Chapter 13, Problem 13.17QP

Determine the overall orders of the reactions to which the following rate laws apply: (a) rate = k[NO₂]², (b) rate = k, (c) rate = k[H₂], (d) rate = k[NO]² [O₂].

Interpretation Introduction

Interpretation:

The overall order for the reaction to which the following rate law applies has to be determined.

$rate=k{\left[N{O}_2\right]}^2$

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Rate law: It is an equation that related to the rate of reaction to the concentrations or pressures of substrates (reactants).  It is also said to be as rate equation.

Answer to Problem 13.17QP

${\text{rate = k[NO}}_{\text{2}}{\text{]}}^{\text{2}}$ The order of reaction is $2$

Explanation of Solution

Given,

${\text{rate = k[NO}}_{\text{2}}{\text{]}}^{\text{2}}$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are raised.

$\text{Order}\text{= }\text{x+y}$

Therefore the order for the reaction with the above rate equation is $2$

Interpretation Introduction

Interpretation:

The overall order for the reaction to which the following rate law applies has to be determined.

$rate=k$

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Rate law: It is an equation that related to the rate of reaction to the concentrations or pressures of substrates (reactants).  It is also said to be as rate equation.

Answer to Problem 13.17QP

$rate=k$ , The order of reaction is $0$

Explanation of Solution

Given,

$rate=k$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are raised.

Therefore the order for the reaction with the above rate equation is $0$

Interpretation Introduction

Interpretation:

The overall order for the reaction to which the following rate law applies has to be determined.

${\text{rate = k[H}}_2\text{]}$

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Rate law: It is an equation that related to the rate of reaction to the concentrations or pressures of substrates (reactants).  It is also said to be as rate equation.

Answer to Problem 13.17QP

${\text{rate = k[H}}_2\text{]}$  The order of reaction is $1$

Explanation of Solution

Given,

${\text{rate = k[H}}_2\text{]}$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Therefore the order for the reaction with the above rate equation is $1$

Interpretation Introduction

Interpretation:

The overall order for the reaction to which the following rate law applies has to be determined.

${\text{rate = k[NO]}}^{\text{2}}\left[{\text{O}}_{\text{2}}\right]$

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Rate law: It is an equation that related to the rate of reaction to the concentrations or pressures of substrates (reactants).  It is also said to be as rate equation.

Answer to Problem 13.17QP

The given reaction follows is third order kinetics.

Explanation of Solution

Given,

${\text{rate = k[NO]}}^{\text{2}}\left[{\text{O}}_{\text{2}}\right]$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Here,

$\begin{array}{c}Order=2+1\\ =3\end{array}$

Therefore the given reaction follows is third order kinetics.