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)
A0.93 K·kg/mol
B1.86 K·kg/mol
C0.465 K·kg/mol
D3.72 K·kg/mol
Correct Answer:
B. 1.86 K·kg/mol
EXPLANATION
ΔTf = Kf × m, where m = molality = 0.5 mol/1 kg (approximately). ΔTf = 0.93°C, so Kf = 0.93/0.5 = 1.86 K·kg/mol.
What is the order of the reaction if its half-life is independent of initial concentration?
AZero order
BFirst order
CSecond order
DCannot be determined
Correct Answer:
B. First order
EXPLANATION
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.
For the reaction: N₂O₄(g) ⇌ 2NO₂(g), if Kp = 0.5 atm at 298 K, what is Kc at the same temperature?
A0.5/(RT)
B0.5 × RT
C0.5 × (RT)²
D0.5/(RT)²
Correct Answer:
D. 0.5/(RT)²
EXPLANATION
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.
An endothermic reaction has ΔH = +50 kJ/mol. For this reaction to be spontaneous at all temperatures, which condition must be satisfied?
AΔS must be positive and large (TΔS > ΔH)
BΔS must be negative
CΔG must always be positive
DTemperature must be very low
Correct Answer:
A. ΔS must be positive and large (TΔS > ΔH)
EXPLANATION
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.