Chapter 13, Problem 13.141QP

A hypothetical reaction has the two-step mechanism

$\begin{array}{c}\text{AB}+\text{C}\stackrel{}{\to }\text{ABC}\\ \text{ABC}+\text{C}\stackrel{}{\to }\text{AC}+\text{BC}\end{array}$

The potential-energy curve for the reaction is

1. a Write the chemical formulas of the reactants, products, and the reaction intermediate on the potential energy curve.
2. b From the mechanism, what is the overall reaction?
3. c What is the rate-limiting step for the reaction?
4. d Propose a rate law based on the rate-limiting step.
5. e Is the reaction exothermic or endothermic?

Interpretation Introduction

Interpretation:

The explanations for the given set have to be answered.

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.

The overall chemical equation is represented by the net result of two elementary reactions in the mechanism. This is obtained by summing up the steps and canceling the species that occur in either side of the reactions.

A catalyst is substance that provides a pathway for the reaction to occur rapidly than in mechanism of an uncatalyzed reaction.

The catalyst gets consumed in the first step of the reaction and it can be regenerated in the later step of the reaction.

A species that is formed during a chemical reaction which does not appear in overall reacts due its presence in the following step in the mechanism is called Reaction intermediate.

To write the chemical formula of the reactants, products and the reaction intermediate

Explanation of Solution

In the potential energy diagram given below, the dotted lines represents the bonds that are formed or broken.

Figure 1

Interpretation Introduction

Interpretation:

The explanations for the given set have to be answered.

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.

The overall chemical equation is represented by the net result of two elementary reactions in the mechanism. This is obtained by summing up the steps and canceling the species that occur in either side of the reactions.

A catalyst is substance that provides a pathway for the reaction to occur rapidly than in mechanism of an uncatalyzed reaction.

The catalyst gets consumed in the first step of the reaction and it can be regenerated in the later step of the reaction.

A species that is formed during a chemical reaction which does not appear in overall reacts due its presence in the following step in the mechanism is called Reaction intermediate.

To write the overall reaction

Explanation of Solution

The overall reaction is given by addition of two steps of the mechanism and by eliminating intermediate ABC.

The overall reaction is given as,

$\text{AB+2C}\to \text{AC+BC}$

Interpretation Introduction

Interpretation:

The explanations for the given set have to be answered.

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.

The overall chemical equation is represented by the net result of two elementary reactions in the mechanism. This is obtained by summing up the steps and canceling the species that occur in either side of the reactions.

A catalyst is substance that provides a pathway for the reaction to occur rapidly than in mechanism of an uncatalyzed reaction.

The catalyst gets consumed in the first step of the reaction and it can be regenerated in the later step of the reaction.

A species that is formed during a chemical reaction which does not appear in overall reacts due its presence in the following step in the mechanism is called Reaction intermediate.

To identify the rate limiting step

Explanation of Solution

The second step of the reaction is the rate limiting step since it has the highest overall energy of activation.

Interpretation Introduction

Interpretation:

The explanations for the given set have to be answered.

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.

The overall chemical equation is represented by the net result of two elementary reactions in the mechanism. This is obtained by summing up the steps and canceling the species that occur in either side of the reactions.

A catalyst is substance that provides a pathway for the reaction to occur rapidly than in mechanism of an uncatalyzed reaction.

The catalyst gets consumed in the first step of the reaction and it can be regenerated in the later step of the reaction.

A species that is formed during a chemical reaction which does not appear in overall reacts due its presence in the following step in the mechanism is called Reaction intermediate.

To propose a rate law based on rate limiting step

Explanation of Solution

The rate is written on the slow step,

${\text{Rate=k}}_{\text{2}}\left[\text{ABC}\right]\left[\text{C}\right]$

The first step reaches the state of equilibrium rapidly and the rate of the forward reaction is equal to the rate of the reverse. This is given as,

${\text{Rate}}_{\text{f}}{\text{=k}}_{\text{f}}\left[\text{AB}\right]\left[\text{C}\right]{\text{=Rate}}_{\text{r}}{\text{=k}}_{\text{r}}\left[\text{ABC}\right]$

Rearranging this equation and solve for $\left[\text{ABC}\right]$

$\left[\text{ABC}\right]\text{=}\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}\left[\text{AB}\right]\left[\text{C}\right]$

Substitute the above in the rate law to eliminate $\left[\text{ABC}\right]$ and the rate law can be obtained as,

Rate= ${\text{k}}_{\text{2}}\left\{\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}\left[\text{AB}\right]\left[\text{C}\right]\right\}\left[\text{C}\right]\text{=k}\left[\text{AB}\right]{\left[\text{C}\right]}^{\text{2}}$

Interpretation Introduction

Interpretation:

The explanations for the given set have to be answered.

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.

The overall chemical equation is represented by the net result of two elementary reactions in the mechanism. This is obtained by summing up the steps and canceling the species that occur in either side of the reactions.

A catalyst is substance that provides a pathway for the reaction to occur rapidly than in mechanism of an uncatalyzed reaction.

The catalyst gets consumed in the first step of the reaction and it can be regenerated in the later step of the reaction.

A species that is formed during a chemical reaction which does not appear in overall reacts due its presence in the following step in the mechanism is called Reaction intermediate.

To identify the type of reaction

Explanation of Solution

The reaction is identified as exothermic reaction since the energy per mole of the products is higher than the energy per mole of reactants.