Chapter 20, Problem 1E

In the reaction $2\text{A+B}\text{C+3D}$ , reactant A is found to disappear at the rate of $6.2\times {10}^{-4}\text{M}{\text{s}}^{-4}$ . (a) What is the rate of reaction at this point? (b) What is the rate of rate of disappearance of B? (c) What is the rate of formation of D?

Interpretation Introduction

(a)

Interpretation:

Rate of the reaction at the given point of time is to be calculated.

Concept introduction:

The rate of the reaction is a speed of the reaction at which it proceeds. At any given time it depends upon the concentration of the reactants at that time.

For the general reaction,

$a\text{A}+b\text{B}\to c\text{C}+d\text{D}$

The ratio of change in reactant concentration or product concentration to change in time is known as rate of reaction.

$r=-\frac{1}{a}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{1}{b}\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{1}{c}\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{d}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(1)

Answer to Problem 1E

Rate of the reaction at the given point of time is $3.1\times {10}^{-4}{\text{ Ms}}^{-1}$.

Explanation of Solution

The given reaction is,

$2\text{A}+\text{B}\to \text{C}+3\text{D}$

Substitute 2 for value of $a$, 1 for value of $b$, 1 for value of $c$, and 3 for value of $d$ in equation (1) to calculate the expression of rate of reaction.

$r=-\frac{1}{2}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{3}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(2)

Rate of disappearance of $\text{A}$ is $6.2\times {10}^{-4}{\text{ Ms}}^{-1}$.

Substitute $6.2\times {10}^{-4}{\text{ Ms}}^{-1}$ for rate of disappearance of $\text{A}$ in equation (2) for the calculation of rate of reaction.

$\begin{array}{c}r=\frac{1}{2}\left(6.2\times {10}^{-4}{\text{ Ms}}^{-1}\right)\\ =3.1\times {10}^{-4}{\text{ Ms}}^{-1}\end{array}$

Interpretation Introduction

(b)

Interpretation:

Rate of disappearance of $\text{B}$ is to be determined.

Concept introduction:

The rate of the reaction is a speed of the reaction at which it proceeds. At any given time it depends upon the concentration of the reactants at that time.

For the general reaction,

$a\text{A}+b\text{B}\to c\text{C}+d\text{D}$

The ratio of change in reactant concentration or product concentration to change in time is known as rate of reaction.

$r=-\frac{1}{a}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{1}{b}\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{1}{c}\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{d}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(1)

Answer to Problem 1E

Rate of disappearance of $\text{B}$ is $3.1\times {10}^{-4}{\text{ Ms}}^{-1}$.

Explanation of Solution

The given reaction is,

$2\text{A}+\text{B}\to \text{C}+3\text{D}$

Substitute 2 for value of $a$, 1 for value of $b$, 1 for value of $c$, and 3 for value of $d$ in equation (1) to calculate the expression of rate of reaction.

$r=-\frac{1}{2}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{3}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(2)

Therefore, the rate ofdisappearance of $\text{B}$ is equal to the rate of reaction and the rate of reaction is equal to $3.1\times {10}^{-4}{\text{ Ms}}^{-1}$.

Substitute the value of rate of reaction in the equation (2) to calculate the value of rate ofdisappearance of $\text{B}$.

$\begin{array}{c}\text{Rate of disappearance of B,}\left(-\frac{\Delta \left[\text{B}\right]}{\Delta t}\right)=r\\ =3.1\times {10}^{-4}{\text{ Ms}}^{-1}\end{array}$

Interpretation Introduction

(c)

Interpretation:

Rate of appearance of $\text{D}$ is to be determined.

Concept introduction:

The rate of the reaction is a speed of the reaction at which it proceeds. At any given time it depends upon the concentration of the reactants at that time.

For the general reaction,

$a\text{A}+b\text{B}\to c\text{C}+d\text{D}$

The ratio of change in reactant concentration or product concentration to change in time is known as rate of reaction.

$r=-\frac{1}{a}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{1}{b}\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{1}{c}\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{d}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(1)

Answer to Problem 1E

Rate of appearance of $\text{D}$ is $9.3\times {10}^{-4}{\text{ Ms}}^{-1}$.

Explanation of Solution

The given reaction is,

$2\text{A}+\text{B}\to \text{C}+3\text{D}$

Substitute 2 for value of $a$, 1 for value of $b$, 1 for value of $c$, and 3 for value of $d$ in equation (1) to calculate the expression of rate of reaction.

$r=-\frac{1}{2}\frac{\Delta \left[\text{A}\right]}{\Delta t}=-\frac{\Delta \left[\text{B}\right]}{\Delta t}=\frac{\Delta \left[\text{C}\right]}{\Delta t}=\frac{1}{3}\frac{\Delta \left[\text{D}\right]}{\Delta t}$   ......(2)

Therefore, rearrange equation (2) to calculate the rate of appearance of $\text{D}$ as follows:

$\frac{\Delta \left[\text{D}\right]}{\Delta t}=3\left(r\right)$

Substitute the value of rate of reaction $\left(r\right)$ in the above equation to calculate the value of rate ofappearance of $\text{D}$.

$\begin{array}{c}\frac{\Delta \left[\text{D}\right]}{\Delta t}=3\left(3.1\times {10}^{-4}{\text{ Ms}}^{-1}\right)\\ =9.3\times {10}^{-4}{\text{ Ms}}^{-1}\end{array}$