each of the eight corners and at the center of each of the six faces of the cube. Many common metals like copper, silver, gold, aluminum, and lead crystallize in an FCC lattice [75](#page=75).
* **Body-centered cubic (BCC) structure:** A BCC unit cell features atoms at each of the eight corners and one additional atom precisely at the center of the cube. Metals such as chromium, iron, and platinum commonly exhibit a BCC structure [75](#page=75) [76](#page=76).
The dimensions of these unit cells vary depending on the atomic radius of the constituent atoms, even if the lattice type is the same [76](#page=76).
> **Tip:** The arrangement of atoms in different crystal structures directly influences the material's properties. Understanding these structures is crucial for materials science and engineering.
#### 3.1.2 Examples of crystal structures
* **Metals:** As mentioned, copper, silver, and gold are FCC metals, while chromium, iron, and platinum are BCC metals [75](#page=75) [76](#page=76).
* **Ionic Compounds:** The structure of sodium chloride (NaCl) is a prominent example. The chloride ions (Cl$^-$) occupy lattice positions corresponding to an FCC unit cell, and the smaller sodium ions (Na$^+$) fill the interstitial spaces between the Cl$^-$ ions. This arrangement is behind the characteristic cubic shape of NaCl crystals. Many alkali halides, like KCl, also crystallize with FCC lattices, though the unit cell size differs due to the varying ionic radii [76](#page=76).
### 3.2 Physical properties and crystal type
The diverse physical properties of solids, such as hardness, melting point, and electrical conductivity, are a consequence of the nature of the particles within the solid and the strength of the attractive forces holding them together. Crystals can be classified into four main types based on these factors [77](#page=77):
Crystal TypeParticles Occupying Lattice SiteType of Attraction ForcesTypical ExamplesTypical Properties1-IonicPositive and negative ionsAttractions between opposite chargesNaCl, CaCl$\_2$, NaNO$\_3$Relatively hard, brittle, high melting points, nonconductors of electricity as solids but conduct when melted2-MolecularAtoms or moleculesDipole-dipole attractions, hydrogen bondingHCl, SO$\_2$, N$\_2$, Ar, CH$\_4$, H$\_2$OSoft, low melting points, nonconductors of electricity in both solid and liquid states3-Covalent (network)AtomsCovalent bond between atomsDiamond, SiC (silicon carbide), SiO$\_2$ (sand, quartz)Very hard, very high melting point, nonconductor of electricity4-MetallicPositive ionsAttractions between positive ions and electron cloudCu, Ag, Fe, Na, HgRange from very hard to very soft, melting point range from high to low, conduct electricity in both solid and liquid
### 3.3 Atomic packing factor (APF)
The atomic packing factor (APF) quantifies how efficiently atoms are packed within a crystal structure. It is defined as the ratio of the total volume of atoms within a unit cell to the total volume of the unit cell [78](#page=78).
* **APF for a simple cubic structure:** The APF for a simple cubic structure is approximately 0.52. This means that about 52% of the unit cell volume is occupied by atoms [79](#page=79).
* **APF for a body-centered cubic structure (BCC):** The APF for BCC is calculated as $\\frac{\\pi\\sqrt{3}}{8}$, which equals approximately 0.68. A BCC unit cell contains 2 atoms per unit cell (1 central atom + 8 corners x 1/8 atom per corner) [80](#page=80).
* **APF for a face-centered cubic structure (FCC):** The APF for FCC is calculated as $\\frac{\\pi}{3\\sqrt{2}}$, which equals approximately 0.74. This represents the most efficient possible packing of identical spheres. An FCC unit cell contains 4 atoms per unit cell (6 faces x 1/2 atom per face + 8 corners x 1/8 atom per corner) [81](#page=81).
> **Example:** Copper, with an FCC structure, has an APF of 0.74, indicating a relatively dense packing of copper atoms.
### 3.4 Theoretical density
The theoretical density ($\\rho$) of a crystalline material can be calculated using the properties of its unit cell. The formula for density is mass divided by volume [81](#page=81).
The mass of atoms per unit cell ($m$) can be determined by multiplying the number of atoms per unit cell by the mass of a single atom. The mass of a single atom is calculated by dividing the atomic weight by Avogadro's number ($N\_A$). The volume of the unit cell is the cube of the lattice constant ($a$), i.e., $a^3$ [81](#page=81).
The formula for theoretical density is: $$ \\rho = \\frac{m}{a^3} $$ where:
* $m$ = mass of atoms per unit cell [81](#page=81).
* $a^3$ = volume of unit cell [81](#page=81).
The mass of atoms per unit cell can be expressed as: $$ m = (\\text{number of atoms per unit cell}) \\times \\left( \\frac{\\text{atomic weight}}{N\_A} \\right) $$
This allows for the calculation of theoretical density, which can then be compared to experimentally measured densities to validate the crystal structure and atomic parameters of a material [82](#page=82).
> **Example:** For copper (FCC structure), with an atomic weight of 63.55 g/mol and an atomic radius of 0.128 nm, the theoretical density can be calculated and compared to its actual measured density. Using the provided data for copper, the theoretical density is calculated to be approximately 8.89 g/cm$^3$, which is very close to the actual density of 8.94 g/cm$^3$ [82](#page=82).
* * *
# Solutions and their properties
This chapter introduces solutions as homogeneous mixtures and explores their various types, solubility, colligative properties, and methods of concentration measurement [84](#page=84).
### 4.1 Types of solutions
A solution is a homogeneous mixture of two or more substances, where a solute dissolves in a solvent. The solvent is typically the substance present in the greater amount, and solutions adopt the physical state of their solvent [85](#page=85).
#### 4.1.1 Gaseous solutions
In gaseous solutions, only gases can dissolve in a gaseous solvent. Air, a mixture of gases dissolved in nitrogen, is an example. These solutions are often considered trivial due to minimal molecular interactions [85](#page=85).
#### 4.1.2 Liquid solutions
If the solvent is a liquid, gases, liquids, and solids can be dissolved [85](#page=85).
* **Gas in liquid:** Oxygen in water is an example. Carbon dioxide in water involves a chemical reaction forming ions [85](#page=85).
* **Liquid in liquid:** Alcoholic beverages are solutions of ethanol in water, and petroleum is a solution of hydrocarbons [85](#page=85).
* **Solid in liquid:** Sucrose or salts dissolved in water are common examples. Solutions of salts in water form electrolytes, as the salt dissociates into ions [86](#page=86).
Colloids, suspensions, and emulsions are not considered solutions because they are not homogeneous. Body fluids are complex liquid solutions containing various solutes, including ions and molecules, and are often electrolytes [86](#page=86).
