Sagina maam notes till 2nd term.pdf

# Periodic trends in atomic properties This section summarizes the periodic variations observed in key atomic properties, including atomic radius, ionization potential, electron affinity, and electronegativity, across periods and down groups of the periodic table [2](#page=2). ### 1.1 Atomic radius Atomic radius, or atomic size, refers to the size of an atom and can be determined by measuring the distance between atoms in a combined state. Different types of atomic radii exist, including covalent radius (distance between the nuclei of two bonded atoms, measured at the mean position of shared electrons) and ionic radius (distance between the nuclei of neighboring cations and anions) [3](#page=3) [4](#page=4). #### 1.1.1 Periodic variation in atomic radius * **Across a period:** Atomic size generally decreases as one moves from left to right across a period. This occurs because, while electrons are added to the same valence shell, the nuclear charge increases with increasing atomic number. This leads to a stronger attraction between the nucleus and the outermost electrons, reducing the atomic radius [6](#page=6) [7](#page=7). * **Down a group:** Atomic size generally increases as one moves down a group. Here, added electrons occupy new valence shells, and although the nuclear charge increases, the outermost electrons are further from the nucleus and shielded by inner electrons. This weaker attraction results in a larger atomic radius [8](#page=8) [9](#page=9). #### 1.1.2 Atomic radius of ions * **Cations:** Cations are smaller than their parent atoms. When an atom loses an electron to form a cation, the nuclear charge remains the same while the number of electrons decreases. This leads to an increased effective nuclear charge, pulling the remaining electrons closer to the nucleus and reducing the atomic size. For example, Na+ is smaller than Na [11](#page=11) [12](#page=12) [13](#page=13) [17](#page=17). * **Anions:** Anions are larger than their parent atoms. When an atom gains an electron to form an anion, the nuclear charge remains the same, but the number of electrons increases. This results in a decreased effective nuclear charge, weakening the attraction between the nucleus and the outermost electrons, and thus increasing the atomic size. For example, Br– is larger than Br [14](#page=14) [15](#page=15) [17](#page=17). #### 1.1.3 Isoelectronic species Isoelectronic species are atoms and ions that share the same electronic configuration, meaning they have the same number of electrons. Examples include N3-, O2-, and Na+. When comparing the size of isoelectronic species, the one with the greater nuclear charge will be smaller because its nucleus exerts a stronger pull on the electron cloud. For instance, among N3-, O2-, and Na+, Na+ is the smallest due to its higher nuclear charge [18](#page=18) [19](#page=19). ### 1.2 Ionization potential Ionization potential, also known as ionization energy or ionization enthalpy, is defined as the minimum energy required to remove the most loosely bound electron from an isolated atom in its gaseous state. This process can be represented as [22](#page=22): $$A_{(g)} + \text{Energy} \rightarrow A^{+}_{(g)} + e^-$$ [22](#page=22). The first ionization energy ($I_1$) is the energy to remove the first electron, the second ionization energy ($I_2$) is for the second electron, and so on. Successive ionization energies increase ($I_1 < I_2 < I_3$) because it becomes progressively harder to remove an electron from a positively charged ion due to increased effective nuclear charge [22](#page=22) [23](#page=23). #### 1.2.1 Periodic variation in ionization potential * **Across a period:** Ionization potential generally increases from left to right across a period. This trend mirrors the decrease in atomic radius. As the nuclear charge increases while electrons are added to the same valence shell, the attraction between the nucleus and the outermost electrons strengthens, requiring more energy to remove an electron [26](#page=26). * **Down a group:** Ionization potential generally decreases from top to bottom down a group. This correlates with the increase in atomic radius. As electrons are added to new shells and shielding increases, the attraction of the nucleus for the outermost electron weakens, making it easier to remove and thus lowering the ionization potential [27](#page=27). #### 1.2.2 Factors affecting ionization potential 1. **Atomic size:** As atomic size increases, the attraction between the nucleus and the outermost electron decreases, leading to a lower ionization potential. The relationship is inverse: atomic size $\propto \frac{1}{\text{ionization potential}}$ [28](#page=28). 2. **Nuclear charge:** A greater nuclear charge leads to a stronger attraction for electrons, resulting in a higher ionization potential. The relationship is direct: nuclear charge $\propto$ ionization potential. For instance, Carbon (atomic number 6, nuclear charge +6) has a higher ionization potential than Boron (atomic number 5, nuclear charge +5) [29](#page=29). 3. **Shielding effect:** Increased shielding by inner electrons reduces the effective nuclear charge experienced by the outermost electrons, decreasing the force of attraction and thus lowering the ionization potential. The relationship is inverse: shielding effect $\propto \frac{1}{\text{I.P}}$ [31](#page=31). 4. **Electronic configuration:** Atoms with stable electronic configurations, such as half-filled or fully-filled valence shells, have higher ionization potentials. This is because removing an electron from such a stable configuration would disrupt it, requiring more energy. For example, Nitrogen, with its half-filled 2p orbital ($2p^3$), has a higher ionization potential than Oxygen ($2p^4$), despite Oxygen having a greater nuclear charge. Similarly, elements like Neon (fully filled $2p^6$) have very high ionization potentials [32](#page=32) [33](#page=33) [34](#page=34). ### 1.3 Electron affinity Electron affinity is defined as the energy released when an electron is added to a neutral atom in the gaseous state to form a negative ion. It is also referred to as electron gain enthalpy. The process can be represented as [38](#page=38): $$A_{(g)} + e^- \rightarrow A^{-}_{(g)} + \text{Electron Affinity}$$ [38](#page=38). #### 1.3.1 Factors affecting electron affinity 1. **Atomic size:** As atomic size decreases, the attraction between the nucleus and the incoming electron increases, leading to a greater release of energy and thus higher electron affinity. The relationship is inverse: atomic size $\propto \frac{1}{\text{electron affinity}}$ [40](#page=40). * Across a period: Electron affinity generally increases from left to right due to decreasing atomic size and increasing nuclear charge [40](#page=40). * Down a group: Electron affinity generally decreases from top to bottom due to increasing atomic size [40](#page=40). 2. **Nuclear charge:** A greater nuclear charge results in a stronger attraction for an incoming electron, leading to higher electron affinity. The relationship is direct: nuclear charge $\propto$ electron affinity. For example, Fluorine (nuclear charge +9) has a greater electron affinity than Oxygen (nuclear charge +8) [41](#page=41). 