Daily Olympiad: Chemistry - Physical Chemistry [20260511] – 6 Practice Problems & Printable PDF

1. A reaction with ΔH° = -50 kJ/mol and ΔS° = -100 J/mol·K is spontaneous at 298 K. What is the temperature range (in K) where the reaction becomes non-spontaneous?

A. T < 500 K B. T > 500 K C. Always spontaneous D. Never spontaneous

Solution

Correct: B

Using ΔG° = ΔH° - TΔS°, for ΔG° ≥ 0 (non-spontaneous), T ≥ ΔH°/ΔS° = (-50 x 10³ J/mole)/(-100 J/mol·K) = 500 K. Thus, reaction is non-spontaneous above 500 K.

2. The van der Waals equation for a real gas is (P + a/n²V²)(V - nb) = nRT. Which term accounts for molecular volume?

A. a/V² B. b C. a/n²V² D. b/n²V

Solution

Correct: B

The term 'b' corrects for the finite volume of gas molecules, reducing the available volume to (V - nb) in the equation.

3. A 0.1 M solution of acetic acid (Ka = 1.8 × 10⁻⁵) is mixed with 0.2 M HCl. Calculate the degree of dissociation of acetic acid.

A. 9.0 × 10⁻⁵ B. 1.8 × 10⁻⁴ C. 3.6 × 10⁻⁴ D. 4.5 × 10⁻⁵

Solution

Correct: D

HCl provides [H⁺] = 0.2 M, suppressing acetic acid dissociation. Using Ka = [H⁺][CH3COO⁻]/[CH3COOH], solve for α = (Ka × 0.1)/[(0.2)^2] = 4.5 × 10⁻⁵.

4. In a first-order reaction, the time required for 99% completion is

A. 100 × t₅₀% B. 4.60 × t₅₀% C. 2 × t₅₀% D. 20 × t₅₀%

Solution

Correct: B

For first-order reactions, t = (1/k) ln([A₀]/[A]). t₉₉% = (1/k) ln(100), t₅₀% = (1/k) ln(2). Thus t₉₉% ≈ 4.60 × t₅₀%.

5. The molar heat capacity at constant pressure for CO₂ (gas) is 37.1 J/mol·K. Calculate q when 2 moles of CO₂ expand irreversibly from 1 L to 2 L at 1 atm.

A. 74.2 J B. 37.1 J C. 3710 J D. 3.71 × 10⁵ J

Solution

Correct: A

Irreversible work is -PΔV. Heat q = nCpΔT from ΔT = (PΔV)/nR = (101.325 kPa)(2-1)L/(8.314 × 2). Calculations yield q ≈ 74.2 J.

6. The rate law for 2NO + O₂ → 2NO₂ is rate = k[NO]²[O₂]. If [NO] doubles and [O₂] halves, the rate

A. Doubles B. Increases by 4× C. Decreases by 2× D. Quadruples

Solution

Correct: A

Rate depends on [NO]²×[O₂]. Doubling [NO] increases rate by 4×, halving [O₂] halves rate. Net factor: 4×0.5 = 2. Rate doubles.

Daily Olympiad: Chemistry - Physical Chemistry [20260511]

1. A reaction with ΔH° = -50 kJ/mol and ΔS° = -100 J/mol·K is spontaneous at 298 K. What is the temperature range (in K) where the reaction becomes non-spontaneous?

2. The van der Waals equation for a real gas is (P + a/n²V²)(V - nb) = nRT. Which term accounts for molecular volume?

3. A 0.1 M solution of acetic acid (Ka = 1.8 × 10⁻⁵) is mixed with 0.2 M HCl. Calculate the degree of dissociation of acetic acid.

4. In a first-order reaction, the time required for 99% completion is

5. The molar heat capacity at constant pressure for CO₂ (gas) is 37.1 J/mol·K. Calculate q when 2 moles of CO₂ expand irreversibly from 1 L to 2 L at 1 atm.

6. The rate law for 2NO + O₂ → 2NO₂ is rate = k[NO]²[O₂]. If [NO] doubles and [O₂] halves, the rate

Related Practice Tests

Daily Olympiad: Chemistry - Surface Chemistry [20260511]

Daily Olympiad: Chemistry - Organic Chemistry [20260512]

Daily Olympiad: Chemistry - Inorganic Chemistry [20260511]

Discussion & Comments