#### 4.1.3 Solid solutions
If the solvent is a solid, gases, liquids, and solids can be dissolved [86](#page=86).
* **Gas in solid:** Hydrogen dissolves well in metals like palladium for hydrogen storage [86](#page=86).
* **Liquid in solid:** Mercury in gold forms an amalgam, and hexane in paraffin wax is another example [86](#page=86).
* **Solid in solid:** Steel (carbon in iron) and alloys like bronze are solid solutions [86](#page=86).
### 4.2 Solubility
Solubility is the ability of one compound to dissolve in another [86](#page=86).
* **Miscible liquids:** Liquids that can completely dissolve in each other are miscible [86](#page=86).
* **Immiscible liquids:** Substances that cannot mix to form a solution are immiscible [86](#page=86).
All solutions have a positive entropy of mixing. If solute-solvent interactions are unfavorable, the free energy decreases with increasing solute concentration. When the energy loss outweighs the entropy gain, the solution becomes saturated. Environmental factors like temperature, pressure, and contamination can affect saturation points. Supersaturated solutions can be prepared by increasing solubility and then slowly decreasing it [87](#page=87).
Generally, higher solvent temperatures increase the solubility of solid solutes. However, the solubility of most gases and some compounds decreases with increased temperature due to an exothermic enthalpy of solution. The solubility of liquids in liquids is less sensitive to temperature changes than solids or gases [87](#page=87).
### 4.3 Properties of solutions
The physical properties of compounds, such as melting and boiling points, change when other compounds are added. These are known as colligative properties. Concentration quantifies the amount of solute dissolved in a solvent [87](#page=87).
#### 4.3.1 Polarity and solubility
The solubility of substances is influenced by their molecular polarity, following the principle "like dissolves like" [90](#page=90).
* **Polar solutions:** Polar molecules have an uneven distribution of electron density, creating partial positive and negative charges (dipoles). Water is a polar molecule due to the higher electronegativity of oxygen compared to hydrogen, causing shared electrons to spend more time around oxygen. Polar molecules are attracted to each other [88](#page=88) [89](#page=89).
* **Aqueous solutions:** Water's polarity is responsible for many of its unique properties and its ability to dissolve polar solutes and ionic compounds. Ionic compounds like sodium chloride dissolve in water because the positive sodium ions (Na+) are attracted to the negative end of water molecules, and the negative chloride ions (Cl-) are attracted to the positive ends. This process is called hydration. The presence of ions in aqueous salt solutions makes them electrolytes, capable of conducting electricity [88](#page=88) [89](#page=89).
* Non-ionic solutes like ethanol and table sugar are soluble in water due to the presence of polar O-H groups, allowing them to form hydrogen bonds with water molecules [89](#page=89).
* **Non-polar solutions:** Non-polar molecules have symmetrical electron distribution and no overall dipole. They do not dissolve in polar solvents like water. Examples include long-chain hydrocarbons, oils, and greases. Non-polar solutes require non-polar solvents [90](#page=90).
* Methane (CH4) is non-polar despite having polar C-H bonds due to the symmetrical tetrahedral arrangement of these bonds [90](#page=90).
#### 4.3.2 Ideal solutions
The properties of ideal solutions can be calculated as a linear combination of their components' properties. When solute and solvent are in equal quantities, the distinction between them becomes less relevant [87](#page=87).
### 4.4 Concentration
Concentration measures the amount of a substance within a mixture, most commonly referring to the amount of solute in a solvent in homogeneous solutions [91](#page=91).
* **Concentrating a solution:** Involves adding more solute or reducing the amount of solvent [91](#page=91).
* **Diluting a solution:** Involves adding more solvent or reducing the amount of solute [91](#page=91).
A saturated solution can no longer dissolve additional solute; adding more will result in phase separation or a suspension, unless supersaturation occurs. The saturation point depends on temperature and the chemical nature of the solute and solvent [91](#page=91).
#### 4.4.1 Mass versus volume measures
Quantitative measures of concentration are essential for scientific applications. These measures can be based on mass, volume, or both, and converting between them may require density information, especially if temperatures vary. Volume-based measures are less reliable for non-dilute solutions or significant temperature changes due to the variability of volume with temperature and pressure. Mass measurements are generally more precise and less affected by environmental conditions [92](#page=92).
#### 4.4.2 Molarity
Molarity (M) is the number of moles of solute per liter of solution [93](#page=93). $$ M = \\frac{\\text{moles of solute}}{\\text{liters of solution}} $$ The formula for preparation is often expressed as: $$ \\text{mg} = M \\times \\text{Mwt} \\times V $$ where `mg` is the weight of the solute in grams, `Mwt` is the molecular weight of the solute, `V` is the volume of the solution in milliliters, and `M` is the molarity. A 0.5 molar solution contains 0.5 moles of solute in 1.0 liter of solution, not 1.0 liter of solvent [93](#page=93).
NIST considers molarity an obsolete term, preferring "amount-of-substance concentration" ($c$) with units of mol/m³ or mol/L. For minute concentrations, units like millimolar (mM), micromolar (μM), and nanomolar (nM) are used [93](#page=93) [94](#page=94).
**Disadvantages of molarity:**
* Volume measurement is often less precise than mass measurement [94](#page=94).
* Molarity changes with temperature due to thermal expansion [94](#page=94).
* For non-dilute solutions, molar volume can be concentration-dependent, making volumes not strictly additive [94](#page=94).
#### 4.4.3 Molality
Molality ($m$) is the number of moles of solute per kilogram of solvent [94](#page=94). $$ m = \\frac{\\text{moles of solute}}{\\text{kilograms of solvent}} $$ A solution with 1.0 mole of solute in 2.0 kilograms of solvent has a molality of 0.50 mol/kg. NIST suggests the term 'molality of substance B' ($m\_B$) with units mol/kg [94](#page=94).
**Advantages of molality:**
* It is independent of physical conditions like temperature and pressure because it is mass-based [94](#page=94).
* In dilute aqueous solutions near room temperature and standard pressure, molarity and molality values are very similar because 1 kg of water is approximately 1 L, and the solute's volume contribution is negligible [95](#page=95).
#### 4.4.4 Mole fraction
Mole fraction ($\\chi$) is the ratio of the moles of a solute to the total number of moles in a solution [95](#page=95). $$ \\chi\_A = \\frac{\\text{moles of A}}{\\text{total moles of all components}} $$ Mole fractions are dimensionless quantities. Mole percentage (100% times mole fraction) is also used [95](#page=95).
