Chapter 17, Problem 17.1P

Interpretation Introduction

Interpretation:

The expression of rate of reaction in terms of rate of concentration change for each of three species involved has to be expressed.

Concept Introduction:

Rate of reaction:  It is defined as change in concentration of species with respect to change in time.  An expression for rate of a general reaction is given by

    $\begin{array}{l}\text{aA + bB }\stackrel{}{\to }\text{cC + dD}\\ \\ \text{Rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{1}}{\text{a}}\left(\frac{\text{Δ[A]}}{\text{Δt}}\right)\text{=}\text{-}\frac{\text{1}}{\text{b}}\left(\frac{\text{Δ[B]}}{\text{Δt}}\right)\text{=}\frac{\text{1}}{\text{c}}\left(\frac{\text{Δ[C]}}{\text{Δt}}\right)\text{=}\frac{\text{1}}{\text{d}}\left(\frac{\text{Δ[D]}}{\text{Δt}}\right)\end{array}$

Explanation of Solution

Given,

    ${\text{2 NOCl}}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{ 2 NO}}_{\left(\text{g}\right)}{\text{ + Cl}}_{\text{2}\left(\text{g}\right)}$

The rate of loss of nitrosyl chloride is twice as great as the rate of production of ${\text{Cl}}_2$ because two $\text{NOCl}$ molecules are consumed for each ${\text{Cl}}_2$ molecule produced.

    $\text{Rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{1}}{2}\frac{\text{Δ[NOCl]}}{\text{Δt}}\text{=}\frac{{\text{Δ[Cl}}_{\text{2}}\text{]}}{\text{Δt}}$

The rate of loss of nitrosyl chloride is same as the rate of production of $\text{NO}$ because two $\text{NOCl}$ molecules are consumed for two $\text{NO}$ molecule produced.

    $\begin{array}{l}\text{Rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{1}}{\text{2}}\frac{\text{Δ[NOCl]}}{\text{Δt}}\text{=}\frac{\text{1}}{\text{2}}\frac{\text{Δ[NO]}}{\text{Δt}}\\ \\ \text{Rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{1}}{\text{2}}\frac{\text{Δ[NOCl]}}{\text{Δt}}\text{=}\frac{\text{1}}{\text{2}}\frac{\text{Δ[NO]}}{\text{Δt}}\text{=}\frac{{\text{Δ[Cl}}_{\text{2}}\text{]}}{\text{Δt}}\end{array}$