For the reaction: A → B, if the order is 2 and rate constant k = 0.5 L·mol⁻¹·s⁻¹, find the half-life when initial concentration is 2 M.
Answer: A
For a second-order reaction, the half-life depends inversely on both the rate constant and the initial concentration.
Step 1: [Identify the Reaction Order and Given Data]
We are dealing with a second-order reaction (order = 2) with rate constant k = 0.5 L·mol⁻¹·s⁻¹ and initial concentration [A]₀ = 2 M. We need to find the time required for the concentration to reduce to half its initial value.
Order=2,k=0.5 L⋅mol−1⋅s−1,[A]0=2 M
Step 2: [Apply the Half-Life Formula for Second-Order Reaction]
For a second-order reaction, the half-life formula is derived from the integrated rate law and is expressed as:
t1/2=k[A]01
Substituting the values:
t1/2=0.5×21=1.01=1.0 s
The half-life is 1.0 s, so the answer is (A).
Q.25Medium
What is the entropy change when 18 g of ice at 273 K is converted to water at 273 K? (ΔfusH = 6 kJ/mol)
Answer: A
ΔS = ΔH/T = (6000 J/mol) / 273 K = 22.0 J/(mol·K). For 18 g (1 mole) of ice, ΔS = 22.0 J/K.
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Q.26Medium
A buffer solution contains 0.1 M acetic acid and 0.1 M sodium acetate. If Ka = 1.8 × 10⁻⁵, calculate the pH:
The osmotic pressure of a solution is given by π = iMRT. If 0.1 M glucose solution has osmotic pressure 2.46 atm at 273 K, what is the van't Hoff factor?
Answer: B
i = π/(MRT) = 2.46/(0.1 × 0.0821 × 273) ≈ 1. Glucose is non-electrolyte with i = 1
Q.28Medium
For the exothermic reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), increasing temperature will:
Answer: B
For exothermic reactions, increasing temperature decreases Kc (unfavorable) and shifts equilibrium left (Le Chatelier's principle).
Q.29Medium
A buffer solution is prepared by mixing 100 mL of 0.1 M CH₃COOH and 100 mL of 0.1 M CH₃COONa. The pKa of acetic acid is 4.74. What is the pH?
For a spontaneous process at constant temperature and pressure:
Answer: C
For spontaneous process: ΔG < 0. Generally also ΔS > 0 for most spontaneous processes. (ΔH < 0 is not always required)
Q.34Medium
An endothermic reaction has ΔH = +50 kJ/mol. For this reaction to be spontaneous at all temperatures, which condition must be satisfied?
Answer: A
For an endothermic reaction (ΔH > 0) to be spontaneous, ΔG = ΔH - TΔS must be negative. This requires ΔS > 0 and TΔS > ΔH, making entropy-driven spontaneity essential.
Q.35Medium
The rate constant for a reaction doubles when temperature increases from 300 K to 310 K. What is the approximate activation energy (Ea)?
For the reaction: N₂O₄(g) ⇌ 2NO₂(g), if Kp = 0.5 atm at 298 K, what is Kc at the same temperature?
Answer: D
Relationship: Kp = Kc(RT)^Δn, where Δn = 2 - 1 = 1. Therefore, Kc = Kp/(RT) = 0.5/(RT). But using proper units, Kc = 0.5/(RT)² when pressure is in atm and volume in L.
Q.37Medium
What is the order of the reaction if its half-life is independent of initial concentration?
Answer: B
For first-order reactions, t₁/₂ = 0.693/k, which is independent of initial concentration. For zero and second-order reactions, t₁/₂ depends on initial concentration.
Q.38Medium
The cell potential (E°cell) for a reaction is -0.5 V. Which statement is correct?
Answer: B
When E°cell is negative, ΔG° = -nFE°cell is positive, making the reaction non-spontaneous. Also, negative E°cell indicates Kequilibrium < 1.
Q.39Medium
A solution containing 0.5 mol of a non-volatile, non-electrolyte solute in 1 L of water shows a freezing point of -0.93°C. What is the cryoscopic constant (Kf) of water? (Tf of pure water = 0°C)
Answer: B
ΔTf = Kf × m, where m = molality = 0.5 mol/1 kg (approximately). ΔTf = 0.93°C, so Kf = 0.093.5 = 1.86 K·kg/mol.
Q.40Medium
The osmotic pressure of a solution is 10 atm at 27°C. What is the molarity of the solution?
Answer: A
π = MRT, where π = 10 atm, T = 300 K, R = 0.0821 L·atm/(mol·K). M = π/(RT) = 10/(0.0821 × 300) ≈ 0.41 M.