**Advantages of mole fraction:**
* Not temperature dependent [95](#page=95).
* Does not require knowledge of densities [95](#page=95).
* Can be prepared by weighing constituents [95](#page=95).
* It is symmetrical, meaning the roles of 'solute' and 'solvent' are reversed when $\\chi$ is swapped (e.g., 0.1 vs. 0.9) [95](#page=95).
#### 4.4.5 Mass percentage
Mass percentage denotes the mass of a substance as a percentage of the total mass of the mixture [96](#page=96). $$ \\text{Mass %} = \\left( \\frac{\\text{mass of solute}}{\\text{mass of solution}} \\right) \\times 100% $$ Mass fraction ($x\_m$) is the mass percentage divided by 100. It is often referred to as weight-weight percentage (w/w%). For example, 40 grams of ethanol in 60 grams of water yields a 40% ethanol solution by mass [96](#page=96).
#### 4.4.6 Mass-volume percentage
Mass-volume percentage (% m/v or % w/v) describes the mass of solute in grams per 100 mL of the resulting solution [96](#page=96). $$ \\text{Mass-volume %} = \\left( \\frac{\\text{mass of solute (g)}}{\\text{volume of solution (mL)}} \\right) \\times 100% $$ This is commonly used for solutions made from solid solutes dissolved in liquids [96](#page=96).
#### 4.4.7 Volume-volume percentage
Volume-volume percentage (% v/v) describes the volume of the solute in mL per 100 mL of the resulting solution [97](#page=97). $$ \\text{Volume-volume %} = \\left( \\frac{\\text{volume of solute (mL)}}{\\text{volume of solution (mL)}} \\right) \\times 100% $$ This is most useful for liquid-liquid solutions and mixtures of gases, though percentages are only strictly additive for ideal gases [97](#page=97).
#### 4.4.8 Normality
Normality (N) represents the number of gram equivalent weights of a solute per liter of solution [97](#page=97). $$ N = \\frac{\\text{gram equivalents of solute}}{\\text{liters of solution}} $$ The formula for preparation is often expressed as: $$ \\text{mg} = N \\times \\text{Eq wt} \\times V $$ where `mg` is the weight of the solute in grams, `Eq wt` is the equivalent weight of the solute, `V` is the volume of the solution in milliliters, and `N` is the normality [97](#page=97).
Normality accounts for the reactive species in a solution, such as ions. The definition of a gram equivalent varies based on the chemical reaction (acid-base, redox, precipitation). It measures a single ion's contribution. For example, 2 Normal sulfuric acid (H2SO4) means the normality of H+ ions is 2, implying a molarity of 1 for H2SO4 [97](#page=97) [98](#page=98).
**Specific definitions for normality:**
* **Acid-base chemistry:** Expresses the concentration of protons or hydroxide ions. Normality can differ from molarity by an integer (e.g., 1 M Ca(OH)2 is 2 N in hydroxide) [98](#page=98).
* **Redox reactions:** Measures the oxidizing or reducing agent quantity that can accept or furnish one mole of electrons. Normality often scales from molarity by a fractional value [98](#page=98).
* **Precipitation reactions:** Measures the concentration of ions that will precipitate in a given reaction. Normality scales from molarity by an integer [98](#page=98).
Normality is useful for titrations, where $N\_aV\_a = N\_bV\_b$ for reacting species. However, normality is no longer widely used to represent solution concentration as it depends on the specific reaction. NIST also considers it an obsolete unit [98](#page=98) [99](#page=99).
#### 4.4.9 Equivalents
Concentration can be expressed in equivalents per liter (Eq/L) or milliequivalents per liter (mEq/L), based on the same principle as normality. This unit is losing favor but is still used in medical reporting [99](#page=99).
#### 4.4.10 Formal concentration
Formal concentration (F) is similar to molarity but is calculated based on the formula weights of chemicals per liter of solution. It indicates moles of the original chemical formula added, regardless of the species that actually exist in solution at equilibrium [99](#page=99).
#### 4.4.11 "Parts-per" notation
This notation is used for convenience and relates to mass fraction [100](#page=100).
* **Parts per hundred (% or pph):** Amount per 100 total parts [100](#page=100).
* **Parts per thousand (‰ or ppt):** Amount per 1000 total parts [100](#page=100).
* **Parts per million (ppm):** Amount per 1,000,000 total parts [100](#page=100).
* **Parts per billion (ppb):** Amount per 1,000,000,000 total parts [100](#page=100).
* *\_Parts per trillion (ppt):\* Amount per 1,000,000,000,000 total parts [100](#page=100).*
* ***Parts per quadrillion (ppq):*** *Amount per 1,000,000,000,000,000 total parts .*
*For atmospheric chemistry and air pollution, units like ppmv (parts per million by volume) are used for gases, while $\\mu$g/m³ or mg/m³ are used for aerosols and particulate matter to account for density variations. It is crucial to specify whether the "parts-per" notation refers to mass/mass or volume/volume, especially for gases .*
### *4.5 Gas laws related to solutions*
#### *4.5.1 Henry's Law*
*Henry's law states that at a constant temperature, the amount of a given gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid . $$ P = k\_H \\times C $$ where $P$ is the partial pressure of the gas, $C$ is the concentration of the dissolved gas, and $k\_H$ is the Henry's law constant. The constant $k\_H$ depends on the solute, solvent, and temperature .*
***Example:*** *Carbonated soft drinks rely on Henry's law. When a bottle is opened, the reduced pressure above the liquid causes dissolved carbon dioxide to bubble out .*
#### *4.5.2 Raoult's Law*
*Raoult's law states that the partial vapor pressure of a component in a mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. This law applies to ideal mixtures where intermolecular forces between similar molecules equal those between different molecules .*
*For a mixture of liquids A and B: $$ P\_A = P\_A^0 X\_A $$$$ P\_B = P\_B^0 X\_B $$ where $P\_A$ and $P\_B$ are the partial vapor pressures, $P\_A^0$ and $P\_B^0$ are the vapor pressures of the pure components, and $X\_A$ and $X\_B$ are their respective mole fractions . The total vapor pressure of the mixture is the sum of the partial vapor pressures: $$ P\_{\\text{total}} = P\_A + P\_B $$*
***Example:*** *A mixture of 2 moles of methanol ($X\_{\\text{methanol}} = 2/3$) and 1 mole of ethanol ($X\_{\\text{ethanol}} = 1/3$). If the vapor pressure of pure methanol is 81 kPa and pure ethanol is 45 kPa, then: $$ P\_{\\text{methanol}} = 81 \\text{ kPa} \\times \\frac{2}{3} = 54 \\text{ kPa} $$$$ P\_{\\text{ethanol}} = 45 \\text{ kPa} \\times \\frac{1}{3} = 15 \\text{ kPa} $$$$ P\_{\\text{total}} = 54 \\text{ kPa} + 15 \\text{ kPa} = 69 \\text{ kPa} $$*
*Vapor pressure/composition diagrams for ideal mixtures show a linear relationship between partial vapor pressure and mole fraction .*
### *4.6 Colligative properties*
*Colligative properties are physical properties of solutions that depend on the molar concentration of solute particles, not their identity .*