3. **Electronic configuration:** Atoms with stable electronic configurations (half-filled or fully-filled) exhibit lower or even zero electron affinity. Adding an electron to such a stable configuration would disrupt it, reducing the likelihood of electron gain and the energy released. For example, Nitrogen, with its stable half-filled 2p orbital, has a lower electron affinity than Carbon [42](#page=42) [43](#page=43). #### 1.3.2 Important trends in electron affinity * Halogens have the highest electron affinities because they are one electron short of a stable noble gas configuration [44](#page=44). * Chlorine has a higher electron affinity than fluorine, despite fluorine being more electronegative. This anomaly is attributed to strong inter-electronic repulsions within the small fluorine atom, which hinder the addition of an incoming electron [44](#page=44). * Noble gases have zero electron affinity as they already possess stable, complete electronic configurations, making them unwilling to accept additional electrons [44](#page=44). ### 1.4 Electronegativity Electronegativity describes the tendency of an atom to attract electrons towards itself within a chemical bond. Fluorine is the most electronegative element, while Cesium is the least electronegative (most electropositive) [46](#page=46). #### 1.4.1 Periodic trend in electronegativity Electronegativity generally increases across a period and decreases down a group, similar to the trends in ionization potential [47](#page=47). #### 1.4.2 Electronegativity and bond nature The difference in electronegativity between two bonded atoms provides insight into the type of bond formed [48](#page=48): * A large electronegativity difference leads to the formation of an ionic bond (e.g., NaCl, LiF) [48](#page=48). * A small electronegativity difference results in the formation of a covalent bond (e.g., CO, NO) [48](#page=48). --- # Metallurgy and extraction of metals Metallurgy is the process of extracting metals in a pure form from their ores. The extraction method depends on the physical and chemical properties of the metal [51](#page=51). ### 2.1 Mode of occurrence of metals in nature Metals occur in nature in two main states: * **Native State:** Metals are found in a pure, uncombined form. They are typically unreactive and are not easily attacked by moisture, oxygen, or carbon dioxide. Examples include gold (Au) and platinum (Pt) [52](#page=52). * **Combined State:** Metals are found in combined forms, usually as compounds with other elements. These can include oxides, sulfides, carbonates, sulfates, halides, etc. [52](#page=52). * **Oxides:** Bauxite (Al₂O₃), Haematite (Fe₂O₃) [52](#page=52). * **Sulfides:** Copper pyrite (CuFeS₂), Zinc blende (ZnS) [52](#page=52). * **Carbonates:** Calamine (ZnCO₃) [52](#page=52). ### 2.2 Minerals and ores * **Minerals:** All naturally occurring chemical substances in which metals are found in nature, along with impurities [53](#page=53). * **Ores:** Minerals from which the extraction of a metal is economically and conveniently feasible [53](#page=53). * **Example:** Bauxite (Al₂O₃) is an ore of aluminum. Clay (Al₂O₃·2SiO₂·2H₂O) is a mineral, but not typically an ore [53](#page=53). * **Relationship:** Every ore is a mineral, but not every mineral is an ore [53](#page=53). ### 2.3 Types of metallurgical processes Based on the temperature at which extraction takes place, metallurgical processes can be classified into: * **Pyrometallurgy:** Involves extraction at very high temperatures. Metals like copper (Cu), iron (Fe), zinc (Zn), and tin (Sn) are extracted using this method [54](#page=54). * **Hydrometallurgy:** Uses aqueous solutions for metal extraction. Silver (Ag) and gold (Au) are extracted this way [54](#page=54). * **Electrometallurgy:** Involves using electrolytic methods for extraction from molten salt solutions. Highly reactive metals such as sodium (Na), potassium (K), lithium (Li), and calcium (Ca) are extracted using this method [54](#page=54). ### 2.4 General steps of metallurgy The general sequence of steps involved in the metallurgical extraction of metals includes: 1. **Crushing and Pulverization:** Reducing the ore to a fine powder [55](#page=55) [57](#page=57). 2. **Concentration of the ore (Ore Dressing):** Removing unwanted impurities (gangue) from the ore [55](#page=55) [59](#page=59). 3. **Conversion of the concentrated ore into metal oxide:** This prepares the ore for reduction [55](#page=55) [69](#page=69). 4. **Reduction of metal oxide into metal:** Obtaining the metal from its oxide [55](#page=55) [76](#page=76). 5. **Refining:** Purifying the crude metal obtained from reduction [55](#page=55) [80](#page=80). #### 2.4.1 Crushing and pulverization Ores are typically found as large lumps. These are first broken down into smaller pieces using jaw crushers and grinders (crushing). Subsequently, the small pieces are reduced to a fine powder using equipment like ball mills or stamp mills (pulverization) [57](#page=57). #### 2.4.2 Concentration of the ore (Ore dressing) The undesired rocky or earthy impurities associated with an ore are known as the **gangue** or **matrix**. The process of removing the gangue from the ore is called **concentration**. Various methods are employed for concentration, depending on the nature of the ore and the impurities [59](#page=59): ##### 2.4.2.1 Methods of concentration * **A. Hand Picking:** Suitable for ores with visibly distinct impurities that can be identified and removed by hand [61](#page=61). * **B. Hydraulic Washing (Levigation / Gravity Separation):** This method is employed when the ore particles are significantly heavier than the gangue particles. The powdered ore is agitated with water or washed with a stream of water. The heavier ore particles settle down, while the lighter impurities are washed away [61](#page=61). * **C. Froth Floatation:** Primarily used for the concentration of sulfide ores, such as copper pyrite (CuFeS₂), galena (PbS), and zinc blende (ZnS). The powdered ore is mixed with water and pine oil. Air is blown through the mixture, causing the ore particles (which get wet by the oil) to become lighter, rise to the surface as froth, and are then collected. The impurities (gangue), which get wet by water, settle down at the bottom [63](#page=63). * **D. Electromagnetic Separation:** This method is used when either the ore or the impurities possess magnetic properties. For example, magnetite (Fe₃O₄) and chromite (FeO·Cr₂O₃) ores can be concentrated using this method. The powdered ore is fed onto a moving belt that passes over rollers, at least one of which is electromagnetic. Magnetic particles are attracted to the electromagnet and fall closer to the roller, while non-magnetic particles fall away, allowing for their separation [65](#page=65). * **E. Leaching:** This process involves treating the powdered ore with a suitable reagent that selectively reacts with the ore, forming a soluble compound, while leaving the impurities unaffected [67](#page=67). * **Example 1: Leaching of Bauxite (Baeyer's process):** The ore is treated with sodium hydroxide (NaOH) to form soluble sodium meta-aluminate. The insoluble impurities are filtered off, and then aluminum hydroxide is precipitated from the filtrate [67](#page=67). * **Example 2: Leaching of Silver and Gold (Cyanide Process):** Used for extracting silver and gold [67](#page=67). * **F. Electrostatic separation:** (Mentioned in page 60 but not detailed in the provided text beyond its name.) #### 2.4.3 Conversion of the concentrated ore into metal oxide After concentration, the ore is converted into its corresponding metal oxide. This is a crucial step before reduction. The methods depend on the nature of the ore [70](#page=70). ##### 2.4.3.1 Calcination * **Definition:** The process of heating a concentrated ore strongly below its melting point in the absence or limited supply of air [71](#page=71). * **Purpose:** Primarily used to convert metal carbonates and hydroxides into their respective oxides. It also removes moisture, volatile impurities (like S, As, P as their oxides), and organic matter [71](#page=71). * **Examples:** * $CaCO_3 \xrightarrow{Heat} CaO + CO_2\uparrow$ (Limestone) [72](#page=72). * $CaCO_3 \cdot MgCO_3 \xrightarrow{Heat} CaO + MgO + 2CO_2\uparrow$ (Dolomite) [72](#page=72). * $ZnCO_3 \xrightarrow{Heat} ZnO + CO_2\uparrow$ [72](#page=72). ##### 2.4.3.2 Roasting * **Definition:** The process of heating a concentrated ore strongly below its melting point in an excess of air [73](#page=73). * **Purpose:** Commonly used to convert sulfide ores into their respective metal oxides. It also removes moisture, volatile impurities (S, As, P as their oxides), and organic matter [73](#page=73). * **Examples:** * Removal of volatile impurities: * $S_8 + 8O_2 \rightarrow 8SO_2\uparrow$ [74](#page=74). * $P_4 + 5O_2 \rightarrow P_4O_{10}$ [74](#page=74). * $4As + 3O_2 \rightarrow 2As_2O_3\uparrow$ [74](#page=74). * Conversion of sulfide ores to metallic oxides: * $2ZnS + 3O_2 \xrightarrow{Heat} 2ZnO + 2SO_2\uparrow$ [74](#page=74). * $2PbS + 3O_2 \xrightarrow{Heat} 2PbO + 2SO_2\uparrow$ [74](#page=74). * $2Cu_2S + 3O_2 \xrightarrow{Heat} 2Cu_2O + 2SO_2\uparrow$ [74](#page=74). * **Furnace:** Roasting and calcination are typically carried out in a reverberatory furnace [75](#page=75). #### 2.4.4 Reduction of metal oxide into metal The metal oxide obtained from calcination or roasting is then reduced to obtain the crude metal. The choice of reducing agent depends on the reactivity of the metal [76](#page=76) [77](#page=77). * **Highly reactive metals** (e.g., Na, K, Ca, Mg, Al): Reduced by electrolytic methods from their molten salts [77](#page=77). * **Less reactive metals** (e.g., Zn, Fe, Pb, Sn, Cr): Can be reduced by using reducing agents like carbon (coke) or carbon monoxide (CO) [77](#page=77). ##### 2.4.4.1 Smelting * **Definition:** The process of extracting a metal from its metal oxide by reduction using carbon (coke/charcoal) or carbon monoxide [78](#page=78). * **Furnace:** Smelting is commonly carried out in a blast furnace [78](#page=78). ##### 2.4.4.2 Aluminothermite Process (Aluminothermy or Goldschmidt Thermite Process) * **Definition:** This process uses aluminum powder as a reducing agent to extract metals from their oxides [79](#page=79). * **Application:** It is particularly useful for reducing oxides of metals that cannot be easily reduced by carbon or carbon monoxide, such as Fe₂O₃ and Cr₂O₃, because aluminum is highly electropositive [79](#page=79). * **Examples:** * $2Al(s) + Fe_2O_3(s) \rightarrow Al_2O_3(s) + 2Fe(l)$ [79](#page=79). * $2Al + Cr_2O_3 \rightarrow Al_2O_3 + 2Cr$ [79](#page=79). #### 2.4.5 Refining or purification of metals The metal obtained after reduction is usually impure and is called **crude metal**. Impurities can include other metals formed during reduction, non-metals (Si, P), unreacted oxides and sulfides, and residual slag and flux. Refining is the process of purifying the crude metal to obtain pure metal [81](#page=81) [82](#page=82). ##### 2.4.5.1 Common methods for refining * **Poling** [82](#page=82). * **Electro-refining** [82](#page=82). * **Zone refining / Fractional Crystallization** [82](#page=82). * **Vapour-phase refining** [82](#page=82). * **Chromatographic adsorption method** [82](#page=82). * **Distillation** [82](#page=82). ##### 2.4.5.2 Electrolytic refining * **Application:** Used for refining metals like copper (Cu), silver (Ag), gold (Au), lead (Pb), nickel (Ni), chromium (Cr), zinc (Zn), and aluminum (Al) [83](#page=83). * **Process:** In this method, the impure metal is made the anode, and a strip of pure metal of the same kind is made the cathode. Both electrodes are immersed in an electrolyte solution containing metal ions. When an electric current is passed, metal ions from the electrolyte deposit onto the cathode as pure metal. Soluble impurities pass into the electrolyte, while insoluble impurities (like precious metals or unreacted metals) settle down at the bottom as anode mud [83](#page=83). * **Electrode Reactions:** * At Anode: $M(s) \rightarrow M^{n+}(aq) + ne^-$ [84](#page=84). * At Cathode: $M^{n+}(aq) + ne^- \rightarrow M(s)$ [84](#page=84). * **Example: Refining of Copper:** * At anode: $Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-$ [84](#page=84). * At cathode: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$ [84](#page=84). ##### 2.4.5.3 Poling * **Application:** This method is suitable for refining metals that contain impurities in the form of their own oxides, such as impure copper containing copper(I) oxide ($Cu_2O$) [85](#page=85). * **Process:** The molten impure metal is stirred with green poles (often made of wood). The hydrocarbon gases released from the burning wood act as reducing agents, reducing the oxide impurities to the pure metal [85](#page=85). * **Example:** $Cu_2O + CH_4 \rightarrow Cu + H_2O + CO$ [85](#page=85). --- # Alkali and Alkaline Earth Metals This topic explores the properties, extraction, and chemical behavior of alkali metals (Group 1) and alkaline earth metals (Group 2) of the periodic table [96](#page=96). ### 3.1 Alkali metals Alkali metals belong to Group 1 (IA) of the periodic table and include lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr). They are named so because they react with water to form alkalis, which are strong bases capable of neutralizing acids. A general reaction is given by [97](#page=97): `2M + 2H2O → 2MOH + H2` [97](#page=97). where M represents an alkali metal. #### 3.1.1 Extraction of sodium by Down's process Sodium is primarily extracted from sodium chloride (NaCl) due to its abundance and low cost. Chemical reduction is not feasible as alkali metals are strong reducing agents themselves and cannot be reduced by common agents like coke, Al, or others. Pyrometallurgy is also unsuitable because sodium vaporizes at high temperatures and its vapors are highly reactive, making collection difficult. Therefore, electrolysis of molten NaCl is employed (electrometallurgy) [87](#page=87) [88](#page=88). **Challenges in Electrolysis and Down's Process Solution:** * **High Melting Point of NaCl:** NaCl has a high melting point (802°C) making it expensive to maintain the necessary high temperatures for electrolysis [89](#page=89). * **Sodium Vaporization:** The boiling point of sodium (883°C) is close to the melting point of NaCl, leading to sodium vaporization and the formation of metallic fog, which can short-circuit the cell [89](#page=89). * **Reactivity of Products:** The electrolytic products (sodium and chlorine) are highly reactive at high temperatures, corroding the vessel materials [90](#page=90). Down's process overcomes these issues by mixing NaCl with calcium chloride (CaCl2) in a 2:3 ratio. This lowers the melting point to approximately 600°C. At this reduced temperature, sodium and chlorine are less reactive, minimizing corrosion and the formation of metallic fog [90](#page=90). **Electrolysis in Down's Process:** During electrolysis, NaCl dissociates into ions: `NaCl → Na+ + Cl-` [92](#page=92). At the anode (oxidation): `Cl- → Cl + e-` [92](#page=92). `Cl + Cl → Cl2` [92](#page=92). At the cathode (reduction): `Na+ + e- → Na` [92](#page=92). Molten sodium is collected at the cathode, and chlorine gas is collected at the anode [92](#page=92). #### 3.1.2 Physical properties of alkali metals * **Physical state:** Alkali metals are soft, malleable, and ductile solids. They are silvery white when freshly cut but tarnish quickly in air. Softness increases down the group due to weaker metallic bonding as atomic size increases [98](#page=98). * **Atomic size:** Atomic size increases down the group with the addition of electrons in new shells [98](#page=98). * **Ionization energy:** They possess low first ionization energies, indicating a tendency to lose one electron [98](#page=98). * **Melting and boiling points:** These are low due to weak metallic bonding, and they decrease down the group as the metallic bond weakens [99](#page=99). * **Density:** Alkali metals have remarkably low densities, which increase down the group [99](#page=99). * **Conductivity:** They are excellent conductors of heat and electricity [99](#page=99). * **Nature of bond:** They form ionic bonds with non-metals by losing one electron to achieve an octet state [99](#page=99). * **Electronegativity:** Their electronegativity is low due to large atomic size, making them highly electropositive with a greater tendency to lose electrons [100](#page=100). * **Flame colour:** Alkali metals impart characteristic colours to a Bunsen flame: * Li: Crimson [100](#page=100). * Na: Golden yellow [100](#page=100). * K: Violet [100](#page=100). * Rb: Red violet [100](#page=100). #### 3.1.3 Chemical characteristics of alkali metals 1. **Action with air:** Alkali metals react with atmospheric oxygen, causing them to tarnish. They burn in oxygen to form oxides, but the nature of these oxides differs: * Lithium forms a normal oxide: `4 Li + O2 → 2Li2O` (Oxidation state of O = -2) . * Sodium forms a peroxide: `2 Na + O2 → Na2O2` (Oxidation state of O = -1) . * Larger alkali metals like potassium form superoxides: `K + O2 → KO2` (Oxidation state of O = -1/2) . 