Lecture 4 Practice: Feasibility and Reaction Rates

Nine short problems of the kinds you may meet in the assessment, each based on a question type from Lecture 4: deciding between ΔG and rate, true or false, matching, reading an energy profile, finding a mistake, calculating a rate constant and half-life, comparing two temperatures, the effect of an enzyme, and a feasibility calculation from CRC data. Attempt them in any order. Each answer is checked as you go, and the working is shown once each step is correct.

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Equation sheet

Arrhenius equation: k = A e^−E_a/RT
R = 8.314 J K⁻¹ mol⁻¹; E_a in J mol⁻¹; T in K
Half-life (first order): t_½ = ln 2 / k = 0.693 / k
Catalyst (same A and T): k₂/k₁ = e^{(E_a1 − E_a2)/RT}
Two temperatures (same A and E_a): k₂/k₁ = e^{−(E_a/R)(1/T₂ − 1/T₁)}
ΔG = ΔH − TΔS; minimum temperature: T = ΔH / ΔS
Δ_rH° = ΣnΔ_fH°(products) − ΣmΔ_fH°(reactants)
Δ_rS° = ΣnS°(products) − ΣmS°(reactants)
T(K) = T(°C) + 273.15; 1 kJ = 1,000 J
1 h = 3,600 s; 1 day = 86,400 s

About the values

Activation energies, pre-exponential factors and rate constants are illustrative values, as in the lecture.
Standard data in Problem 9 are from the CRC Handbook at 298.15 K and 1 bar. Δ_rH° and Δ_rS° are assumed not to change with temperature.
Numbers can be typed as 1.45e-4 or 1.45 × 10^-4. Small rounding differences are accepted, but keep at least four significant figures in any value that goes into an exponent: e^x magnifies small rounding errors.