#### *4.6.1 Boiling point elevation and freezing point depression*
*While not explicitly detailed in this excerpt, these are key colligative properties that are affected by the addition of solutes, leading to changes in boiling and freezing points [87](#page=87).*
#### *4.6.2 Osmosis*
*Osmosis is the diffusion of solvent (usually water) through a semi-permeable membrane from an area of high water potential (low solute concentration) to an area of low water potential (high solute concentration) .*
* ***Hypotonic solution:*** *A solution with a lower solute concentration than the cell's interior .*
* ***Hypertonic solution:*** *A solution with a higher solute concentration than the cell's interior .*
* ***Isotonic solution:*** *A solution with the same solute concentration as the cell's interior .*
***Osmotic pressure:*** *The pressure required to prevent the passage of solvent across a semi-permeable membrane, thus maintaining equilibrium. It is a colligative property .*
***Examples of osmosis:***
* *Plant roots drawing water from soil .*
* *Potato slices shrinking in concentrated salt solutions .*
* *Effects on blood cells and plant cells in different solutions .*
***Types of osmosis:***
* ***Reverse osmosis:*** *Uses pressure to force a solvent through a membrane from a high solute concentration to a low solute concentration, retaining the solute .*
* ***Forward osmosis:*** *Uses a "draw" solution with higher osmotic pressure to induce water flow from a "feed" solution, concentrating the feed solution and diluting the draw solution .*
### *4.7 Buffer solutions*
*A buffer solution is an aqueous solution of a weak acid and its conjugate base, or a weak base and its conjugate acid, which resists significant pH changes upon addition of small amounts of acid or base .*
* ***Acidic buffer:*** *pH less than 7, typically made from a weak acid and its salt .*
* ***Alkaline buffer:*** *pH greater than 7, typically made from a weak base and its salt .*
#### *4.7.1 How buffers work*
*Buffers neutralize added acid or base by shifting equilibrium reactions .*
* ***Acidic buffer (e.g., ethanoic acid/ethanoate):***
* *Adding acid (H+): Ethanoate ions ($CH\_3COO^-$) react with H+ to form ethanoic acid ($CH\_3COOH$) .*
* *Adding base ($OH^-$): $OH^-$ reacts with ethanoic acid to form ethanoate and water, or with H+ to form water, which then shifts the acid ionization equilibrium .*
* ***Alkaline buffer (e.g., ammonia/ammonium):***
* *Adding acid (H+): Ammonia ($NH\_3$) reacts with H+ to form ammonium ions ($NH\_4^+$) .*
* *Adding base ($OH^-$): $OH^-$ reacts with ammonium ions to form ammonia and water .*
#### *4.7.2 Henderson-Hasselbalch equation*
*This equation calculates the pH of a buffer solution: $$ \\text{pH} = \\text{p}K\_a + \\lg \\left( \\frac{\[\\text{A}^-\]}{\[\\text{HA}\]} \\right) $$ where $\\text{p}K\_a$ is the acid dissociation constant, $\[\\text{A}^-\]$ is the concentration of the conjugate base, and $\[\\text{HA}\]$ is the concentration of the weak acid .*
*For alkaline buffers, a similar equation relates pOH and pKb: $$ \\text{pOH} = \\text{p}K\_b + \\lg \\left( \\frac{\[\\text{HB}^+\]}{\[\\text{B}\]} \\right) $$ And $\\text{pH} + \\text{pOH} = 14$ .*
***Key conclusions from the Henderson-Hasselbalch equation:***
1. *The pKa/pKb and the ratio of salt to acid/base concentrations are crucial for preparing a buffer of a specific pH .*
2. *Dilution of a buffer solution does not change its pH, as both the acid/base and salt concentrations change proportionally .*
#### *4.7.3 Buffer capacity*
*Buffer capacity ($\\beta$) quantifies a buffer's resistance to pH change upon addition of acid or base: $$ \\beta = \\frac{\\Delta \\text{C}\_{\\text{base}}}{\\Delta \\text{pH}} \\quad \\text{or} \\quad \\beta = -\\frac{\\Delta \\text{C}{\\text{acid}}}{\\Delta \\text{pH}} $$ where $\\Delta \\text{C}\_{\\text{base}}$ and $\\Delta \\text{C}{\\text{acid}}$ are the concentrations of strong base or acid added, and $\\Delta \\text{pH}$ is the resulting change in pH .*
#### *4.7.4 Applications of buffers*
*Buffers are essential in chemical manufacturing and biochemical processes due to their pH-stabilizing ability. The ideal buffer for a specific pH has a pKa close to that pH, maximizing buffer capacity .*
* * *
# *Electrochemistry and Rusting*
*Electrochemistry is the study of the relationship between electricity and chemical changes, encompassing both the generation of electricity from chemical reactions and the use of electricity to drive chemical reactions.*
### *5.1 Fundamentals of electrochemistry*
*Electrochemistry deals with the interaction between electrical energy and chemical change. Electrochemical reactions involve the movement of electric charges between electrodes and an electrolyte .*
#### *5.1.1 Redox reactions*
*Oxidation-reduction or redox reactions are chemical reactions where electrons are transferred directly between molecules and/or atoms .*
* ***Oxidation:*** *The loss of electrons from an atom or molecule .*
* ***Reduction:*** *The gain of electrons by an atom or molecule .*
#### *5.1.2 Electrochemical cells*
*An electrochemical cell is a device that produces electric current from the energy released by a spontaneous redox reaction .*
* ***Components of an electrochemical cell:***
* ***Electrodes:*** *Two conductive electrodes, an anode and a cathode .*
* ***Anode:*** *The electrode where oxidation occurs .*
* ***Cathode:*** *The electrode where reduction takes place . Electrodes can be made from various conductive materials, including metals, semiconductors, graphite, and conductive polymers .*
* ***Electrolyte:*** *The substance between the electrodes that contains ions capable of free movement .*
#### *5.1.3 Galvanic cells*
*Galvanic cells, also known as Voltaic cells, are a type of electrochemical cell that generates electric current from spontaneous redox reactions. They utilize two different metal electrodes, each immersed in an electrolyte containing the oxidized form of the electrode metal .*
* ***Mechanism in a Galvanic Cell:***
1. *The anode metal oxidizes, transitioning from an oxidation state of 0 to a positive oxidation state, forming ions in the electrolyte .*
2. *At the cathode, metal ions in the electrolyte gain electrons from the cathode, reducing their oxidation state to 0 and depositing as solid metal .*
3. *An external electrical connection allows electrons to flow from the anode to the cathode, creating an electric current .*
##### *5.1.3.1 Daniell cell example*
*A Daniell cell is a classic example of a galvanic cell using zinc and copper electrodes submerged in zinc sulfate and copper sulfate solutions, respectively .*
* ***Half-reactions:***
* *Zinc electrode (anode): $Zn(s) \\rightarrow Zn^{2+}(aq) + 2e^-$ .*
* *Copper electrode (cathode): $Cu^{2+}(aq) + 2e^- \\rightarrow Cu(s)$ .*
*In this cell, zinc metal is oxidized, and copper ions are reduced and deposited on the copper cathode .*
