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Chapter 13: Problem 88

The rate law for the reaction \(2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) is rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\). Which of the following changes will change the value of \(k ?\) (a) The pressure of \(\mathrm{NO}_{2}\) is doubled. (b) The reaction is run in an organic solvent. (c) The volume of the container is doubled. (d) The temperature is decreased. (e) A catalyst is added to the container.

Short Answer

Expert verified
The changes that will affect the value of \(k\) are (d) decreasing the temperature and (e) adding a catalyst to the container.

Step by step solution

01

Analyze Possible Changes on 'k'

Examine each choice individually to see if it will affect the value of \(k\). Note: \(k\) is a constant and only affected by changes in temperature or the introduction of a catalyst.
02

Examine Change (a)

Doubling the pressure of NO2. Pressure is related to concentration but does not affect \(k\). So, this change will not affect the value of \(k\).
03

Examine Change (b)

Running the reaction in an organic solvent. The solvent is related to the medium in which the reaction takes place. Changing it might affect the rate of the reaction but not the rate constant \(k\). Therefore, this change will not affect the value of \(k\).
04

Examine Change (c)

Doubling the volume of the container. The volume of the container might affect the concentration of the reactants which in turn affects the rate of reaction but not the rate constant \(k\). So, this change will not affect the value of \(k\).
05

Examine Change (d)

Decreasing the temperature. The rate constant \(k\) depends on the temperature. By decreasing the temperature, the value of \(k\) will decrease as well. Therefore, this change will affect the value of \(k\).
06

Examine Change (e)

Adding a catalyst to the container. The catalyst affects the activation energy of the reaction and hence, the rate constant \(k\). Therefore, this change will affect the value of \(k\).

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Most popular questions from this chapter

A factory that specializes in the refinement of transition metals such as titanium was on fire. The firefighters were advised not to douse the fire with water. Why?

What are the characteristics of a catalyst?

Consider the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the rate of \(0.074 M / \mathrm{s}\). (a) At what rate is ammonia being formed? (b) At what rate is molecular nitrogen reacting?

Consider the following mechanism for the enzymecatalyzed reaction: $$ \begin{array}{r} \mathrm{E}+\mathrm{S} \underset{k-1}{\stackrel{k_{1}}{\sum_{-1}}} \mathrm{ES} \\\ \mathrm{ES} \stackrel{k_{2}}{\longrightarrow} \mathrm{E}+\mathrm{P} \end{array} $$ Derive an expression for the rate law of the reaction in terms of the concentrations of \(\mathrm{E}\) and \(\mathrm{S}\). (Hint: To solve for [ES], make use of the fact that, at equilibrium, the rate of forward reaction is equal to the rate of the reverse reaction.

Determine the molecularity and write the rate law for each of the following elementary steps: (a) \(\mathrm{X} \longrightarrow\) products (b) \(\mathrm{X}+\mathrm{Y} \longrightarrow\) products (c) \(\mathrm{X}+\mathrm{Y}+\mathrm{Z} \longrightarrow\) products (d) \(\mathrm{X}+\mathrm{X} \longrightarrow\) products (e) \(\mathrm{X}+2 \mathrm{Y} \longrightarrow\) products
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