Chapter DY, Problem 9PQ

Interpretation Introduction

Interpretation:

Based on the given data, the order for the given reaction has to be found.  The tabulated data given is:

  ${\text{CH}}_{\text{3}}{\text{Cl}}_{\text{(g)}}{\text{+H}}_{\text{2}}{\text{O}}_{\text{(g)}}\stackrel{}{\to }{\text{CH}}_{\text{3}}{\text{OH}}_{\text{(g)}}{\text{+HCl}}_{\text{(g)}}$

    $\begin{array}{l}\text{Initial Concentrations, M;InitialRates,M}{\text{.s}}^{\text{-1}}\\ \text{-------------------------------------------------------}\\ {\text{Exp CH}}_{\text{3}}{\text{Cl H}}_{\text{2}}\text{O Rate}\\ \text{1 0}\text{.100 0}\text{.100 0}\text{.182}\\ \text{2 0}\text{.200 0}\text{.200 1}\text{.45}\\ \text{3 0}\text{.200 0}\text{.400 5}\text{.81}\end{array}$

Concept Introduction:

Rate of a reaction:

Speed at which the chemical reaction happens is known as rate of a reaction.  Slower the speed of the reaction, lower will be the rate.  Concentration, temperature, pressure, catalyst are the factors affecting rate of a reaction.

Rate law – it is a relationship between reaction rates and reactant concentrations

Order of a reaction:

Order of a reaction is the power of the rate on the concentration of each reactant.  Order of a reaction is an experimentally determined one.

Explanation of Solution

Reason for correct option:

The given reaction is:

    ${\text{CH}}_{\text{3}}{\text{Cl}}_{\text{(g)}}{\text{+H}}_{\text{2}}{\text{O}}_{\text{(g)}}\stackrel{}{\to }{\text{CH}}_{\text{3}}{\text{OH}}_{\text{(g)}}{\text{+HCl}}_{\text{(g)}}$.

Rate of the reaction is:

    ${\text{r=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}$.

From the table,

    $\begin{array}{l}{\text{r}}_1{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}=\text{k[0}{\text{.100]}}^{\text{x}}{\text{[0}\text{.100]}}^{\text{y}}=0.182------(1)\\ {\text{r}}_2{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}=\text{k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.200]}}^{\text{y}}=1.45-------(2)\\ {\text{r}}_3{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}=\text{k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.400]}}^{\text{y}}=5.81-------(3)\end{array}$.

Divide the equation (3) by equation (2),

    $\begin{array}{l}{\text{r}}_{\text{2}}{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}\text{=k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.200]}}^{\text{y}}\text{=1}\text{.45-------(2)}\\ {\text{r}}_{\text{3}}{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}\text{=k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.400]}}^{\text{y}}\text{=5}\text{.81-------(3)}\\ {\text{r}}_{\text{3}}{\text{/r}}_{\text{2}}\text{=k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.400]}}^{\text{y}}\text{/k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.200]}}^{\text{y}}\text{=5}\text{.81/1}\text{.45=4}{\text{.00=2}}^{\text{2}}\\ \text{y=2}\end{array}$.

Order is 2 with respect to ${\text{H}}_{\text{2}}\text{O}$.

Divide the equation (2) by equation (1),

    $\begin{array}{l}{\text{r}}_{\text{2}}{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}\text{=k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.200]}}^{\text{y}}\text{=1}\text{.45-------(2)}\\ {\text{r}}_{\text{1}}{\text{=k[CH}}_{\text{3}}{\text{Cl]}}^{\text{x}}{{\text{[H}}_{\text{2}}\text{O]}}^{\text{y}}\text{=k[0}{\text{.100]}}^{\text{x}}{\text{[0}\text{.100]}}^{\text{y}}\text{=0}\text{.182-------(1)}\\ {\text{r}}_{\text{2}}{\text{/r}}_{\text{1}}\text{=k[0}{\text{.200]}}^{\text{x}}{\text{[0}\text{.200]}}^{\text{y}}\text{/k[0}{\text{.100]}}^{\text{x}}{\text{[0}\text{.100]}}^{\text{y}}\text{=1}\text{.45/0}\text{.182=8}\text{.00}\\ {\text{r}}_{\text{2}}{\text{/r}}_{\text{1}}{\text{=[2]}}^{\text{x}}{\text{[2]}}^{\text{y}}\text{=8}\\ {\text{r}}_{\text{2}}{\text{/r}}_{\text{1}}{\text{=[2]}}^{\text{x}}{\text{[2]}}^{\text{2}}\text{=8}\\ {\text{r}}_{\text{2}}{\text{/r}}_{\text{1}}{\text{=[2]}}^{\text{x}}\text{=2}\\ \text{x=1}\end{array}$.

Therefore the order of the reaction is 1 with respect to ${\text{CH}}_{\text{3}}\text{Cl}$.

Hence the option (B) is correct.

Reason for incorrect option:

From the above expression, it is clear that the order of the reaction is 1 with respect to ${\text{CH}}_{\text{3}}\text{Cl}$ and 2 with respect to ${\text{H}}_{\text{2}}\text{O}$.

Hence the options (A), (C) and (D) are incorrect.