#### *5.1.4 Completing the circuit*
*A complete electric circuit in an electrochemical cell requires both an electron conduction path (external circuit) and an ionic conduction path between the anode and cathode electrolytes .*
* ***Ionic conduction paths:***
* ***Liquid junction:*** *A direct connection between electrolytes that allows ion flow but can lead to mixing .*
* ***Porous plug:*** *Allows ion flow while minimizing electrolyte mixing .*
* ***Salt bridge:*** *An inverted U-tube containing a gel saturated with an electrolyte, used to minimize electrolyte mixing while allowing ion flow .*
#### *5.1.5 Cell potential and diagram*
* ***Electromotive force (emf):*** *The electrical potential difference between the anode and cathode, measurable by a voltmeter .*
* ***Cell diagram:*** *A representation used to trace the path of electrons in an electrochemical cell .*
* ***Example (Daniell cell):*** *$Zn(s) | Zn^{2+}(1M) || Cu^{2+}(1M) | Cu(s)$ . \* The reduced form of the metal to be oxidized (anode) is written first, separated by a vertical line from its oxidized form. \* Double vertical lines represent the salt bridge. \* The oxidized form of the metal to be reduced (cathode) is written, separated by a vertical line from its reduced form.*
* *Electrolyte concentrations are specified as they influence cell potential .*
#### *5.1.6 Calculating standard cell potential*
*The standard potential for a redox reaction in a galvanic cell can be calculated by summing the standard reduction potentials of the half-reactions. The more negative reduction potential indicates the species that will be oxidized .*
* ***Example (Daniell cell):***
* *$Cu^{2+} + 2e^- \\rightleftharpoons Cu$: $E^0 = +0.34$ V .*
* *$Zn^{2+} + 2e^- \\rightleftharpoons Zn$: $E^0 = -0.76$ V .*
* *Overall reaction: $Cu^{2+} + Zn \\rightleftharpoons Cu + Zn^{2+}$ .*
* *Standard cell potential: $+0.34$ V $ - (-0.76$ V$) = 1.10$ V .*
### *5.2 Rusting of iron*
*Rusting is the common term for the corrosion of iron and its alloys, such as steel, which involves the formation of iron oxides .*
#### *5.2.1 Definition and composition of rust*
*Rust is primarily iron oxides, typically red oxides formed by the reaction of iron with oxygen in the presence of water or air moisture. Other forms exist, such as green rust, formed in oxygen-deprived environments with chloride ions. Rust consists of hydrated iron(III) oxides ($Fe\_2O\_3 \\cdot nH\_2O$) and iron(III) oxide-hydroxide ($FeO(OH) \\cdot Fe(OH)\_3$) .*
#### *5.2.2 Factors influencing rusting*
* ***Electrochemical process:*** *Rusting is an electrochemical process that begins with electron transfer from iron to oxygen .*
* ***Water and oxygen:*** *Iron metal is relatively unaffected by pure water or dry oxygen. However, the combined action of oxygen and water is crucial for the conversion of the passivating iron oxide layer into rust .*
* ***Electrolytes:*** *The presence of salts, such as in seawater or salt spray, significantly accelerates the rusting process due to electrochemical reactions. Electrolytes increase the conductivity of the water, facilitating ion movement .*
* ***Acids:*** *Acids (e.g., carbon dioxide in water, sulfur dioxide in water) also contribute to corrosion by forming iron hydroxides that do not adhere to the metal surface. The formation of hydroxide ions during oxygen reduction is strongly affected by the presence of acid, with corrosion accelerating at low pH .*
* ***Impurities:*** *Impure iron, like cast iron, rusts more readily than pure iron .*
#### *5.2.3 Chemical reactions involved in rusting*
*Rusting is an electrochemical process involving the following key reactions:*
1. ***Reduction of oxygen:****$O\_2 + 4e^- + 2H\_2O \\rightarrow 4OH^-$ .*
2. ***Oxidation of iron:****$Fe \\rightarrow Fe^{2+} + 2e^-$ .*
3. ***Redox reaction in water (crucial for rust formation):****$4Fe^{2+} + O\_2 \\rightarrow 4Fe^{3+} + 2O^{2-}$ .*
4. ***Acid-base reactions (formation of hydroxides):****$Fe^{2+} + 2H\_2O \\rightleftharpoons Fe(OH)\_2 + 2H^+$ . $Fe^{3+} + 3H\_2O \\rightleftharpoons Fe(OH)\_3 + 3H^+$ .*
5. ***Dehydration equilibria (formation of oxides):****$Fe(OH)\_2 \\rightleftharpoons FeO + H\_2O$ . $Fe(OH)\_3 \\rightleftharpoons FeO(OH) + H\_2O$ . $2FeO(OH) \\rightleftharpoons Fe\_2O\_3 + H\_2O$ .*
*The specific corrosion products depend on the availability of water and oxygen. Limited dissolved oxygen favors iron(II) compounds like FeO, while high oxygen concentrations favor ferric compounds. The presence of other ions, such as $Ca^{2+}$, can accelerate rust formation by acting as electrolytes or precipitating with iron hydroxides and oxides .*
#### *5.2.4 Consequences of rusting*
* ***Structural degradation:*** *Rust is permeable to air and water, meaning corrosion continues beneath the rust layer. This can lead to structural weakening, cracking, flaking, and eventual disintegration of iron or steel .*
* ***Volume expansion:*** *Rust occupies a larger volume than the original iron, which can cause "rust smacking," forcing apart adjacent parts and leading to structural failure. This was a factor in bridge collapses like the Mianus River Bridge and the Silver Bridge .*
* ***Reinforced concrete damage:*** *Rusting of steel reinforcement within concrete can cause internal pressure, leading to spalling and severe structural problems .*
* ***Aesthetic issues:*** *Rust can cause discoloration, such as brown and black water from rusted galvanized pipes .*
### *5.3 Prevention of rusting*
*Preventing or slowing down rust is of significant economic importance and involves various technological approaches .*
#### *5.3.1 Rust-resistant alloys*
*Certain alloys are designed to resist corrosion:*
* ***Stainless steel:*** *Forms a protective passivation layer of chromium(III) oxide .*
* ***Weathering steel (e.g., Cor-Ten):*** *Forms a tightly adhering rust layer that slows down further corrosion, though it still rusts slowly .*
* *Other metals and materials exhibiting passivation include magnesium, titanium, zinc, aluminium, polyaniline, and other electroactive conductive polymers .*
#### *5.3.2 Galvanization*
*Galvanization involves coating iron or steel with a layer of metallic zinc .*
* ***Methods:*** *Hot-dip galvanizing or electroplating .*
* ***Cathodic protection:*** *Zinc provides cathodic protection to the steel. If the zinc layer is damaged, zinc acts as a galvanic anode and corrodes preferentially, sacrificing itself to protect the steel .*
* ***Limitations:*** *Galvanization can fail at seams and holes. The protective zinc layer is consumed over time .*
* ***Modern coatings:*** *Zinc-aluminum (zinc-alume) coatings provide longer protection as aluminum can migrate to cover scratches .*
#### *5.3.3 Plating*
*Coating iron or steel with other metals offers protection:*
* ***Zinc plating (galvanized iron/steel):*** *.*
* ***Tin plating:*** *Mild steel coated with tin .*
* ***Cadmium plating:*** *Preferred in more corrosive environments like saltwater .*
