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CONCEPT:

Equilibrium Constant (K_c)

• For a reversible chemical reaction at equilibrium, the equilibrium constant (K_c) is defined as the ratio of the product of the molar concentrations of the products to the product of the molar concentrations of the reactants, with each concentration raised to a power equal to its stoichiometric coefficient in the balanced chemical equation.
• For a general reaction:

aA + bB ↔ cC

The equilibrium constant expression is:

K_c = [C]^c / ([A]^a[B]^b)

EXPLANATION:

• The given chemical reaction is:

N₂(g) + O₂(g) ↔ 2NO(g)

• From the balanced equation, the stoichiometric coefficients are:
• Nitrogen (N₂): 1
• Oxygen (O₂): 1
• Nitric Oxide (NO): 2
• The given equilibrium concentrations are:
• [N₂] = 0.5 M
• [O₂] = 0.7 M
• [NO] = 0.4 M
• The expression for the equilibrium constant (K_c) is:

K_c = [NO]² / ([N₂][O₂])

• Substituting the given values into the expression:
• K_c = (0.4)² / (0.5 × 0.7)
• K_c = 0.16 / 0.35
• K_c ≈ 0.457
• The calculated value (0.457) is approximately 0.46. Comparing this with the provided options, 0.48 is the most suitable choice.

Therefore, the value of K_c is 0.48.

CONCEPT:

Relative Sweetness of Sugars

• Sweetness is a sensory property of carbohydrates that varies depending on their molecular structure.
• To quantify sweetness, sucrose (common table sugar) is used as a standard reference and is assigned a value of 100. Other sugars are then rated relative to this value.

EXPLANATION:

• Fructose: It is a simple monosaccharide found in honey, fruits, and root vegetables. It is the sweetest of all naturally occurring carbohydrates, with a relative sweetness index of approximately 173 compared to sucrose.
• Glucose: Also known as blood sugar, it is a monosaccharide that serves as a primary energy source. It is less sweet than sucrose, having a relative sweetness index of about 74.
• Maltose: This is a disaccharide consisting of two glucose units. It is significantly less sweet than both fructose and glucose, with a sweetness index of approximately 32.
• Cellulose: It is a complex polysaccharide found in the cell walls of plants. Because it is a large, insoluble molecule, it does not stimulate the sweetness receptors on the tongue and is therefore not sweet.

Therefore, fructose is the sweetest sugar among the given options.

CONCEPT:

Atomic Structure and Ion Notation

• Atomic Number (Z): The identity of an element is determined by the number of protons in its nucleus.
• Mass Number (A): This is the sum of the protons and neutrons in an atom.

A = Number of Protons + Number of Neutrons

• Net Charge: Atoms are neutral when they have an equal number of protons and electrons. If these numbers differ, the particle is an ion with a charge.

Charge = Number of Protons - Number of Electrons

EXPLANATION:

• To identify the correct symbol, we use the given subatomic particles:
• Protons = 20
• Electrons = 18
• Neutrons = 22
• Step 1: Identify the element
• The atomic number is equal to the number of protons. With 20 protons, the atomic number is 20.
• The element with atomic number 20 on the periodic table is Calcium (Ca).
• Step 2: Calculate the net charge
• Charge = Protons - Electrons
• Charge = 20 - 18 = +2
• Since the charge is +2, the symbol must include a ²⁺ superscript.
• Step 3: Determine the mass number (A)
• Mass Number = 20 (protons) + 22 (neutrons) = 42.
• While the options focus on the element and charge, the specific isotope described is ⁴²Ca²⁺.
• Conclusion:
• Combining the element symbol (Ca) and the calculated charge (+2), we get the symbol Ca²⁺.

Therefore, the symbol for an atom containing 20 protons, 18 electrons, and 22 neutrons is Ca²⁺.

CONCEPT:

Electrolytes:

• Electrolytes are substances that produce ions when dissolved in a solvent (like water) or in a molten state, allowing the solution to conduct electricity.
• Strong Electrolytes: These are substances that dissociate or ionize completely into ions in an aqueous solution. This category includes strong acids, strong bases, and most soluble ionic salts.
• Weak Electrolytes: These are substances that only partially ionize in solution, meaning a significant amount of the substance remains as neutral molecules.

