Chapter 13, Problem 13.27QP

Kinetics I

Consider the hypothetical reaction A(g) + 2B(g) h C(g). The four containers below represent this reaction being run with different initial amounts of A and B. Assume that the volume of each container is 1.0 L. The reaction is second order with respect to A and first order with respect to B.

1. a Based on the information presented in the problem, write the rate law for the reaction.
2. b Which of the containers, W, X, Y, or Z, would have the greatest reaction rate? Justify your answer.
3. c Which of the containers would have the lowest reaction rate? Explain.
4. d If the volume of the container X were increased to 2.0 L, how would the rate of the reaction in this larger container compare to the rate of reaction run in the 1.0-L container X? (Assume that the number of A and B atoms is the same in each case.)
5. e If the temperature in container W were increased, what impact would this probably have on the rate of reaction? Why?
6. f If you want to double the rate of reaction in container X, what are some things that you could do to the concentration(s) of A and B?
7. g In which container would you observe the slowest rate of formation of C?
8. h Assuming that A and B are not in great excess, which would have the greater impact on the rate of reaction in container W: removing a unit of B or removing a unit of A? Explain.
9. i Describe how the rate of consumption of A compares to the rate of consumption of B. If you cannot answer this question, what additional information do you need to provide an answer?
10. j If the product C were removed from the container as it formed, what effect would this have on the rate of the reaction?

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To give rate of the reaction

Rate of the reaction is given as $\text{Rate=k}{\left[\text{A}\right]}^{\text{2}}\left[\text{B}\right]$

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To identify and justify the container that has greatest rate of reaction

The container with the highest rate of reaction will have highest value of ${\left[\text{A}\right]}^{\text{2}}\left[\text{B}\right]$.

For container W, the product will be ${\text{(2)}}^{\text{2}}\text{(3)=12}$

For container X, the product will be ${\text{(2)}}^{\text{2}}\text{(4)=16}$

For container Y, the product will be ${\text{(3)}}^{\text{2}}\text{(2)=18}$

For container Z, the product will be ${\text{(5)}}^{\text{2}}\text{(0)=0}$

Hence, the container Y will have the highest rate of reaction.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To identify and justify the container that has lowest rate of reaction

Since the container Z has one of the concentrations of reactant as zero, container Z will have the lowest rate of reaction.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To compare the rate of reaction in the larger container to the rate of reaction in $\text{1}\text{.0}\text{L}$ container X

The concentrations of A and B are decreased by factor 2, when the volume of the container is two times from $\text{1}\text{.0}\text{L}\text{to}\text{2}\text{.0}\text{L}$ .  This represents a reduction in the rate of ${\left(\frac{\text{1}}{\text{2}}\right)}^{\text{2}}\left(\frac{\text{1}}{\text{2}}\right)\text{=}\frac{\text{1}}{\text{8}}$

Therefore, the rate of reaction in larger container is $\frac{\text{1}}{\text{8}}$ times the rate in smaller container.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To give the impact on the rate of reaction if temperature is increased in container W

Increase in temperature, increases the rate of temperature,

At higher temperature molecules collide with other molecules at greater rate and possess greater kinetic energy.

Thus, part of collision with energy in addition of activation energy is greater with increase in rate of reaction.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To explain about the concentrations of $\text{A}\text{and}\text{B}$ if the rate in container X is doubled

The rate of the reactions doubles with rate of products ${\left[\text{A}\right]}^{\text{2}}\left[\text{B}\right]$. This is achieved on doubling the concentration of $\left[\text{B}\right]$ with no change in the concentration of $\left[\text{A}\right]$.  Another possibility is doubling the concentration of $\left[\text{A}\right]$ with reducing concentration of $\left[\text{B}\right]$ by one-half.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To identify the container that shows slowest rate for the formation of C

Container Z shows the slowest rate for the formation of C because its reaction rate is zero.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To identify and explain if removing A or B would have higher impact on rate of reaction of container W

Reaction in A is second order.

Reaction in B is first order.

Changes in concentration of A would have higher impact on rate of reaction; hence removing A would have higher impact on rate of reaction of container W

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To compare the rate of consumptions of A and B

The rate of reactions is,

$\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=-}\frac{\text{1}}{\text{2}}\frac{\text{Δ}\left[\text{B}\right]}{\text{Δt}}$

The rate of consumption of A is half the rate of consumption of B.

Interpretation Introduction

Interpretation:

The explanations for the given set of statements have to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time. The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

To give the rate of reaction if product is taken away from the container

Removing C from the container shoes no effect on the reaction rate because $\left[\text{C}\right]$ doesn’t appear in the rate law.