2. **Action with water:** The reaction is exothermic, and reactivity increases down the group. Lithium reacts gently, sodium reacts vigorously (may catch fire), and potassium reacts violently. The general reaction is : `2M + 2H2O → 2MOH + H2` [93](#page=93). 3. **Action with acids:** Alkali metals react with acids to produce hydrogen gas and metal salts [93](#page=93). `2Na + 2HCl → 2NaCl + H2` [93](#page=93). `2Na + H2SO4 → Na2SO4 + H2` [93](#page=93). 4. **Action with hydrogen:** All alkali metals react with hydrogen at elevated temperatures to form metal hydrides (M=Li, Na, K, Rb, Cs) . `2Na + H2 → 2NaH` (sodium hydride) . 5. **Action with halogens:** Alkali metals react with halogens to form ionic halides . `Na + Cl2 → 2NaCl` [94](#page=94). 6. **Action with non-metals:** They react with non-metals like sulfur and phosphorus to form sulfides and phosphides . `2Na + S → 2Na2S` [94](#page=94). `3Na + P → 2Na3P` . 7. **Reaction with ammonia gas:** Heating alkali metals with ammonia gas produces sodium amide and hydrogen gas [94](#page=94). `2Na + 2NH3 → 2NaNH2 + H2` (sodamide) . `2K + 2NH3 → 2KNH2 + H2` (potassamide) . 8. **Reaction with liquid ammonia:** Alkali metals dissolve in liquid ammonia to form ammoniated metal ions and ammoniated electrons . #### 3.1.4 Sodium carbonate (Na2CO3) **Properties of Sodium Carbonate:** * **Physical properties:** It is a white crystalline solid that forms a decahydrate (Na2CO3·10H2O), known as washing soda. The anhydrous form is called soda ash. It is highly soluble in water . * **Chemical properties:** 1. **Action of water:** Soluble in water due to hydrolysis, forming sodium hydroxide and carbonic acid . 2. **Action of CO2 and SO2:** Passing CO2 or SO2 through aqueous sodium carbonate precipitates sodium bicarbonate (baking soda) or sodium bisulfite, respectively . 3. **Precipitation reaction:** It precipitates metal carbonates from their soluble salt solutions. This property is utilized in water softening to remove permanent hardness caused by soluble calcium and magnesium chlorides and sulfates . `Reaction with lime water (Ca(OH)2):` . **Uses of Sodium Carbonate:** Manufacture of glass, soap, wood pulp, paper; water softening agent; production of baking soda; used in paints and dyes . **Manufacture of Sodium Carbonate by Solvay Process (Ammonia-Soda Process):** This process, developed by Ernest Solvay, involves the reaction of brine saturated with ammonia with carbon dioxide to form sodium bicarbonate, which is sparingly soluble and precipitates out. Heating the filtered sodium bicarbonate yields sodium carbonate . **Process Steps:** 1. **Saturation of brine:** Brine solution is saturated with ammonia in an ammonia absorber. Impurities like CaCl2 and MgCl2 are precipitated as hydroxides and carbonates and removed . 2. **Carbonation:** Ammoniated brine is passed down a tower while CO2 is introduced from the bottom. Sodium bicarbonate (NaHCO3) and ammonium chloride (NH4Cl) are formed. The reaction is: `NaCl + NH3 + CO2 + H2O → NaHCO3 + NH4Cl` . 3. **Recovery of ammonia:** Ammonium chloride reacts with slaked lime in the ammonia generator to regenerate ammonia gas . `2NH4Cl + Ca(OH)2 → 2NH3 + CaCl2 + 2H2O` 4. **Generation of CO2:** Limestone is heated in a lime kiln to produce CO2. The resulting CaO is treated with water to produce slaked lime for ammonia regeneration . `CaCO3 → CaO + CO2` 5. **Calcination:** The filtered sodium bicarbonate is heated to obtain anhydrous sodium carbonate . `2NaHCO3 → Na2CO3 + H2O + CO2` 6. **Crystallization:** Aqueous sodium carbonate is crystallized to obtain washing soda . #### 3.1.5 Sodium hydroxide (NaOH) NaOH is also known as Caustic Soda . **Properties of NaOH:** * **Physical properties:** It is a white, crystalline, deliquescent solid that absorbs moisture from the air. It is highly soluble in water . * **Chemical properties:** 1. **Precipitation reactions:** NaOH precipitates metallic hydroxides from their salt solutions. Some amphoteric metal hydroxides are soluble in excess NaOH . 2. **Action with CO:** Reacts with carbon monoxide at high temperature and pressure to form the sodium salt of formic acid, which yields formic acid upon acidification . **Uses of NaOH:** Manufacture of pulp, paper, soaps, and detergents; cleansing agent for grease, fats, and proteins; refining of vegetable oils; extraction of aluminum; reagent in laboratory reactions . **Manufacture of Sodium Hydroxide using Diaphragm Cell:** NaOH is produced by the electrolysis of aqueous NaCl solution. The cell uses a titanium oxide anode, a steel mesh cathode enclosed in a Teflon diaphragm, and brine as the electrolyte . **Electrolysis Reactions:** The aqueous solution ionizes as: `NaCl → Na+ + Cl-` . `H2O → H+ + OH-` . At the anode (oxidation): Cl- ions have a lower discharge potential than OH- ions, so chlorine gas is liberated. `2Cl- → Cl2 + 2e-` . At the cathode (reduction): H+ ions have a lower discharge potential than Na+ ions, so hydrogen gas is formed. The ion-exchange membrane allows selective ion flow to the cathode . `2H+ + 2e- → H2` . **Recovery of NaOH:** The solution in the cathode compartment, containing excess Na+ and OH- ions, is periodically removed and concentrated. Sodium chloride crystallizes out, leaving a concentrated NaOH solution, which can be evaporated to dryness to obtain solid NaOH . ### 3.2 Alkaline earth metals Alkaline earth metals are elements of Group 2 of the periodic table . #### 3.2.1 Physical properties of alkaline earth metals * **Physical state:** They are soft but harder than alkali metals due to stronger metallic bonding . * **Atomic size:** They are larger than alkali metals but smaller than Group 1 elements due to a greater nuclear charge. Atomic size increases down the group . * **Ionization energy:** They have low first ionization energies, but these are higher than alkali metals because they need to lose two electrons . * **Melting and boiling points:** These are low but higher than those of alkali metals . * **Density:** They have low densities, higher than alkali metals due to smaller atomic size . * **Electronegativity:** Their electronegativity is low due to large atomic size, making them highly electropositive but less so than alkali metals . * **Conductivity:** They are excellent conductors of heat and electricity . * **Flame colour:** Except for Be and Mg, they impart characteristic colours to a Bunsen flame: * Ca: Brick red . * Sr: Crimson red . * Ba: Apple green . * **Nature of bond:** They form ionic bonds with non-metals by losing two electrons to achieve an octet state (valency = 2) . #### 3.2.2 Chemical characteristics of alkaline earth metals 1. **Action with air:** Alkaline earth metals react with atmospheric oxygen, causing them to tarnish. They burn in oxygen to form oxides . `2Mg + O2 → 2MgO` . `2 Ca + O2 → 2CaO` . 2. **Action with H2O:** Beryllium (Be) does not react with water. Magnesium (Mg) reacts with hot water. Calcium (Ca), Strontium (Sr), and Barium (Ba) react with cold water to form hydroxides and liberate hydrogen gas . `Mg + 2H2O → Mg(OH)2 + H2` (hot water) . `Ca + 2H2O → Ca(OH)2 + H2` (cold water) . `Ba + 2H2O → Ba(OH)2 + H2` (cold water) . 3. **Action with hydrogen:** They react with hydrogen at elevated temperatures to form metal hydrides, except for Be . `Mg + H2 → MgH2` . `Ca + H2 → CaH2` . 4. **Action with nitrogen:** They react with nitrogen at elevated temperatures to form metal nitrides, except for Be . `Mg + N2 → Mg3N2` . 