EXPLANATION:

• Analyzing the given options:
• HF (Hydrofluoric Acid): Although it is a halogen acid, it is a weak acid. It does not dissociate completely in water due to the high bond enthalpy of the H-F bond.
• NH₃ (Ammonia): It is a weak base. In water, it only partially reacts to form NH₄⁺ and OH^- ions.
• CaCl₂ (Calcium Chloride): It is a highly soluble ionic salt. In an aqueous solution, it dissociates completely into its constituent ions:

CaCl₂(aq) → Ca²⁺(aq) + 2Cl^-(aq)

Because it ionizes 100%, it acts as a strong electrolyte.

• AgCl₂: Silver salts like AgCl are generally sparingly soluble in water, and the formula AgCl₂ is not a standard stable simple salt compared to the highly soluble CaCl₂.
• Among the substances listed, CaCl₂ is a soluble ionic salt that dissociates fully into ions, making it the strongest electrolyte.

Therefore, CaCl₂ is the strongest electrolyte.

CONCEPT:

Lattice Energy

• Lattice energy is defined as the energy required to completely separate one mole of a solid ionic compound into its constituent gaseous ions.
• It can also be defined as the energy released when gaseous ions come together to form one mole of an ionic crystal.
• This value reflects the stability of the ionic crystal; higher lattice energy indicates a more stable compound.

EXPLANATION:

• The process described in the question involves breaking the bonds within a solid lattice to produce free ions in the gas phase.

Example: MX(s) → M⁺(g) + X^-(g)

• Let's look at the other terms:
• Ionization energy: This is the energy required to remove an electron from an isolated gaseous atom.
• Electron gain enthalpy: This is the energy change when an electron is added to an isolated gaseous atom.
• Sublimation energy: This is the energy required to convert a solid directly into a gas, but it does not necessarily involve the separation into ions.
• By definition, the specific energy associated with separating an ionic solid into its gaseous ions is the Lattice energy.

Therefore, the energy required to completely separate one mole of solid ionic compound into gaseous constituent ions is called Lattice energy.

CONCEPT:

• Friedel-Crafts Reaction: This is an electrophilic aromatic substitution reaction that requires a Lewis acid catalyst, such as anhydrous AlCl₃, to generate an electrophile.
• Gabriel Phthalimide Synthesis: This is a method used for the preparation of primary amines. It involves the nucleophilic substitution (S_N2) of an alkyl halide by the phthalimide anion.

EXPLANATION:

• Statement 1: Aniline does not give Friedel Crafts reaction.
• Aniline is a Lewis base because of the lone pair of electrons on the nitrogen atom of the -NH₂ group.
• The catalyst used in Friedel-Crafts reactions, anhydrous AlCl₃, is a strong Lewis acid.
• Instead of catalyzing the substitution on the ring, AlCl₃ reacts with aniline to form a salt complex (C₆H₅NH₂⁺AlCl₃^-).
• The positive charge on the nitrogen atom in this complex makes the group strongly electron-withdrawing, which deactivates the benzene ring and prevents the electrophilic substitution. Thus, the statement is correct.
• Statement 2: Aromatic primary amines cannot be prepared by Gabriel phthalimide synthesis.
• Gabriel synthesis involves a nucleophilic attack by the phthalimide anion on an organic halide.
• To prepare aromatic primary amines, one would need to use an aryl halide (like chlorobenzene).
• Aryl halides do not undergo nucleophilic substitution (S_N2) under ordinary conditions because the C-X bond has partial double bond character due to resonance, and the carbon atom is sp² hybridized. Thus, the statement is correct.

Therefore, both statements I and II are correct.

CONCEPT:

Catalytic Activity of Transition Elements

• Transition metals and their compounds are well-known for their exceptional catalytic properties in various chemical reactions.
• This catalytic activity is primarily attributed to two main factors:
• The ability to exhibit variable oxidation states.
• The ability to form complex compounds or intermediates.
• By changing oxidation states, transition metals can form unstable intermediate compounds with reactants, providing an alternative reaction pathway with a lower activation energy.

EXPLANATION:

• Transition elements act as efficient catalysts because they can easily transition between different oxidation states.
• For example, in the reaction between iodide (I^-) and persulphate (S₂O₈^2-) ions, Iron (Fe) acts as a catalyst by switching between Fe²⁺ and Fe³⁺ states.
• In the Contact process, Vanadium pentoxide (V₂O₅) acts as a catalyst where Vanadium changes its oxidation state to facilitate the conversion of SO₂ to SO₃.
• Furthermore, transition metals have vacant d-orbitals that allow them to form coordination complexes with reactant molecules. This weakens the bonds within the reactants and brings them closer together on the catalyst surface.
• While surface area is important in heterogeneous catalysis (providing more sites for adsorption), the fundamental chemical reason for the versatile catalytic nature of transition elements is their electronic configuration allowing variable oxidation states.

