MChem Master of Chemistry Master of Chemistry: Physical Chemistry 4 — Questions and Answers
Question 1: For a second-order reaction A → products with rate law v = k[A]², the half-life t₁/₂ depends on initial concentration [A]₀ as:
- t₁/₂ = ln2 / k
- t₁/₂ = 1 / (k[A]₀) (Correct answer)
- t₁/₂ = [A]₀ / (2k)
- t₁/₂ = 2 / (k[A]₀)
Correct answer: t₁/₂ = 1 / (k[A]₀)
Integration of the second-order rate law gives t₁/₂ = 1/(k[A]₀), showing the half-life is inversely proportional to initial concentration.
Question 2: The Arrhenius equation k = Ae^(−Ea/RT) predicts that a plot of ln k versus 1/T has a slope of:
- Ea/R
- −Ea/R (Correct answer)
- Ea/k_B
- −Ea
Correct answer: −Ea/R
Taking the natural log: ln k = ln A − Ea/(RT), so the slope of ln k vs. 1/T equals −Ea/R.
Question 3: In transition state theory (Eyring theory), the rate constant is expressed as k = (k_BT/h)·K‡. The transmission coefficient κ is often set to 1, which assumes:
- No quantum tunneling occurs
- Every activated complex that reaches the transition state proceeds to products (Correct answer)
- The reaction is barrierless
- The pre-exponential factor equals k_BT/h
Correct answer: Every activated complex that reaches the transition state proceeds to products
κ = 1 assumes all transition state complexes proceed forward to products without recrossing the barrier.
Question 4: The Nernst equation for an electrochemical cell at 298 K modifies the standard cell potential as E = E° − (0.0257/n)·ln Q. For a cell with n=2 and reaction quotient Q=100, the correction to E° is approximately:
- −0.059 V (Correct answer)
- +0.059 V
- −0.118 V
- +0.118 V
Correct answer: −0.059 V
ΔE = −(0.0257/2)·ln(100) = −(0.01285)·4.605 ≈ −0.059 V.
Question 5: The Butler-Volmer equation describes electrode kinetics. At large overpotentials η >> RT/F, the current simplifies to the Tafel equation. What does the Tafel slope b represent?
- The standard exchange current density
- The rate of change of ln|i| with overpotential η (Correct answer)
- The transfer coefficient α directly
- The equilibrium potential at zero current
Correct answer: The rate of change of ln|i| with overpotential η
The Tafel slope b = d(η)/d(log|i|) and equals 2.303RT/(αF), characterizing how current varies with applied overpotential.
Question 6: For a chain reaction mechanism, the steady-state approximation applied to radical intermediates gives the rate law. Which step determines the overall reaction order for a long chain?
- The initiation step
- The propagation step (Correct answer)
- The termination step
- The branching step
Correct answer: The propagation step
In a long chain where the chain length >> 1, propagation steps dominate and determine the observed rate law and reaction order.
Question 7: Collision theory predicts the pre-exponential factor A in the Arrhenius equation. The steric factor p (0 < p ≤ 1) corrects for:
- The fraction of collisions with sufficient energy
- The fraction of collisions with the correct molecular orientation (Correct answer)
- The reduced mass of the colliding pair
- Quantum tunneling through the barrier
Correct answer: The fraction of collisions with the correct molecular orientation
The steric factor p accounts for the fact that not all geometrically successful collisions have the correct orientation for reaction.
MChem Master of Chemistry Master of Chemistry: Physical Chemistry 4
For a second-order reaction A → products with rate law v = k[A]², the half-life t₁/₂ depends on initial concentration [A]₀ as: