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Ch.15 - Chemical Kinetics
All textbooksTro 5th EditionCh.15 - Chemical KineticsProblem 100
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Chapter 15, Problem 100

The reaction 2 N2O5 → 2 N2O4 + O2 takes place at around room temperature in solvents such as CCl4. The rate constant at 293 K is found to be 2.35⨉10-4 s-1, and at 303 K the rate constant is found to be 9.15⨉10-4 s-1. Calculate the frequency factor for the reaction.

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1
Identify that the problem involves calculating the frequency factor (A) using the Arrhenius equation: k = A * e^(-Ea/(RT)), where k is the rate constant, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Use the Arrhenius equation in its logarithmic form: ln(k2/k1) = -(Ea/R) * (1/T2 - 1/T1), where k1 and k2 are the rate constants at temperatures T1 and T2, respectively.
Substitute the given values into the logarithmic form of the Arrhenius equation: ln(9.15⨉10^-4 / 2.35⨉10^-4) = -(Ea/R) * (1/303 - 1/293).
Solve for the activation energy (Ea) using the rearranged equation: Ea = -R * ln(k2/k1) / (1/T2 - 1/T1).
Once Ea is determined, use the Arrhenius equation k = A * e^(-Ea/(RT)) to solve for the frequency factor (A) by rearranging it to A = k / e^(-Ea/(RT)) and substituting the known values.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. Understanding this equation is crucial for calculating the frequency factor, as it provides the relationship between temperature and reaction rates.
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Rate Constant

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, indicating the speed of the reaction at a given temperature. It varies with temperature and is influenced by factors such as the nature of the reactants and the presence of catalysts. In this question, the rate constants at two different temperatures are provided, which are essential for determining the frequency factor using the Arrhenius equation.
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Temperature Dependence of Reaction Rates

The temperature dependence of reaction rates is a fundamental concept in chemical kinetics, indicating that reaction rates generally increase with temperature. This is due to the increased kinetic energy of molecules, leading to more frequent and effective collisions. In the context of the question, the provided rate constants at different temperatures allow for the analysis of how temperature affects the reaction rate, which is key to calculating the frequency factor.
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Related Practice
Textbook Question

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. b. If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb (leave the surface)? For 50% to desorb?

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Textbook Question

The evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92⨉1013 molecules/cm2•s at 120 K. a. If the initial surface coverage is 8.9⨉1016 molecules/cm2, how long will it take for one-half of the film to evaporate?

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Textbook Question

The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)

C2H5Br(aq) + OH- (aq) → C2H5OH(l) + Br- (aq)

Temperature (°C) k (L,mol •s)

25 8.81⨉10-5

35 0.000285

45 0.000854

55 0.00239

65 0.00633

b. Determine the rate constant at 15 °C.

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Textbook Question

This reaction has an activation energy of zero in the gas phase: CH3 + CH3 → C2H6 a. Would you expect the rate of this reaction to change very much with temperature?

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Textbook Question

Consider the two reactions:

O + N2 → NO + N Ea = 315 kJ/mol

Cl + H2 → HCl + H Ea = 23 kJ/mol

a. Why is the activation barrier for the first reaction so much higher than that for the second?

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Textbook Question

Consider the two reactions:

O + N2 → NO + N Ea = 315 kJ/mol

Cl + H2 → HCl + H Ea = 23 kJ/mol

b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.

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