Ch.15 - Chemical Kinetics

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.15 - Chemical Kinetics

Problem 105b

Chapter 15, Problem 105b

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.

Verified step by step guidance

Identify that the problem involves determining the rate constant at a different temperature using the Arrhenius equation.

The Arrhenius equation is given by: k = A * e^(-Ea/(RT)), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant (8.314 J/mol*K), and T is the temperature in Kelvin.

To find the rate constant at 15 °C, first convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature.

Use the given rate constants at different temperatures to plot ln(k) versus 1/T (in Kelvin) and determine the slope, which is equal to -Ea/R.

Once the activation energy (Ea) is determined, use the Arrhenius equation to calculate the rate constant at 15 °C by substituting the values of Ea, R, and the temperature in Kelvin into the equation.

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Key Concepts

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

Reaction Order

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. In this case, the reaction is first order in each reactant, meaning the rate is directly proportional to the concentration of each reactant. Understanding reaction order is crucial for determining how changes in concentration affect the reaction rate.

Arrhenius Equation

The Arrhenius equation describes how the rate constant (k) of a reaction changes with temperature. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This relationship allows us to estimate the rate constant at different temperatures, which is essential for solving the given problem.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It varies with temperature and is specific to each reaction. In this question, determining the rate constant at 15 °C requires understanding how k changes with temperature, which can be inferred from the provided data.

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Equilibrium Constant K

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

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 E_a = 315 kJ/mol

Cl + H₂ → HCl + H E_a = 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

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?

Consider the two reactions:

O + N₂ → NO + N E_a = 315 kJ/mol

Cl + H₂ → HCl + H E_a = 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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