5. **Action with halogen, S, and P:** They react with halogens, sulfur, and phosphorus to form respective halides, sulfides, and phosphides . `Ca + Cl2 → CaCl2` . `Ca + S → CaS` . `3Ca + 2P → Ca3P2` . #### 3.2.3 Compounds of Ca and Mg 1. **Quick Lime (CaO):** Chemically known as Calcium oxide . * **Uses:** Fertilizer, preparation of cement, glass, bleaching powder; drying agent for gases like ammonia; flux in metallurgy; basic lining in furnaces . 2. **Magnesia (MgO):** Chemically known as Magnesium oxide . * **Uses:** Making crucibles; antacid in medicine; refractory material in furnaces and bricks . 3. **Plaster of Paris (CaSO4·1/2 H2O):** Also known as Gypsum plaster; chemically Calcium sulfate hemihydrate . * **Uses:** Building material for walls and ceilings; plastering fractured bones; making statues and molds . 4. **Bleaching powder (CaOCl2):** Chemically Calcium hypochlorite . * **Uses:** Household bleaching agent, stain remover; manufacturing chloroform; disinfectant for sterilizing water; germicide . 5. **Epsom salt ((MgSO4·7H2O)):** Chemically Magnesium sulfate heptahydrate . * **Uses:** Bath salts; purgative in medicine; mordant for cotton in dyeing; anhydrous form used as a desiccant . #### 3.2.4 Solubility of hydroxides, carbonates, and sulfates of alkaline earth metals * **Solubility of hydroxide:** Alkaline earth metals form basic hydroxides that are fairly soluble in water. Solubility increases down the group. The order is: `Be(OH)2 < Mg(OH)2 < Ca(OH)2 < Sr(OH)2 < Ba(OH)2`. `Ba(OH)2` is the most soluble . > **Tip:** The increase in solubility down the group is due to the lattice enthalpy decreasing faster than the hydration enthalpy as the cation size increases . * **Solubility of carbonate:** Alkaline earth metal carbonates are sparingly soluble in water. Solubility decreases down the group due to a decrease in hydration energy relative to lattice energy. The order is: `BeCO3 > MgCO3 > CaCO3 > SrCO3 > BaCO3`. `BaCO3` is the most insoluble . * **Solubility of sulfate:** Alkaline earth metal sulfates are soluble in water. Solubility decreases down the group due to a decrease in hydration energy relative to lattice energy. The order is: `BeSO4 > MgSO4 > CaSO4 > SrSO4 > BaSO4`. `BaSO4` is the most insoluble. The BaCl2 test for sulfate ions relies on the formation of a white precipitate of BaSO4 . > **Tip:** The change in ion distances for sulfate is less significant compared to hydroxides, causing lattice enthalpy to decrease slower, leading to a decrease in solubility down the group for sulfates . #### 3.2.5 Stability of carbonate and nitrate of alkaline earth metals * **Stability of carbonate:** Group 2 metal carbonates are fairly stable to heat. Thermal stability increases from top to bottom in a group, indicated by increasing decomposition temperatures. Metal carbonates decompose to yield metal oxides and carbon dioxide . `CaCO3 → CaO + CO2` . * **Stability of nitrate:** Group 2 metal nitrates are also stable to heat, with thermal stability increasing down the group. The stability order is: `Be(NO3)2 < Mg(NO3)2 < Ca(NO3)2 < Sr(NO3)2 < Ba(NO3)2`. Metal nitrates decompose to produce metal oxides, nitrogen dioxide, and oxygen . `Ca(NO3)2 → CaO + NO2 + O2` . --- # Bioinorganic Chemistry and Metal Toxicity Bioinorganic chemistry investigates the crucial interactions between inorganic substances and biological systems, distinguishing between essential macro- and micronutrients and examining the detrimental effects of toxic metals . ### 4.1 Bioinorganic chemistry fundamentals Bioinorganic chemistry bridges the fields of inorganic chemistry and biochemistry, focusing on the roles of inorganic compounds within living organisms. These compounds can range from simple metal ions like potassium ($K^{+}$), iron ($Fe^{2+}$), and sodium ($Na^{+}$), to complex ions such as molybdate, coordination compounds like cisplatin, and inorganic molecules including carbon monoxide (CO), nitric oxide (NO), and ozone ($O_3$) . ### 4.2 Essential and trace elements: macro and micronutrients Approximately 40 of the 118 known elements are involved in life processes, with about 30 being essential for human health . #### 4.2.1 Macronutrients Elements required in large quantities are classified as macronutrients and are also known as essential elements. Their absence leads to death or severe organ malfunction. Examples include sodium ($Na$), potassium ($K$), magnesium ($Mg$), calcium ($Ca$), and chlorine ($Cl$) . #### 4.2.2 Micronutrients Elements needed in smaller amounts are termed micronutrients or trace elements. Despite their small quantities, they play vital roles in biological systems, and their deficiency can cause serious defects. Examples include iron ($Fe$), zinc ($Zn$), copper ($Cu$), and cobalt ($Co$) . ### 4.3 Importance of metal ions in biological systems Various metal ions are critical for numerous biological functions: * **Sodium ($Na$):** Regulates osmotic pressure, aids in the absorption of glucose and amino acids, and maintains nerve impulses. Low intake can cause weakness, headache, and potentially kidney and heart failure . * **Potassium ($K$):** Regulates osmotic pressure, facilitates body metabolism, prevents muscle cramps, and offers protection against brain and heart strokes, and osteoporosis. Insufficient intake may lead to fatigue, weakness, and abnormal heart rhythms . * **Calcium ($Ca$):** Essential for the growth and development of healthy bones, facilitates communication between the brain and body parts, and helps maintain blood pressure . * **Magnesium ($Mg$):** Plays a role in the production of enzymes and proteins, supports the proper functioning of DNA and RNA, and maintains electrolytic balance for active ion transport . * **Iron ($Fe$):** Crucial for rapid growth and development during pregnancy; low intake can lead to anemia and internal bleeding . * **Copper ($Cu$):** Maintains nerve cells and the immune system, and assists in iron absorption and energy production . * **Zinc ($Zn$):** Supports nerve cells and the immune system, and promotes wound healing and skin repair . * **Nickel ($Ni$):** Aids in glucose breakdown, supports milk production in mammary glands, and is involved in iron metabolism . * **Cobalt ($Co$):** An integral component of Vitamin B12, it is involved in the metabolism of fatty acids and folic acid, and aids in red blood cell production . * **Chromium ($Cr$):** Enhances insulin production and contributes to weight loss and muscle strengthening . ### 4.4 The sodium-potassium pump The sodium-potassium pump is a primary active transport system that actively moves sodium ($Na^{+}$) ions out of the cytoplasm and potassium ($K^{+}$) ions into the cytoplasm. This process is also referred to as the sodium pump . #### 4.4.1 Mechanism of the sodium-potassium pump The pump binds ATP and three sodium ions ($Na^{+}$) from the cytoplasm. ATP then phosphorylates the pump, causing a conformational change that opens to the extracellular space. The sodium ions are released, and two potassium ions ($K^{+}$) are bound. Finally, the phosphate group is cleaved, returning the pump to its original conformation and releasing potassium ions into the cell . #### 4.4.2 Importance of the sodium-potassium pump The unequal distribution of ions across the cell membrane, with an excess of negative charge inside and positive charge outside, creates an electrical potential gradient essential for transmitting nerve signals in animals. The pump also drives secondary active transport systems for nutrients like amino acids and glucose, and it plays a role in maintaining cellular osmosis . ### 4.5 The sodium-glucose pump The sodium-glucose pump is a secondary active transport system that facilitates glucose absorption into cells using the concentration gradient of sodium ions. The primary active transport of the $Na^{+}-K^{+}$ pump establishes a high extracellular concentration of $Na^{+}$ and a low intracellular concentration. This gradient drives $Na^{+}$ ions to move into the cell, co-transporting glucose molecules. The intracellular glucose is then broken down to produce ATP for cellular functions. This pump is vital for transporting glucose from the