* ***Chrome plating:*** *Electrolytically applied chromium provides rust protection and a polished appearance .*
#### *5.3.4 Cathodic protection*
*This technique inhibits corrosion on buried or immersed structures by supplying an electrical charge to suppress the electrochemical reaction .*
* ***Sacrificial anode:*** *Attaching a material with a more negative electrode potential (e.g., zinc, aluminum, magnesium) makes the iron or steel the cathode in the formed cell. The sacrificial anode corrodes instead of the protected metal .*
* ***Impressed current:*** *Using an electrical device to induce an appropriate electric charge on the metal to be protected .*
#### *5.3.5 Coatings and painting*
*Applying physical barriers isolates iron from the environment:*
* ***Paint, lacquer, varnish:*** *These coatings prevent contact with air and moisture .*
* ***Wax-based products (slushing oils):*** *Injected into enclosed sections of large structures like ships and automobiles, often containing rust inhibitors .*
* ***Concrete:*** *Covering steel with concrete provides some protection due to the alkaline pH environment at the interface .*
* ***Oils, grease, and specialized mixtures:*** *Used for temporary protection during storage or transport (e.g., Cosmoline) .*
* ***Anti-seize lubricants:*** *Mixtures of grease with metal powders (copper, zinc, aluminum) to protect threads and machined surfaces .*
#### *5.3.6 Bluing*
*A technique for small steel items (e.g., firearms) that provides limited rust resistance when combined with a water-displacing oil .*
#### *5.3.7 Inhibitors*
*Corrosion inhibitors can be used in sealed systems to prevent corrosion. They are ineffective in open systems with air circulation that disperses them and introduces fresh oxygen and moisture .*
#### *5.3.8 Humidity control*
*Controlling atmospheric moisture is crucial:*
* ***Silica gel packets:*** *Used to manage humidity in equipment shipped by sea .*
### *5.4 Economic impact of rusting*
*Rusting leads to the degradation of iron-based tools and structures, causing significant economic losses. The structural failures caused by rust, such as bridge collapses, have resulted in fatalities and substantial repair costs. The term "Rust Belt" is used to describe regions historically dominated by heavy industry that have experienced economic decline, symbolizing decay .*
* * *
## *Common mistakes to avoid*
* *Review all topics thoroughly before exams*
* *Pay attention to formulas and key definitions*
* *Practice with examples provided in each section*
* *Don't memorize without understanding the underlying concepts*
Glossary
| Term | Definition |
|------|------------|
| States of Matter | Refers to the distinct forms in which matter can exist, commonly solid, liquid, and gas, each characterized by different properties of their constituent particles. |
| Gas | A state of matter where particles are far apart, move freely at high speeds, and assume the shape and volume of their container. Gases are highly compressible and flow easily. |
| Liquid | A state of matter where particles are close together but can move past each other. Liquids take the shape of their container but retain a definite volume, are nearly incompressible, and flow. |
| Solid | A state of matter where particles are tightly packed, usually in a regular pattern, and vibrate in place. Solids have a fixed shape and volume and are rigid. |
| Plasma | The fourth state of matter, consisting of an ionized gaseous substance that is highly electrically conductive, dominated by electric and magnetic fields. |
| Condensed Phases | Refers to the liquid and solid states of matter, where particles are held very close together. |
| Kinetic Theory of Gases | A scientific theory that explains the macroscopic properties of gases in terms of the motion of their constituent molecules. It postulates that gas molecules are in constant, random motion. |
| Pressure | The force exerted per unit area, typically by gas molecules colliding with the walls of a container. Measured in units like Pascal (Pa), atmosphere (atm), and torr. |
| Temperature | A measure of the average kinetic energy of the particles in a substance. In gases, higher temperatures lead to increased molecular velocity and kinetic energy. |
| Volume | The amount of space that a gas occupies, which is typically the volume of its container. The volume of a gas is influenced by its pressure, temperature, and the number of moles. |
| Number of Moles (n) | A unit representing the amount of substance, defined as the number of elementary entities (e.g., atoms, molecules) in a sample. It is calculated as mass divided by molecular weight. |
| U-tube Manometer | A device used to measure pressure, consisting of a U-shaped glass tube containing a liquid, often mercury. The difference in liquid levels indicates the pressure difference. |
| Atmospheric Pressure | The pressure exerted by the weight of the Earth's atmosphere. It is often used as a standard unit of pressure, equivalent to 760 mmHg. |
| Boyle's Law | States that for a given mass of gas at constant temperature, the pressure is inversely proportional to its volume ($P \propto 1/V$ or $PV = \text{constant}$). |
| Charles's Law | States that for a given mass of gas at constant pressure, the volume is directly proportional to its absolute temperature ($V \propto T$ or $V/T = \text{constant}$). |
| Avogadro's Hypothesis | States that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. This implies that volume is directly proportional to the number of moles ($V \propto n$). |
| Ideal Gas | A theoretical gas that perfectly obeys the ideal gas law ($PV = nRT$) under all conditions of temperature and pressure. It assumes that gas molecules have no volume and no intermolecular forces. |
| Ideal Gas Law | An equation of state that describes the behavior of an ideal gas: $PV = nRT$, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is absolute temperature. |
| Gas Constant (R) | A proportionality constant in the ideal gas law. Its value depends on the units used for pressure, volume, and temperature. Common values include 0.0821 L·atm/(mol·K) and 8.314 J/(mol·K). |
| Standard Temperature and Pressure (STP) | A set of standard conditions for experimental measurements, typically defined as 0°C (273.15 K) and 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies 22.4 liters. |
| Dalton's Law of Partial Pressures | States that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases ($P_{\text{total}} = P_1 + P_2 + \dots$). |
| Partial Pressure | The pressure that a single gas in a mixture would exert if it occupied the entire volume of the container by itself at the same temperature. |
| Mole Fraction (X) | The ratio of the number of moles of a component in a mixture to the total number of moles of all components ($X_i = n_i / n_{\text{total}}$). It is a dimensionless quantity. |
| Diffusion | The spontaneous mixing of substances, typically gases or liquids, due to the random motion of their particles. |
