Worksheet: The Arrhenius Equation

In this worksheet, we will practice using the Arrhenius equation to calculate reaction activation energies and frequency (preexponential) factors.

Q1:

When the temperature increases from 30C to 37C, the rate of an enzyme-catalyzed reaction increases by a factor of 1.47. Calculate, to 3 significant figures, the activation energy for this reaction. Give your answer to 1 decimal place.

Q2:

A sample of hydrogen peroxide decomposes with a rate constant of 2.20×10 s−1 at 80C and 5.65×10 s−1 at 35C. Calculate, to 3 significant figures, the activation energy for this reaction.

Q3:

Butene can decompose to two molecules of ethene when heated. The rate constant for the decomposition reaction at 325C is 6.10×10 s−1 and the activation energy is 261.0 kJ/mol. Estimate the frequency (preexponential) factor for the reaction, to 2 significant figures.

  • A1.2×10 s−1
  • B6.3×10 s−1
  • C3.0×10 s−1
  • D3.8×10 s−1
  • E5.4×10 s−1

Q4:

The rate constant for a reaction, 𝑘, was measured over a range of reaction temperatures, 𝑇. The data were plotted on a graph of ln𝑘 against 1𝑇. What is the frequency (preexponential) factor for the reaction in terms of the gradient of the plot 𝑚 and the 𝑦-intercept 𝑐?

  • Ae
  • Bln(𝑚)
  • Cln(𝑐)
  • De
  • Ee

Q5:

Hydrolysis of the sugar sucrose (CHO122211) produces glucose and fructose. This first-order reaction has a rate constant of 2.10×10s at 27C and 8.50×10s at 37C.

Calculate the activation energy for this reaction, to three significant figures.

Calculate the rate constant for this reaction at 47C, to two significant figures.

  • A3.2×10 s−1
  • B1.1×10 s−1
  • C4.6×10 s−1
  • D6.3×10 s−1
  • E2.5×10 s−1

Estimate, to two significant figures, the time needed for the concentration of a 0.150 M sucrose solution to decrease to 1.65×10 M at 20C.

  • A1.9×10 days
  • B2.1×10 days
  • C7.6×10 days
  • D5.0×10 days
  • E9.2×10 days

Q6:

A sample of dinitrogen pentoxide (NO)25 decomposes with a rate constant of 1.66 L/mol⋅s at 650 K and 7.39 L/mol⋅s at 700 K. Calculate, to 3 significant figures, the activation energy for this reaction.

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