Chapter 13, Problem 2SAQ

Interpretation Introduction

Interpretation:

The initial rate of the reaction is given. The option corresponding to the correct rate of change of the concentration of ${\text{N}}_{\text{2}}\text{O}\left(\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]/\Delta t\right)$ is to be identified.

Concept introduction: The rate of a reaction is defined as the change in concentration of the reactants or the products per unit time.

To determine: The option corresponding to the correct rate of change of the concentration of ${\text{N}}_{\text{2}}\text{O}\left(\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]/\Delta t\right)$ .

Correct answer: The correct option is (c).

Reason for correct answer: The initial rate of the reaction is $0.022\text{M/s}$ .

The reaction for the decomposition of Dinitrogen monoxide is,

  ${\text{2N}}_{\text{2}}\text{O}\left(g\right)\stackrel{}{\to }{\text{2N}}_{\text{2}}\left(g\right)+{\text{O}}_{\text{2}}\left(g\right)$

The rate of change in the concentration of ${\text{N}}_{\text{2}}\text{O}\left(\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]/\Delta t\right)$ is given by the expression,
  $\text{Rate}=-\frac{1}{2}\frac{\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]}{\Delta t}$

Substitute the value of initial rate of a reaction in the above expression to calculate the rate of change in the concentration of ${\text{N}}_{\text{2}}\text{O}\left(\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]/\Delta t\right)$ .

  $\begin{array}{c}0.022\text{M/s}=-\frac{1}{2}\frac{\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]}{\Delta t}\\ 0.022\text{M/s}\times \text{2}=-\frac{\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]}{\Delta t}\\ 0.044\text{M/s}=-\frac{\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]}{\Delta t}\\ \frac{\Delta \left[{\text{N}}_{\text{2}}\text{O}\right]}{\Delta t}=-0.044\text{M/s}\end{array}$