Chapter 17, Problem 17A.2P

(a)

Interpretation Introduction

Interpretation:

The order of reaction with respect to the complex and Y has to be found from the following data.

    $\begin{array}{l}{\text{[complex]/(mmoldm}}^{\text{-3}}\text{)}\text{8}\text{.01}\text{9}\text{.22}\text{12}\text{.11}\\ {\text{υ}}_{\text{0}}{\text{/(moldm}}^{\text{-3}}{\text{s}}^{\text{-1}}\text{)}\text{(i)}\text{125}\text{144}\text{190}\\ \text{(ii)}\text{640}\text{730}\text{960}\end{array}$

Concept Introduction:

Rate of a reaction:

Rate of a reaction is the change in concentration of reactant or product per unit time.  It is expressed in terms of decrease in concentration of any of the reactants and increase in concentration of any of the products.

Rate Law:

Rate law is experimentally determined and is used to predict the relationship between the rate of a reaction and concentration of the reactants.

For the general reaction:

    $\text{aA + bB }\stackrel{}{\to }\text{cC + dD}$

${\text{rate = k[A]}}^{\text{m}}{\text{[B]}}^{\text{n}}$

Explanation of Solution

For experiments (I):

  $\text{ν = k[complex]}$

  $\begin{array}{l}\frac{{\text{ν}}_{\text{2}}}{{\text{ν}}_{\text{1}}}\text{ = }\frac{{\text{k[complex}}^1\text{]}}{\text{k[complex]}}\\ \\ \frac{144}{125}\text{ = }\frac{\text{k(9}{\text{.22 × 10}}^{\text{-3}}{\text{)}}^{\text{x}}}{\text{k(8}{\text{.01×10}}^{\text{-3}}{\text{)}}^{\text{x}}}\text{, x is the order of the reaction}\\ \\ \text{1}\text{.15 = (1}{\text{.15)}}^{\text{x}}\\ \\ {1.15}^1\text{= (1}{\text{.15)}}^{\text{x}}\\ \\ \text{x = 1}\end{array}$

Experiment (I) is a first order with respect to complex.

For experiments (I):

  $\text{ν = k[Y]}$

  $\begin{array}{l}\frac{{\text{ν}}_{\text{2}}}{{\text{ν}}_{\text{1}}}\text{ = }\frac{{\text{k[Y}}^{\text{'}}\text{]}}{\text{k[Y]}}\\ \\ \frac{144}{125}\text{ = }\frac{\text{k(9}{\text{.22 × 10}}^{\text{-3}}{\text{)}}^{\text{x}}}{\text{k(8}{\text{.01×10}}^{\text{-3}}{\text{)}}^{\text{x}}}\text{, x is the order of the reaction}\\ \\ \text{1}\text{.15 = (1}{\text{.15)}}^{\text{x}}\\ \\ {1.15}^1\text{= (1}{\text{.15)}}^{\text{x}}\\ \\ \text{x = 1}\end{array}$

For experiments (II):

  $\text{ν = k[Y]}$

  $\begin{array}{l}\frac{{\text{ν}}_{\text{2}}}{{\text{ν}}_{\text{1}}}\text{ = }\frac{{\text{k[Y}}^{\text{'}}\text{]}}{\text{k[Y]}}\\ \\ \frac{730}{640}\text{ = }\frac{\text{k(9}{\text{.22 × 10}}^{\text{-3}}{\text{)}}^{\text{x}}}{\text{k(8}{\text{.01×10}}^{\text{-3}}{\text{)}}^{\text{x}}}\text{, x is the order of the reaction}\\ \\ \text{1}\text{.1 = (1}{\text{.1)}}^{\text{x}}\\ \\ {1.15}^1\text{= (1}{\text{.15)}}^{\text{x}}\\ \\ \text{x = 1}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The rate constant has to be found from the following data.

    $\begin{array}{l}{\text{[complex]/(mmoldm}}^{\text{-3}}\text{)}\text{8}\text{.01}\text{9}\text{.22}\text{12}\text{.11}\\ {\text{υ}}_{\text{0}}{\text{/(moldm}}^{\text{-3}}{\text{s}}^{\text{-1}}\text{)}\text{(i)}\text{125}\text{144}\text{190}\\ \text{(ii)}\text{640}\text{730}\text{960}\end{array}$

Concept Introduction:

Rate of a reaction:

Rate of a reaction is the change in concentration of reactant or product per unit time.  It is expressed in terms of decrease in concentration of any of the reactants and increase in concentration of any of the products.

Rate Law:

Rate law is experimentally determined and is used to predict the relationship between the rate of a reaction and concentration of the reactants.

For the general reaction:

    $\text{aA + bB }\stackrel{}{\to }\text{cC + dD}$

${\text{rate = k[A]}}^{\text{m}}{\text{[B]}}^{\text{n}}$

Explanation of Solution

For experiment (I)

According to rate law:

  $\text{ν = k[complex]}$

  Rate constant, k $\text{= }\frac{\text{ν}}{\text{complex}}\text{ = }\frac{{\text{125 mol dm}}^{\text{-3}}{\text{s}}^{\text{-1}}}{\text{(8}{\text{.01×10}}^{\text{-3}}{\text{mol dm}}^{\text{-3}}\text{)}}\text{ = 15}{\text{.65 ×10}}^{\text{-3}}{\text{s}}^{\text{-1}}$

According to rate law:

  $\text{ν = k[Y]}$

  Rate constant, k $\text{= }\frac{\text{ν}}{\text{Y}}\text{ = }\frac{{\text{125 mol dm}}^{\text{-3}}{\text{s}}^{\text{-1}}}{\text{(2}{\text{.7×10}}^{\text{-3}}{\text{mol dm}}^{\text{-3}}\text{)}}\text{ = 46}{\text{.29 ×10}}^{\text{-3}}{\text{s}}^{\text{-1}}$

For experiment (II)

According to rate law:

  $\text{ν = k[complex]}$

  Rate constant, k $\text{= }\frac{\text{ν}}{\text{complex}}\text{ = }\frac{{\text{640 mol dm}}^{\text{-3}}{\text{s}}^{\text{-1}}}{\text{(8}{\text{.01×10}}^{\text{-3}}{\text{mol dm}}^{\text{-3}}\text{)}}\text{ = 79}{\text{.90 ×10}}^{\text{-3}}{\text{s}}^{\text{-1}}$

According to rate law:

  $\text{ν = k[Y]}$

  Rate constant, k $\text{= }\frac{\text{ν}}{\text{Y}}\text{ = }\frac{{\text{640 mol dm}}^{\text{-3}}{\text{s}}^{\text{-1}}}{\text{(6}{\text{.1×10}}^{\text{-3}}{\text{mol dm}}^{\text{-3}}\text{)}}{\text{ = 104 ×10}}^{\text{-3}}{\text{s}}^{\text{-1}}$