| Effusion | The process by which a gas escapes through a small opening or pinhole into a region of lower pressure or vacuum. |
| Graham's Law of Diffusion | States that under the same conditions of temperature and pressure, the rates of diffusion of different gases are inversely proportional to the square roots of their molecular masses ($r_1/r_2 = \sqrt{M_2/M_1}$). |
| Real Gas | A gas that deviates from ideal gas behavior due to intermolecular forces and the finite volume of gas molecules. |
| Deviation from Ideal Behavior | The extent to which a real gas's properties differ from those predicted by the ideal gas law. This is influenced by pressure and temperature. |
| Intermolecular Forces | Attractive or repulsive forces between molecules. In gases, these forces become significant at high pressures and low temperatures. |
| van der Waals Equation of State | An equation of state for real gases that accounts for the volume of molecules and intermolecular attractive forces: $(P + a(n/V)^2)(V - nb) = nRT$. |
| van der Waals Constants (a and b) | Constants in the van der Waals equation that correct for intermolecular attractions (a) and the volume of molecules (b). They are specific to each gas. |
| Critical Temperature (Tc) | The temperature above which a gas cannot be liquefied, regardless of the pressure applied. |
| Critical Pressure (Pc) | The minimum pressure required to liquefy a gas at its critical temperature. |
| Critical Volume (Vc) | The volume occupied by one mole of a gas at its critical temperature and critical pressure. |
| Joule-Thomson Effect | The phenomenon where a gas cools upon expansion from a region of high pressure to a region of low pressure, typically through a porous plug, when the process is nearly adiabatic. |
| Inversion Temperature (Ti) | The temperature at which the Joule-Thomson effect changes from cooling to heating. Below Ti, expansion causes cooling; above Ti, expansion causes heating. |
| Linde's Method | A process used for liquefying gases that utilizes the Joule-Thomson effect through repeated cycles of compression, cooling, and expansion. |
| Isothermal Process | A thermodynamic process that occurs at constant temperature. Work is done during volume changes. |
| Work Done | The energy transferred when a force acts over a distance. In gas expansions, work is done by the gas, and in compressions, work is done on the gas. |
| Reversible Process | A thermodynamic process that can be reversed without leaving any change in the system or surroundings. |
| Irreversible Process | A thermodynamic process that cannot be reversed without leaving a net change in the system and surroundings. |
| Liquid State | A state of matter characterized by definite volume but no fixed shape, with particles in close contact but able to move past each other. |
| Vapor Pressure | The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. |
| Boiling Point | The temperature at which the vapor pressure of a liquid equals the ambient atmospheric pressure, allowing the liquid to vaporize throughout its bulk. |
| Surface Tension | The elastic tendency of a fluid surface to acquire the least surface area possible, resulting from cohesive forces between liquid molecules. |
| Capillarity | The ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity, due to surface tension and adhesive forces. |
| Heat of Vaporization | The amount of heat energy required to convert a substance from a liquid to a gas at a constant temperature. Also known as enthalpy of vaporization. |
| Solid State | A state of matter characterized by rigidity, fixed shape, and fixed volume, with particles held tightly together in an ordered arrangement. |
| Crystalline Solids | Solids in which the constituent atoms, molecules, or ions are arranged in a highly ordered, repeating three-dimensional pattern called a crystal lattice. |
| Amorphous Solids | Solids that lack a regular, ordered atomic structure, often exhibiting properties of both liquids and crystalline solids. |
| Crystal Lattice | A three-dimensional array of points that describes the arrangement of atoms, ions, or molecules in a crystalline solid. |
| Unit Cell | The smallest repeating unit of a crystal lattice that, when translated in three dimensions, generates the entire crystal structure. |
| Simple Cubic (SC) | A crystal structure where atoms are located only at the corners of a cubic unit cell. |
| Body-Centered Cubic (BCC) | A crystal structure where atoms are located at the corners and one atom is at the center of a cubic unit cell. |
| Face-Centered Cubic (FCC) | A crystal structure where atoms are located at the corners and one atom is at the center of each of the six faces of a cubic unit cell. |
| Atomic Packing Factor (APF) | The fraction of the volume of a unit cell that is occupied by atoms. It represents how efficiently spheres are packed in a crystal structure. |
| Theoretical Density | The density of a crystalline material calculated based on its crystal structure, atomic weight, and Avogadro's number. |
| Solutions | Homogeneous mixtures composed of two or more substances, where a solute is dissolved in a solvent. |
| Solute | The substance that is dissolved in a solvent to form a solution. |
| Solvent | The substance that dissolves a solute to form a solution. It is usually present in a greater amount than the solute. |
| Solubility | The ability of a substance (solute) to dissolve in another substance (solvent) to form a solution. It is often expressed as the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. |
| Miscible | Describes two liquids that can mix in all proportions to form a homogeneous solution. |
| Immiscible | Describes two liquids that do not mix to form a homogeneous solution, separating into distinct layers. |
| Saturated Solution | A solution that contains the maximum amount of solute that can be dissolved in the solvent at a given temperature and pressure. |
| Supersaturated Solution | A solution that contains more dissolved solute than a saturated solution, usually achieved by preparing a saturated solution at a higher temperature and then cooling it carefully. |
| Colligative Properties | Properties of solutions that depend on the concentration of solute particles rather than their identity, such as boiling point elevation, freezing point depression, and osmotic pressure. |
| Concentration | A measure of the amount of solute present in a given amount of solvent or solution. Common measures include molarity, molality, mole fraction, and mass percentage. |
| Molarity (M) | The number of moles of solute per liter of solution (mol/L). |
| Molality (m) | The number of moles of solute per kilogram of solvent (mol/kg). |
| Mole Fraction (X) | The ratio of moles of solute to the total moles of all components in a solution. |
| Mass Percentage | The mass of the solute as a percentage of the total mass of the solution (mass of solute / mass of solution * 100%). |
