Chapter 18, Problem 103A

Interpretation Introduction

Interpretation : The order of the reaction with respect to ammonium ion and nitrite ion and the overall order of the reaction is to be analyzed.

Concept Introduction : The rate is a method for determining how much something changes over a predetermined period of time. The amount of reactant or product that changes per unit of time is the reaction rate.

Answer to Problem 103A

The order of the reaction with respect to ${\text{NO}}_{\text{2}}^{-}$ is one.

The order of the reaction with respect to ${\text{NH}}_{\text{4}}^{\text{+}}$ is one.

The overall order of the reaction is two.

Explanation of Solution

The power dependence of rate on the concentration of all reactants can be used to define the order of reaction.

The link between a chemical reaction's rate and the concentration of the species involved is referred to as the order of reaction.

To find the order of ${\text{NO}}_{\text{2}}^{-}$ , take the experiments 1 and 2 where the concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ remains the same.

In the first two cases, the concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ remains the same.

As the concentration of ${\text{NO}}_{\text{2}}^{-}$ increases, the rate of the reaction also increases.

The ratio of concentration of ${\text{NO}}_{\text{2}}^{-}$ is given as

  $\begin{array}{c}\frac{{\left[{\text{NO}}_2^{-}\right]}_2}{{\left[{\text{NO}}_2^{-}\right]}_1}=\frac{0.02}{0.01}\\ =2\end{array}$

The ratio of rate constant with respect to concentration of ${\text{NO}}_{\text{2}}^{-}$ is given as

  $\begin{array}{c}\frac{{\text{rate}}_{\text{2}}}{{\text{rate}}_{\text{1}}}\text{=}\frac{\text{10}{\text{.8×10}}^{-\text{7}}}{\text{5}{\text{.4×10}}^{-\text{7}}}\\ \text{= 2}\end{array}$

The concentration of ${\text{NO}}_{\text{2}}^{-}$ is directly proportional to the rate since the ratios are same.

The order of ${\text{NO}}_{\text{2}}^{-}$ is one.

To find the order of ${\text{NH}}_{\text{4}}^{\text{+}}$ , take the experiments 5 and 6 where the concentration of ${\text{NO}}_{\text{2}}^{-}$ remains the same.

In the experiments 5 and 6, the concentration of ${\text{NO}}_{\text{2}}^{-}$ remains the same.

As the concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ increases, the rate of the reaction also increases.

The ratio of concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ is given as

  $\begin{array}{c}\frac{{\left[{\text{NH}}_{\text{4}}^{\text{+}}\right]}_2}{{\left[{\text{NH}}_{\text{4}}^{\text{+}}\right]}_1}=\frac{0.0404}{0.0202}\\ =2\end{array}$

The ratio of rate constant with respect to concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ is given as

  $\begin{array}{c}\frac{{\text{rate}}_{\text{2}}}{{\text{rate}}_{\text{1}}}\text{=}\frac{\text{21}{\text{.6×10}}^{-\text{7}}}{\text{10}{\text{.8×10}}^{-\text{7}}}\\ \text{= 2}\end{array}$

The concentration of ${\text{NH}}_{\text{4}}^{\text{+}}$ is directly proportional to the rate since the ratios are same.

The order of ${\text{NH}}_{\text{4}}^{\text{+}}$ is one.

The overall order of the reaction is sum of the individual order of the reactants involved.

The rate law for the reaction is given as

  $rate=k\left[{\text{NO}}_2^{-}\right]\left[{\text{NH}}_4^{+}\right]$

The overall order is 2.