MChem Master of Chemistry Master of Chemistry: Physical Chemistry 4

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:

Accepted Answer

t₁/₂ = 1 / (k[A]₀)

Answer

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:

Accepted Answer

−Ea/R

Answer

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:

Accepted Answer

Every activated complex that reaches the transition state proceeds to products

Answer

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:

Accepted Answer

−0.059 V

Answer

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?

Accepted Answer

The rate of change of ln|i| with overpotential η

Answer

The Tafel slope b = d(η)/d(log|i|) and equals 2.303RT/(αF), characterizing how current varies with applied overpotential.

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Master of Chemistry: Physical Chemistry 4