Therefore, the catalytic activity of transition elements is related to their variable oxidation states.

CONCEPT:

Catalysis in Industrial Processes

• Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process. They work by providing an alternative reaction pathway with a lower activation energy.
• Transition metals and their compounds are frequently used as catalysts in industrial applications due to their ability to change oxidation states and form complexes.

EXPLANATION:

• Wilkinson Catalyst: The complex $[RhCl(PPh_{3})_{3}]$ (often referred to in variations like the one in Option A) is a well-known homogeneous catalyst used for the hydrogenation of alkenes.
• Ziegler-Natta Catalyst: This is a mixture typically consisting of titanium tetrachloride ($TiCl_{4}$) and triethylaluminium [$Al(C_{2}H_{5})_{3}$]. it is used for the polymerization of ethene and propene to produce high-density plastics.
• Hydrogenation of Oils: Finely divided Nickel (Ni) is the standard catalyst used in the industrial hydrogenation of vegetable oils (unsaturated fats) to produce vanaspati ghee (saturated fats).
• Haber-Bosch Process: This process for the manufacture of ammonia ($NH_{3}$) uses finely divided Iron (Fe) as the catalyst, often with molybdenum or alumina as promoters.
• Vanadium pentoxide ($V_{2}O_{5}$) or other vanadium oxides are used as catalysts in the Contact Process for the oxidation of sulfur dioxide ($SO_{2}$) to sulfur trioxide ($SO_{3}$), not in the Haber-Bosch process.

Therefore, the wrong pair is V₂O₃ : Haber Bosch process.

CONCEPT:

Polysaccharides

• Polysaccharides are complex carbohydrates formed by the polymerization of a large number of monosaccharide units joined together by glycosidic linkages.
• Cellulose: It is the most abundant organic substance in the plant kingdom and a major constituent of cell walls. It is a straight-chain polysaccharide.
• Starch: It is the main storage polysaccharide of plants. It is a polymer of α-glucose and consists of two components: Amylose and Amylopectin.

EXPLANATION:

Analysis of Statement 1: Cellulose

• Cellulose is a linear polymer of β-D-glucose units.

• The glucose units are joined by glycosidic linkages between C₁ of one glucose unit and C₄ of the next glucose unit (β-1,4-glycosidic linkage).

• There is no branching in cellulose, so it contains only C₁-C₄ linkages. Hence, statement 1 is correct.

• Analysis of Statement 2: Starch

• Starch is made up of two components:

• Amylose: A water-soluble component which is a long unbranched chain with α(1→4) glycosidic linkages.

• Amylopectin: A water-insoluble component which is a branched-chain polymer. The main chain is formed by α(1→4) glycosidic linkages, while branching occurs by C₁-C₆ glycosidic linkages.

• Since starch contains both amylose and amylopectin, it possesses both C₁-C₄ and C₁-C₆ linkages. Hence, statement 2 is correct.

Both statements I and II are correct.

CONCEPT:

Werner's Theory of Coordination Compounds

• Alfred Werner proposed that in coordination compounds, central metal atoms exhibit two types of valencies:
• Primary Valency: This corresponds to the oxidation state of the metal ion. These valencies are ionizable and are satisfied by negative ions.
• Secondary Valency: This corresponds to the coordination number of the metal ion. These valencies are non-ionizable. They are satisfied by ligands (neutral molecules or negative ions) and have a fixed orientation in space.

EXPLANATION:

• Based on the postulates of Werner's theory:
• Primary valencies are the bonds that can break in a solution to form ions. For example, in [Co(NH₃)₆]Cl₃, the three chloride ions satisfy the primary valency and can be ionized in aqueous solution.
• Secondary valencies are the coordinate bonds between the metal and the ligands inside the coordination sphere. These do not dissociate into ions in solution.
• Evaluating the logical nature of the statements:
• The statement 'Primary valency can be ionized' is correct because primary valencies represent the ionic part of the complex that dissociates in water.
• The statement 'Secondary valency can be ionized' is incorrect because coordination bonds do not ionize.
• The statement 'Primary and secondary valency do not ionize' is incorrect because the primary valency is ionizable.
• The statement 'Only primary valency does not ionize' is incorrect because it is the secondary valency that does not ionize.

Therefore, the logical statement according to Werner's theory is that primary valency can be ionized.