MChem Master of Chemistry Master of Chemistry: Physical Chemistry 5

Question 1

The Clausius-Clapeyron equation dp/dT = ΔH_vap/(TΔV) describes the liquid-vapor coexistence curve. Assuming ideal gas and negligible liquid volume, the equation integrates to give ln(p₂/p₁) proportional to:

Accepted Answer

(1/T₁ − 1/T₂)

Answer

Integration yields ln(p₂/p₁) = −ΔH_vap/R · (1/T₂ − 1/T₁) = ΔH_vap/R · (1/T₁ − 1/T₂).

Question 2

Henry's law states that the partial pressure of a volatile solute above a dilute solution is p_i = K_H · x_i. In contrast, Raoult's law applies to:

Accepted Answer

The solvent (or any component in the limit x_i → 1)

Answer

Raoult's law (p_i = x_i · p*_i) is obeyed by the solvent and by any component as its mole fraction approaches unity.

Question 3

The diffusion coefficient D of a spherical particle in solution is given by the Stokes-Einstein equation D = k_BT/(6πηr). If the solvent viscosity η doubles at lower temperature while T decreases by 10%, D:

Accepted Answer

Decreases significantly

Answer

D ∝ T/η; if η doubles and T falls ~10%, D decreases by roughly half (D ≈ 0.9T / 2η ≈ 0.45× original), a significant decrease.

Question 4

In Density Functional Theory (DFT), the Hohenberg-Kohn theorem proves that the ground-state energy of a many-electron system is a unique functional of:

Accepted Answer

The electron density ρ(r)

Answer

The first Hohenberg-Kohn theorem establishes a one-to-one mapping between the ground-state electron density ρ(r) and the external potential, making all ground-state properties functionals of ρ(r).

Question 5

In NMR spectroscopy, the chemical shift δ (in ppm) is defined relative to a reference compound (TMS). A nucleus with greater electron density around it will resonate at:

Accepted Answer

Lower δ (upfield)

Answer

Greater electron density increases diamagnetic shielding, reducing the effective field at the nucleus and shifting the resonance upfield (lower δ).

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Master of Chemistry: Physical Chemistry 5