| Mass-Volume Percentage (% m/v) | The mass of solute in grams per 100 mL of solution. |
| Volume-Volume Percentage (% v/v) | The volume of solute in milliliters per 100 mL of solution. |
| Normality (N) | The number of gram equivalent weights of a solute per liter of solution. It is used to express concentrations in reactions where the stoichiometry is based on equivalents. |
| Equivalent Weight | The mass of a substance that will react with or supply one mole of an H+ ion (in acids), OH- ion (in bases), or electrons (in redox reactions). |
| Formal Concentration (F) | The number of moles of the original chemical formula per liter of solution, without regard for the species that actually exist in solution. |
| Parts-per Notation | A way to express concentration as a ratio of a component to the whole, such as parts per hundred (%), parts per thousand (‰), parts per million (ppm), and parts per billion (ppb). |
| Henry's Law | States that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid ($P = k_H \times C$). |
| Henry's Law Constant (kH) | A proportionality constant in Henry's law that depends on the solute, solvent, and temperature. |
| Raoult's Law | For ideal solutions, states that the partial vapor pressure of a component is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution ($P_A = X_A P_A^\circ$). |
| Vapor Pressure / Composition Diagram | A graphical representation showing the relationship between the mole fraction of components in a mixture and the vapor pressure of the mixture at a given temperature. |
| Boiling Point / Composition Diagram | A graphical representation showing the relationship between the mole fraction of components in a liquid mixture and the boiling points of the mixture. |
| Phase Diagram | A graphical representation that shows the stable phases of a substance or mixture under different conditions of temperature, pressure, and composition. |
| Fractional Distillation | A separation technique used to separate components of a liquid mixture based on differences in their boiling points, involving repeated vaporization and condensation. |
| Osmosis | The net movement of solvent molecules through a selectively permeable membrane from an area of higher solvent potential (lower solute concentration) to an area of lower solvent potential (higher solute concentration). |
| Semi-permeable Membrane | A membrane that allows certain molecules or ions to pass through it by diffusion while blocking others. |
| Osmotic Pressure | The minimum pressure that needs to be applied to a solution to prevent the inward flow of its pure solvent across a semi-permeable membrane. It is a colligative property. |
| Hypotonic Solution | A solution with a lower solute concentration (and thus higher water concentration) compared to another solution. |
| Hypertonic Solution | A solution with a higher solute concentration (and thus lower water concentration) compared to another solution. |
| Isotonic Solution | A solution with the same solute concentration (and thus the same water concentration) as another solution. |
| Buffer Solution | An aqueous solution that resists changes in pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. |
| Henderson-Hasselbalch Equation | An equation used to calculate the pH of a buffer solution: $pH = pK_a + \log([\text{conjugate base}]/[\text{weak acid}])$. |
| pKa | The negative logarithm of the acid dissociation constant ($K_a$). It is a measure of the acidity of a weak acid. |
| Buffer Capacity | A quantitative measure of a buffer solution's resistance to pH change upon the addition of an acid or base. |
| Electrochemistry | The branch of physical chemistry that studies the relationship between electricity and chemical reactions, particularly those involving electron transfer. |
| Electrochemical Reaction | A chemical reaction that involves the transfer of electrons between chemical species, either producing electricity or being driven by an external electric current. |
| Oxidation | The loss of electrons from a chemical species, resulting in an increase in its oxidation state. |
| Reduction | The gain of electrons by a chemical species, resulting in a decrease in its oxidation state. |
| Redox Reaction | A reaction that involves both oxidation and reduction. |
| Electrochemical Cell | A device that converts chemical energy into electrical energy (galvanic/voltaic cell) or uses electrical energy to drive a non-spontaneous chemical reaction (electrolytic cell). |
| Electrode | A conductor through which electric current enters or leaves an electrolytic solution or other medium. |
| Anode | The electrode where oxidation occurs in an electrochemical cell. |
| Cathode | The electrode where reduction occurs in an electrochemical cell. |
| Galvanic Cell (Voltaic Cell) | An electrochemical cell that produces electrical energy from spontaneous redox reactions. |
| Daniell Cell | A specific type of galvanic cell that uses zinc and copper electrodes in solutions of their respective sulfates, producing a standard potential of 1.10 V. |
| Salt Bridge | A component of an electrochemical cell that connects two half-cells, allowing ion flow to complete the electrical circuit while preventing excessive mixing of the electrolytes. |
| Electromotive Force (emf) | The potential difference between the electrodes of an electrochemical cell, also known as cell voltage. |
| Rust | Iron oxides and hydroxides formed by the corrosion of iron and its alloys (like steel) in the presence of oxygen and moisture. |
| Corrosion | The gradual destruction of materials, usually metals, by chemical or electrochemical reaction with their environment. |
| Passivation Layer | A thin, protective oxide film that forms on the surface of some metals, inhibiting further corrosion. |
| Galvanization | A process of applying a protective zinc coating to steel or iron to prevent rusting. Zinc acts as a sacrificial anode. |
| Cathodic Protection | A technique used to prevent corrosion by making the metal to be protected the cathode of an electrochemical cell, often by connecting it to a more easily corroded metal (sacrificial anode). |
| Plating | The process of coating a metal surface with another metal using electrolysis or other methods, often for protection or decoration. |
| Coatings | Protective layers applied to surfaces to prevent corrosion, such as paint, lacquer, or wax. |
| Bluing | A passivation process for steel that forms a protective layer of black iron oxide, offering limited resistance to rusting. |
| Corrosion Inhibitors | Substances that, when added in small concentrations to an environment, reduce the corrosion rate of a metal. |
| Humidity Control | Managing the moisture content in the atmosphere to prevent or slow down rust formation. |
| Rust Belt | A term referring to industrial regions in the United States characterized by declining heavy industry, particularly steel production, often associated with rust and decay. |