extracellular fluid into the cytoplasm of cells, where it can be metabolized for energy . ### 4.6 Metal toxicity Metal toxicity refers to the harmful effects of certain metals in specific forms and doses on living organisms. Exposure to high concentrations of metals can occur through food, air, water pollution, medications, food containers, industrial settings, or even lead-based paints. The toxicity depends on the absorbed dose, route of exposure, and duration (acute or chronic) . Common toxic effects include gastrointestinal and kidney dysfunction, nervous system disorders, skin lesions, vascular damage, immune system dysfunction, birth defects, and cancer. Metals that humans can absorb in toxic amounts include mercury, lead, cadmium, arsenic, and iron . #### 4.6.1 Effects of mercury toxicity Mercury toxicity can lead to a lack of coordination, muscle weakness, hearing and speech difficulties, and damage to nerves in the hands and face. A notable example is Minamata disease in Japan, caused by methyl-mercury poisoning, which resulted in neurological damage affecting speech and sight . #### 4.6.2 Effects of iron toxicity Iron toxicity can cause problems in the lungs, stomach, and intestines, as well as heart and blood-related issues. It can also lead to liver and skin problems, including liver cancer, and nervous system issues. In cases of overdose, it is linked to diseases like Alzheimer's and Parkinson's . #### 4.6.3 Effects of lead toxicity Acute lead exposure can cause constipation, aggressive behavior, high blood pressure, fatigue, and sleep difficulties. Chronic exposure can result in mental retardation, birth defects, autism, and paralysis . #### 4.6.4 Effects of arsenic toxicity Arsenic toxicity may manifest as unusual heart rhythms, muscle cramps, stomach pain, and red or swollen skin. It can also cause wart-like spots on the skin. Chronic toxicity leads to arsenicosis, characterized by skin lesions and pigmentation changes . #### 4.6.5 Effects of cadmium toxicity Cadmium toxicity can decrease hemoglobin levels, leading to anemia, and cause muscle pain and osteoporosis. Chronic exposure can damage the kidneys, liver, and lungs. Itai-Itai disease in Japan, meaning "it hurts-it hurts," is an example of cadmium toxicity, characterized by softening of bones and severe bone and muscle pain . --- # Gas Laws This section explores fundamental gas laws that describe the macroscopic behavior of gases concerning pressure, volume, and temperature . ### 5.1 Properties of gases Gases are characterized by maximum inter-particle space and minimal forces of attraction between particles. Their particles are free to move in any direction, making them highly compressible and lacking fixed shape, size, or volume. Gases also exhibit low density. The behavior of gases can be predicted using variables such as pressure, volume, amount (moles), and temperature . ### 5.2 Gas laws Gas laws provide quantitative relationships between the mass, volume, pressure, and temperature of a gas. They describe the interrelationship between two variables while keeping others constant. Key gas laws include Boyle's Law, Charles' Law, Avogadro's Law, Dalton's Law of Partial Pressure, and Graham's Law of Diffusion . #### 5.2.1 Boyle's law Boyle's Law, formulated by Robert Boyle, establishes a relationship between the pressure (P) and volume (V) of a given mass of gas at a constant temperature . **Statement:** At a constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure . **Mathematical Expression:** The relationship can be expressed as: $P \propto \frac{1}{V}$ or, $P = k \frac{1}{V}$, where $k$ is a proportionality constant . Rearranging this gives: $PV = k$ . **Explanation:** If $V_1$ is the initial volume of a given mass of gas at pressure $P_1$ and temperature $T$, then $P_1V_1 = k$. If the final volume and pressure are $V_2$ and $P_2$ respectively, then $P_2V_2 = k$. Therefore, according to Boyle's Law : $P_1V_1 = P_2V_2 = k$ . This equation signifies that as volume increases, the gas pressure decreases proportionally, and vice-versa. For instance, doubling the pressure at constant temperature will halve the gas volume . **Graphical Representation:** Boyle's Law can be graphically represented by plotting pressure against volume at a constant temperature, yielding a curve known as an isotherm. Further graphical representations include plots of volume versus the reciprocal of pressure ($1/P$), and the product of pressure and volume ($PV$) versus pressure ($P$) . > **Tip:** An isotherm is a graph representing the relationship between pressure and volume of a gas at a constant temperature . **Applications of Boyle's Law:** Boyle's Law helps explain phenomena like why mountaineers need oxygen cylinders at high altitudes. As altitude increases, atmospheric pressure decreases, leading to an increased volume of air and thus lower air density. This reduced air density means less oxygen is available for breathing, necessitating the use of supplemental oxygen cylinders . **Numerical Formulas and Units:** * $PV = k$ . * $P_1V_1 = P_2V_2$ . * $\frac{P_1}{D_1} = \frac{P_2}{D_2}$, where $D$ is density and assuming mass is constant. (Derived from volume = mass/density, so $V = M/D$. If $M$ is constant, $V \propto 1/D$. Substituting into $P_1V_1 = P_2V_2$ yields $P_1(M/D_1) = P_2(M/D_2)$, which simplifies to $\frac{P_1}{D_1} = \frac{P_2}{D_2}$) . **Units:** * **Pressure:** 1 atm = 101,325 Pa, 1 atm = 760 mm Hg = 760 torr . * **Volume:** SI unit is m³. Commonly used units include cm³, liters (l), and milliliters (ml). 1 ml = 1 cc, 1 l = 1000 ml . * **Temperature:** SI unit is Kelvin (K). Other units include Fahrenheit (℉) and Celsius (℃) . **Numerical Examples:** * **Example 1:** 250 ml of a gas at 650 mm pressure expands to 500 ml at the same temperature. What is the final pressure? Given: $P_1 = 650$ mm, $V_1 = 250$ ml, $V_2 = 500$ ml. Using $P_1V_1 = P_2V_2$: $650 \text{ mm} \times 250 \text{ ml} = P_2 \times 500 \text{ ml}$ $P_2 = \frac{650 \text{ mm} \times 250 \text{ ml}}{500 \text{ ml}} = 325 \text{ mm}$ . * **Example 2:** A weather balloon has a volume of 174 liters at 1 atm pressure. What is its volume when the atmospheric pressure is 0.80 atm, assuming constant temperature? Given: $V_1 = 174$ l, $P_1 = 1$ atm, $P_2 = 0.80$ atm. Using $P_1V_1 = P_2V_2$: $1 \text{ atm} \times 174 \text{ l} = 0.80 \text{ atm} \times V_2$ $V_2 = \frac{1 \text{ atm} \times 174 \text{ l}}{0.80 \text{ atm}} = 217.5 \text{ l}$ . * **Example 3:** The density of a gas is 32 at 760 mm pressure. What will be its density at 570 mm pressure, if the temperature is constant? Using $\frac{P_1}{D_1} = \frac{P_2}{D_2}$: $\frac{760 \text{ mm}}{32} = \frac{570 \text{ mm}}{D_2}$ $D_2 = \frac{32 \times 570 \text{ mm}}{760 \text{ mm}} = 24$ . * **Example 4:** A gas occupies 250 cc at 700 mm pressure and 25℃. What additional pressure is needed to reduce its volume to 4/5th of its original volume at the same temperature? Given: $V_1 = 250$ cc, $P_1 = 700$ mm. New volume $V_2 = \frac{4}{5} \times 250 \text{ cc} = 200$ cc. Using $P_1V_1 = P_2V_2$: $700 \text{ mm} \times 250 \text{ cc} = P_2 \times 200 \text{ cc}$ $P_2 = \frac{700 \text{ mm} \times 250 \text{ cc}}{200 \text{ cc}} = 875$ mm. Additional pressure required = $P_2 - P_1 = 875 \text{ mm} - 700 \text{ mm} = 175$ mm . * **Example 5:** A cylinder contains 30 liters of oxygen at 50 atm. How many gas jars, each of 400 cc capacity, can be filled from the cylinder at 750 mm pressure? Initial volume $V_1 = 30$ l $= 30,000$ cc. Initial pressure $P_1 = 50$ atm. Final pressure $P_2 = 750$ mm Hg. We need to convert atm to mm Hg. 1 atm = 760 mm Hg. So, $P_1 = 50 \text{ atm} \times 760 \frac{\text{mm Hg}}{\text{atm}} = 38000$ mm Hg. Using $P_1V_1 = P_2V_2$: $38000 \text{ mm Hg} \times 30000 \text{ cc} = 750 \text{ mm Hg} \times V_2$ $V_2 = \frac{38000 \text{ mm Hg} \times 30000 \text{ cc}}{750 \text{ mm Hg}} = 1,520,000$ cc. Number of gas jars = $\frac{\text{Total volume}}{\text{Volume per jar}} = \frac{1,520,000 \text{ cc}}{400 \text{ cc/jar}} = 3800$ jars . #### 5.2.2 Charles' law Charles' Law, named after Jacques Charles, describes the relationship between the volume (V) and temperature (T) of a given mass of gas at constant pressure . **Statement:** At a constant pressure, the volume of a given mass of a gas changes by $\frac{1}{273}$ of its original volume for every one degree Celsius rise or fall in temperature . **Mathematical Expression:** Let $V_0$ be the volume of a given mass of gas at 0℃. The volume at $t$℃ is given by: $V_{t℃} = V_0 + \frac{t}{273} V_0$ . $V_{t℃} = V_0 \left(1 + \frac{t}{273}\right)$ This can be rewritten as: $V_{t℃} = V_0 \left(\frac{273 + t}{273}\right)$ If $T$ is the temperature in Kelvin, where $T = 273 + t$, then the equation becomes: $V_{t℃} = V_0 \left(\frac{T}{273}\right)$ This implies that $V \propto T$ at constant pressure . Thus, Charles' Law can also be stated as: "At a constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature (in Kelvin)" . For two different sets of conditions ($V_1, T_1$) and ($V_2, T_2$) at constant pressure: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ . **Absolute Temperature:** At -273℃, the volume of a gas theoretically becomes zero: $V_{-273℃} = V_0 \left(1 + \frac{-273}{273}\right) = V_0(1 - 1) = 0$ . This temperature, -273℃ or 0 Kelvin, is known as absolute zero, the theoretical temperature at which all molecular motion ceases and the properties of a gas vanish. However, gases typically liquefy or solidify before reaching this temperature . **Graphical Representation:** Charles' Law can be represented graphically by plotting volume against temperature (in ℃) at constant pressure, resulting in a curve called an isobar. Plotting volume against absolute temperature (in Kelvin) yields a straight line passing through the origin . > **Tip:** Always convert temperatures from Celsius to Kelvin by adding 273.15 (or approximately 273 for most calculations) when using Charles' Law . **Applications of Charles' Law:** * **Hot Air Balloons:** When air inside a hot air balloon is heated, its volume increases ($V \propto T$). This causes the density of the hot air to decrease relative to the cooler surrounding air, allowing the balloon to float . **Numerical Formulas and Units:** * $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, where $T_1$ and $T_2$ are temperatures in Kelvin . **Conversion:** * Temperature in Kelvin = Temperature in ℃ + 273 . * Example: 10℃ = 10 + 273 = 283 K . * Example: -5℃ = -5 + 273 = 268 K . **Numerical Examples:** * **Example 1:** 200 cc of nitrogen gas at 27℃ is cooled to -20℃. Find the new volume, assuming constant pressure. Given: $V_1 = 200$ cc, $T_1 = 27℃ = 27 + 273 = 300$ K, $T_2 = -20℃ = -20 + 273 = 253$ K. Using $\frac{V_1}{T_1} = \frac{V_2}{T_2}$: $\frac{200 \text{ cc}}{300 \text{ K}} = \frac{V_2}{253 \text{ K}}$ $V_2 = \frac{200 \text{ cc} \times 253 \text{ K}}{300 \text{ K}} = 168.67 \text{ cc}$ . * **Example 2:** 400 ml of oxygen gas at -150℃ is heated to 20℃ at constant pressure. Find the new volume. Given: $V_1 = 400$ ml, $T_1 = -150℃ = -150 + 273 = 123$ K, $T_2 = 20℃ = 20 + 273 = 293$ K. Using $\frac{V_1}{T_1} = \frac{V_2}{T_2}$: $\frac{400 \text{ ml}}{123 \text{ K}} = \frac{V_2}{293 \text{ K}}$ $V_2 = \frac{400 \text{ ml} \times 293 \text{ K}}{123 \text{ K}} = 952.85 \text{ ml}$ . * **Example 3:** 400 ml of N2 gas at 27℃ is cooled to -5℃ without change in pressure. Calculate the contraction in volume. Given: $V_1 = 400$ ml, $T_1 = 27℃ = 300$ K, $T_2 = -5℃ = 268$ K. First, find $V_2$: $\frac{400 \text{ ml}}{300 \text{ K}} = \frac{V_2}{268 \text{ K}}$ $V_2 = \frac{400 \text{ ml} \times 268 \text{ K}}{300 \text{ K}} = 357.33$ ml. Contraction in volume = $V_1 - V_2 = 400 \text{ ml} - 357.33 \text{ ml} = 42.67$ ml . * **Example 4:** When a vessel containing 400 cc of air at 7℃ is heated to 27℃ at the same pressure, what volume of air will be increased? Given: $V_1 = 400$ cc, $T_1 = 7℃ = 280$ K, $T_2 = 27℃ = 300$ K. First, find $V_2$: $\frac{400 \text{ cc}}{280 \text{ K}} = \frac{V_2}{300 \text{ K}}$ $V_2 = \frac{400 \text{ cc} \times 300 \text{ K}}{280 \text{ K}} = 428.57$ cc. Increase in volume = $V_2 - V_1 = 428.57 \text{ cc} - 400 \text{ cc} = 28.57$ cc . * **Example 5:** What fraction of air would have been expelled out when an open vessel at a temperature of 25℃ was heated to 400℃ at constant pressure? Let initial volume be $V_1$ at $T_1 = 25℃ = 298$ K. Let final volume be $V_2$ at $T_2 = 400℃ = 673$ K. From Charles' Law, $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, so $V_2 = V_1 \frac{T_2}{T_1} = V_1 \frac{673 \text{ K}}{298 \text{ K}} = 2.258 V_1$. The problem implies that the vessel is open, so as it heats up, the volume of air *inside* the vessel expands. If the vessel's capacity is fixed, then air is expelled. However, the question is asking about the *fraction of air expelled* from an open vessel, suggesting we consider the expansion relative to the initial volume. The wording is a bit ambiguous. Assuming the question means: If a fixed amount of air occupies volume $V_1$ at $T_1$, what volume $V_2$ does it occupy at $T_2$? The difference $V_2 - V_1$ represents the *expansion*. The *fraction expelled* from an open vessel could be interpreted as the *additional volume* compared to the initial volume. Let's re-interpret: If we have a certain volume of air at $T_1$, and heat it to $T_2$. The *new volume* it would occupy is $V_2$. If the original volume was $V_1$, the *amount expelled* is related to the increase in volume. Using the provided answer: 0.556. Let's assume $V_1$ is the initial volume at $T_1$. The amount expelled is the volume that *would have been* occupied by this air at $T_2$ if it remained at $T_1$, but is now at $T_2$. If $V_1$ is the volume at $T_1 = 298$ K, then at $T_2 = 673$ K, the new volume would be $V_2 = V_1 \frac{673}{298}$. The fraction expelled could be $\frac{V_2 - V_1}{V_1} = \frac{V_2}{V_1} - 1 = \frac{T_2}{T_1} - 1 = \frac{673}{298} - 1 = 2.258 - 1 = 1.258$. This does not match the answer. Let's assume the question means what fraction of the *final volume* was added. Alternatively, if we consider the initial amount of air as $n_1$ and final as $n_2$. At constant pressure and volume of the vessel: This question seems to imply that the vessel itself is not the constraint, but rather we are looking at the expansion of a quantity of air. Let's consider the *fraction expelled* from an open vessel. If a vessel is open and contains $V_1$ volume of air at $T_1$. When heated to $T_2$, the air expands. The amount of air that *escapes* is the amount corresponding to the volume difference. If $V_1$ is the initial volume at $T_1=298$ K. If the air were to occupy volume at $T_2=673$ K, its volume would be $V_2 = V_1 \times \frac{673}{298}$. The fraction of air expelled is the ratio of the increase in volume to the final volume, if the vessel could accommodate that. Let's consider the fraction of the *initial volume* that is expelled. Fraction expelled = $\frac{\text{Volume at } T_2 \text{ corresponding to } V_1 \text{ air} - V_1}{V_1}$ Fraction expelled = $\frac{V_2 - V_1}{V_1} = \frac{T_2}{T_1} - 1 = \frac{673}{298} - 1 \approx 1.258$. Still not matching. Let's consider the fraction of the initial amount of air that is expelled. If $n_1$ moles of air are present at $T_1$, and $n_2$ moles are present at $T_2$ within the same volume $V$ (if the vessel were closed). Since it's open, the air expands. The amount of air *remaining* in the vessel at $T_2$ is the amount that would occupy volume $V_1$ at $T_2$. Amount at $T_2$ remaining = $n_{rem} \propto V_1$ (at $T_2$) Initial amount = $n_1 \propto V_1$ (at $T_1$) Amount expelled = $n_1 - n_{rem}$. Fraction expelled = $\frac{n_1 - n_{rem}}{n_1} = 1 - \frac{n_{rem}}{n_1}$. Since $n \propto V/T$, and $V$ is constant in this interpretation. Let's consider the amount of air in moles. $PV = nRT$. At constant P, $V/T = nR$. So $n \propto V/T$. If the vessel has a fixed volume $V$. Initial moles $n_1 \propto V/T_1$. Final moles $n_2 \propto V/T_2$. Number of moles expelled $= n_1 - n_2$. Fraction expelled $= \frac{n_1 - n_2}{n_1} = 1 - \frac{n_2}{n_1} = 1 - \frac{V/T_2}{V/T_1} = 1 - \frac{T_1}{T_2}$. Fraction expelled $= 1 - \frac{298 \text{ K}}{673 \text{ K}} = 1 - 0.44279 = 0.5572$. This is very close to the answer 0.556. So the fraction of air expelled from an open vessel when heated is $1 - \frac{T_{initial}}{T_{final}}$. Fraction expelled = $1 - \frac{25 + 273}{400 + 273} = 1 - \frac{298}{673} \approx 0.557$ . * **Example 6:** How much increase in temperature is required to increase the volume of half a liter of gas by 30% at 27℃ at constant pressure? Given: Initial volume $V_1 = 0.5$ l, $T_1 = 27℃ = 300$ K. The volume is increased by 30%, so the new volume $V_2 = V_1 + 0.30 V_1 = 1.30 V_1$. $V_2 = 1.30 \times 0.5 \text{ l} = 0.65$ l. We need to find the final temperature $T_2$. Using $\frac{V_1}{T_1} = \frac{V_2}{T_2}$: $\frac{0.5 \text{ l}}{300 \text{ K}} = \frac{0.65 \text{ l}}{T_2}$ $T_2 = \frac{0.65 \text{ l} \times 300 \text{ K}}{0.5 \text{ l}} = 390$ K. Increase in temperature = $T_2 - T_1 = 390 \text{ K} - 300 \text{ K} = 90$ K . * **Example 7:** A balloon can hold 1000 cc of air before bursting. It contains 900 cc of air at -1℃. Will it burst at 27℃? If not, find the temperature above which the balloon bursts. Given: Maximum volume $V_{max} = 1000$ cc. Initial conditions: $V_1 = 900$ cc, $T_1 = -1℃ = 272$ K. We need to find the volume at $T_2 = 27℃ = 300$ K. Using $\frac{V_1}{T_1} = \frac{V_2}{T_2}$: $\frac{900 \text{ cc}}{272 \text{ K}} = \frac{V_2}{300 \text{ K}}$ $V_2 = \frac{900 \text{ cc} \times 300 \text{ K}}{272 \text{ K}} = 992.65$ cc. Since $V_2 (992.65 \text{ cc}) < V_{max} (1000 \text{ cc})$, the balloon will not burst at 27℃ . To find the temperature above which the balloon bursts, we set $V_2 = V_{max} = 1000$ cc and use the initial conditions ($V_1 = 900$ cc, $T_1 = 272$ K) to find the bursting temperature $T_{burst}$. $\frac{V_1}{T_1} = \frac{V_{burst}}{T_{burst}}$ $\frac{900 \text{ cc}}{272 \text{ K}} = \frac{1000 \text{ cc}}{T_{burst}}$ $T_{burst} = \frac{1000 \text{ cc} \times 272 \text{ K}}{900 \text{ cc}} = 302.22$ K. Convert this back to Celsius: $302.22 \text{ K} - 273 = 29.22℃$. So, the balloon bursts at temperatures above 29.22℃ . --- ## 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

| Term | Definition | |------|------------| | Atomic radius | The atomic size can be determined by knowing the distance between the atoms in the combined state. It is a measure of the size of an atom. | | Covalent radius | It is defined as half the distance between the nuclei of two identical atoms that are bonded together covalently. It represents the size of an atom in a covalent bond. | | Ionic radius | It is the distance between the nuclei of neighboring cation and anion in an ionic compound. It reflects the size of an ion in a crystal lattice. | | Effective nuclear charge | The net positive charge experienced by an electron in a polyelectronic atom, resulting from the attraction of the nucleus and the repulsion from other electrons. | | Isoelectronic species | Atoms and ions that have the same electronic configuration and thus the same number of electrons. | | Ionization potential (or energy/enthalpy) | The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom or ion. It indicates how strongly an electron is held by the nucleus. | | Electron Affinity | The amount of energy released when an electron is added to a neutral gaseous atom to form a negative ion. It signifies the tendency of an atom to accept an electron. | | Electronegativity | The tendency of an atom to attract a shared pair of electrons towards itself in a covalent bond. It influences the polarity of chemical bonds. | | Metallurgy | The process of extraction of metals in a pure form from their ores. It involves a series of steps to isolate and purify metals. | | Ore | A mineral containing a valuable deposit of ore, from which a metal can be economically extracted. | | Gangue (or Matrix) | The unwanted earthy and siliceous impurities associated with ores. Removal of gangue is crucial in ore concentration. | | Pyrometallurgy | A metallurgical process where extraction of metals occurs at very high temperatures, often involving smelting or roasting. | | Hydrometallurgy | A process for extracting metals using aqueous solutions, often involving leaching and precipitation. | | Electrometallurgy | The extraction of metals from molten salts or solutions using electrolytic methods. | | Calcination | A process of heating an ore strongly below its melting point in the absence or limited supply of air, typically used to remove volatile impurities and moisture, or to convert carbonates and hydroxides to oxides. | | Roasting | A process of heating an ore strongly below its melting point in excess of air, commonly used to convert sulphide ores to their respective metal oxides and remove volatile impurities. | | Smelting | The process of extracting a metal from its oxide by reduction, typically using carbon or carbon monoxide at high temperatures in a blast furnace. | | Refining | The process of purifying a crude metal obtained after extraction to remove remaining impurities and obtain a pure metal. | | Electrolytic refining | A refining method where the impure metal acts as the anode and a pure metal strip as the cathode in an electrolytic cell, separating the pure metal through electrolysis. | | Poling | A refining method used for crude metals containing oxide impurities, involving stirring the molten metal with green poles of wood which reduce the oxide impurities. | | Alkali metals | The elements of Group 1 (IA) of the periodic table: lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr). They are highly reactive and form alkalis when reacting with water. | | Alkaline earth metals | The elements of Group 2 (IIA) of the periodic table: beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They are reactive metals that form basic oxides and hydroxides. | | Deliquescent | A substance that absorbs moisture from the air to such an extent that it dissolves in the absorbed water, forming an aqueous solution. | | Amphoteric | A compound that can act as both an acid and a base. For example, some metal hydroxides are amphoteric and can dissolve in excess strong acid or strong base. | | Bioinorganic Chemistry | The study of the role of inorganic substances in biological systems, focusing on the interactions between inorganic chemistry and biochemistry. | | Macronutrients | Elements required by living organisms in large amounts for essential life processes, such as Na, K, Mg, Ca, and Cl. | | Micronutrients (Trace elements) | Elements required by living organisms in small quantities but are still vital for biological systems, such as Fe, Zn, Cu, and Co. | | Sodium-Potassium Pump (Na+-K+ pump) | A primary active transport system that moves sodium ions out of the cell and potassium ions into the cell across the cell membrane, utilizing ATP. | | Sodium-Glucose Pump | A secondary active transport system that uses the concentration gradient of Na+ ions (established by the Na+-K+ pump) to drive the transport of glucose into the cell. | | Metal toxicity | The toxic effect of metals in certain forms and doses on living organisms, which can result from exposure through food, air, water, or industrial sources. | | Boyle's Law | A gas law stating that at constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure. Mathematically, $PV = k$. | | Isotherm | A curve plotted on a graph representing the relationship between two variables (like pressure and volume) at a constant temperature. | | Charles' Law | A gas law stating that at constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature (in Kelvin). Mathematically, $V/T = k$. | | Isobar | A curve plotted on a graph representing the relationship between two variables (like volume and temperature) at a constant pressure. | | Absolute zero | The theoretical temperature at which the volume of an ideal gas would become zero, approximately -273.15 degrees Celsius or 0 Kelvin. |