Chemistry Test - 34

A fuel cell is an electrochemical device that directly converts the chemical energy of a fuel (such as hydrogen) into electrical energy, making statement (A) correct. The net cell reaction in a hydrogen-oxygen fuel cell is 2H2(g) + O2(g) --> 2H2O(l), confirming statement (B). Statement (C) is incorrect because a fuel cell is not rechargeable; it continuously generates electricity as long as fuel and oxidant are supplied from external sources. Statement (D) is correct because the only by-product of a hydrogen-oxygen fuel cell is water, which makes it a clean and eco-friendly energy device.

Kohlrausch's law of independent migration of ions states that the molar conductivity of an electrolyte at infinite dilution is the algebraic sum of the limiting molar conductivities of its individual ions, confirming statement (A). Statement (B) is incorrect; for strong electrolytes, molar conductivity increases only gradually and linearly with dilution (following Debye-Huckel-Onsager equation), not sharply. Weak electrolytes, such as acetic acid, cannot be brought to infinite dilution experimentally, but their limiting molar conductivity can be calculated using Kohlrausch's law by summing the ionic contributions, making statement (C) correct. Using the ratio of molar conductivity at a given concentration to the limiting molar conductivity gives the degree of dissociation, confirming statement (D).

The lead storage battery is a secondary (rechargeable) cell widely used in automobiles, operating on lead and lead dioxide electrodes in sulphuric acid (II). The nickel-cadmium battery is also a rechargeable secondary battery, commonly used in portable electronics (III). Corrosion is the process of oxidation of metals — methods like galvanisation and painting are used to prevent rusting (I). Faraday's laws of electrolysis relate the mass of substance deposited at an electrode to the quantity of electricity passed through the electrolyte (IV).

For a zero order reaction, the rate constant has units of mol L^-1 s^-1, since rate = k and rate has these units (II). For a first order reaction, the rate constant k has units of s^-1, derived from rate = k[A] (I). For a second order reaction, the units of k are L mol^-1 s^-1, obtained from rate = k[A]² (III). A pseudo first order reaction is one that is higher order overall but appears first order because one reactant is in large excess and its concentration remains effectively constant (IV).

According to the Arrhenius equation, k = A·e^(−Eₐ/RT). The rate constant (and hence the rate) is inversely related to activation energy — a lower activation energy means a larger fraction of molecules have sufficient energy to react, resulting in a faster reaction. Therefore, the reaction with the lowest Eₐ has the highest rate: Eₐ = 10 < 30 < 50 < 80 kJ/mol means rate (A) > (D) > (C) > (B).

First ionisation enthalpies (approximate values): Sc ≈ 631 kJ/mol, Fe ≈ 762 kJ/mol, Cr ≈ 653 kJ/mol (slightly higher than Sc due to half-filled 3d stability), and Zn ≈ 906 kJ/mol (highest among 3d metals due to fully filled 3d¹⁰ configuration which offers extra stability). Therefore, the increasing order is: Sc < Fe < Cr < Zn, i.e., (C) < (D) < (A) < (B).

Concept:

• Our periodic table as given by Moseley and has in total 7 periods running horizontally and 18 groups running vertically.
• They are also further divided into s, p, d, and f blocks depending on the placement of the outermost electrons.
• Elements belonging to the same blocks resemble in their chemical and physical properties.
• The s block elements lie in the 1st and 2nd groups.
• The p block elements belong to groups 13-18.
• The d and f block elements lie in the middle of group numbers 3-12.

Explanation:

A: Correct. Actinoids are highly reactive metals, especially in powdered form, due to their low ionization energies and large atomic sizes.

B: Correct. Actinoid contraction (due to poor shielding by 5f electrons) is more significant than Lanthanoid contraction (due to 4f electrons).

C: Incorrect. Many trivalent Lanthanoid ions (e.g., Pr³⁺, Nd³⁺, Er³⁺) are colored due to f-f electronic transitions, even in the solid state.

D: Correct. Lanthanoids are good conductors of heat and electricity, like most metals.

Thus, C is the wrong statement.

Wurtz Reaction: Couples two alkyl halides (R–X) with sodium in dry ether to form alkanes (R–R). E.g., 2R–Cl + 2Na → R–R + 2NaCl.

Sandmeyer Reaction: Converts a primary aromatic amine (Ar–NH₂) to an aryl halide (Ar–X) via a diazonium salt (Ar–N₂⁺) treated with CuCl or CuBr. E.g., Ar–N₂⁺Cl⁻ + CuCl → Ar–Cl + N₂.

Fittig Reaction: Couples two aryl halides (Ar–X) with sodium in dry ether to form biaryls (Ar–Ar). E.g., 2Ar–Cl + 2Na → Ar–Ar + 2NaCl.

Gattermann Reaction: Converts benzene diazonium chloride (C₆H₅N₂⁺Cl⁻) to chlorobenzene or bromobenzene using copper powder with HCl or HBr. E.g., C₆H₅N₂⁺Cl⁻ + Cu/HCl → C₆H₅Cl + N₂. Without the lists, I assume:

List I: (a) Wurtz, (b) Sandmeyer, (c) Fittig, (d) Gattermann

List II: (i) Forms biaryls, (ii) Forms alkanes, (iii) Forms chlorobenzene, (iv) Forms aryl halides Matches:

(a) → (ii): Wurtz → Forms alkanes

(b) → (iv): Sandmeyer → Forms aryl halides

(c) → (i): Fittig → Forms biaryls

(d) → (iii): Gattermann → Forms chlorobenzene

Thus, the correct answer is A ((a) → (ii), (b) → (iv), (c) → (i), (d) → (iii)).

• Concept:
• The freezing point of a substance may be defined as the temperature at which the vapour pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase.
• When a non-volatile solid is added to the solvent its vapour pressure decreases and now it would become equal to that of solid solvent at lower temperature.
• Thus, the freezing point of the solvent decreases. 
• It is given by expression:
• 
• where ΔTf is the freezing point of pure solvent and Tf is its freezing point when a non-volatile solute is dissolved is known as depression in freezing point.
• Expression: ΔT_f = K_f. m
• Kf is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant, m is the molality.

Given that ΔTf = 5.0 ºC

and Kf = 1.86 ºC molal^–1 .

Therefore, molality is

Molality = ΔT/K_f

= 5.0/1.86

= 2.7/molal

Therefore, the number of moles of ethylene glycol is found from the relation 

2.7 = n/5.0

⇒ n = 13.5 mol

Molar mass of ethylene glycol is = 2 × 12 + 4 × 1 + 2 × 16 = 62 g mol^–1.

Hence, the mass of ethylene glycol to be added to water is 

13.5mol × 62g/mol

= 837 g

Thus, the mass of ethylene glycol should be added to 5.00 kg of water to lower the freezing point to –5.0 ºC will be 837 g.