Chapter 14.3, Problem 3PE

(a)

Interpretation Introduction

Interpretation:

The time taken for the reactant A to decreases from $0.0092M$ to $3.7\times {10}^{-3}M$ has to be given.

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Intergrated rate eqaution for a second order reaction is,

$\frac{1}{\left[A\right]}=\frac{1}{{\left[A\right]}_0}+kt$

$\left[A\right]$ is the concentration of reactant A at time t ${\left[A\right]}_0$ is the  initial concentration of reactant, k is the rate constant.

(b)

Interpretation Introduction

Interpretation:

The half-life the given reaction has to be calculated.

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

$Rate=\underset{\begin{array}{l}rate\\ constat\end{array}}{k}\left[A\right]\left[B\right]$

The rate of the reaction is proportinal to the concentration of A to the power of x, is ${\left[A\right]}^x$

The rate of the reaction is proportional to the concentration of B to the power of y is ${\left[B\right]}^y$

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of this reaction is the sum of the powers to which all reactant concentrations appearing in the rate law are  raised.

$\text{Order}\text{= }\text{x+y}$

Half-life is the time required for one half of a reactant to react.

Half-life for a second order reaction is

${\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}\text{=}\frac{\text{1}}{\text{k}{\left[\text{A}\right]}_{\text{0}}}\text{where}{\left[\text{A}\right]}_{\text{0}}\text{is}\text{the}\text{initial}\text{concentration}\text{of}\text{reactant}\text{A}$