Chapter 12, Problem 12.24CP

The following reaction is first order in A (red spheres) and first order in B (blue spheres):

$\text{A}+\text{B}\stackrel{}{\to }\text{Products}\text{Rate}=k[\text{A}][\text{B}]$

1. (a) What are the relative rates of this reaction in vessels (1)–(4)? Each vessel has the same volume.
2. (b) What are the relative values of the rate constant k for cases (1)–(4)?

Interpretation Introduction

Interpretation:

The relative rates of the reaction in the given vessels has to be given.

Concept introduction:

Rate of reaction:

The rate of a reaction is defined by the change in concentration of substrate (reactant) or target (product) with change in time.

$\text{Rate}\text{=}\frac{\text{Concentration}\text{change}\left(\text{in}\text{reactant}\text{or}\text{product}\right)}{\text{Time}\text{change}}$

Answer to Problem 12.24CP

The relative rates of the reaction in the given vessels (1) – (4) are $2:\text{}1:4:\text{}2$.

Explanation of Solution

Given reaction and information,

$\begin{array}{l}\text{A}\text{+}\text{B}\stackrel{}{\to }\text{Products}\\ \\ \text{A}\text{-}\text{red}\text{spheres}\text{;}\text{B-}\text{blue}\text{spheres}\end{array}$

Figure 1

Given as $\text{Rate}\text{=}\text{k}\left[\text{A}\right]\left[\text{B}\right]$

Hence, the rate of reaction is proportional to the product of the number of $\text{A}$ molecules and the number of $\text{B}$ molecules.

In the vessel (1), the product of $\text{A}\text{and}\text{B}$ is 18.

In the vessel (2), the product of $\text{A}\text{and}\text{B}$ is 9.

In the vessel (3), the product of $\text{A}\text{and}\text{B}$ is 36.

In the vessel (4), the product of $\text{A}\text{and}\text{B}$ is 18.

Therefore, the relative rates of the reaction in the given vessels (1) – (4) are $2:\text{}1:4:\text{}2$.

Interpretation Introduction

Interpretation:

The relative values of rate constants of the given reaction has to be given.

Concept introduction:

Rate law:

It is an equation that related to the dependence of the reaction rate on the concentration of each substrates (reactants).

$\begin{array}{l}\text{For}\text{a}\text{reaction}\\ \\ \text{aA}\text{+}\text{bB}\stackrel{}{\to }\text{Products}\\ \\ \text{A}\text{and}\text{B}\text{are}\text{reactants}\text{and}\text{a}\text{and}\text{b}\text{are}\text{stoichiometric}\text{coefficients}\text{.}\\ \\ \text{Rate}\text{=}\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=}\text{k}{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}\\ \\ \text{where,}\text{k}\text{-}\text{rate}\text{constant}\text{.}\end{array}$

Answer to Problem 12.24CP

• The relative values of rate constant for all the given reactions are same.

Explanation of Solution

Given reaction and information,

$\begin{array}{l}\text{A}\text{+}\text{B}\stackrel{}{\to }\text{Products}\\ \\ \text{A}\text{-}\text{red}\text{spheres}\text{;}\text{B-}\text{blue}\text{spheres}\end{array}$

Figure 1

Given as $\text{Rate}\text{=}\text{k}\left[\text{A}\right]\left[\text{B}\right]$

Hence, the rate of reaction is proportional to the product of the number of $\text{A}$ molecules and the number of $\text{B}$ molecules.

The relative of the reaction in vessels (1) – (4) are $2:\text{}1:4:\text{}2$.

The relative value of rate constant for all the given reactions are same.  Since, the same reaction takes place in each of the given vessels (1) – (4).