Chapter 14, Problem 58GQ

(a)

Interpretation Introduction

Interpretation:

Amount of $N{O}_x$ present after 5.25 hours should be determined.

Concept Introduction:

Order of a reaction:  The order of each reactant is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction. The order of the reaction is directly proportional to the concentration of the reactants.

The integrated rate law for the first order is as follows:

  $\begin{array}{c}\text{ln}\left[A\right]=\ln \left[{\text{A}}_{\text{0}}\right]-kt\\ \text{where,}\\ \left[{\text{A}}_{\text{0}}\right]\text{= initial}\text{concentration}\\ \text{k=}\text{rate constant}\\ t=time\\ \left[\text{A}\right]=concentrationaftertimet\end{array}$

Half–life period: It is the time required for the reactant (substrate) concentration to reduce to the one-half of its initial concentration.

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{0.693}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$

(b)

Interpretation Introduction

Interpretation:

Time required to decrease $1.50mg$ of $N{O}_x$ to $2.50\times {10}^{-6}mg$ should be determined.

Concept introduction:

Order of a reaction:  The order of each reactant is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction. The order of the reaction is directly proportional to the concentration of the reactants.

The integrated rate law for the first order is as follows:

  $\begin{array}{c}\text{ln}\left[A\right]=\ln \left[{\text{A}}_{\text{0}}\right]-kt\\ \text{where,}\\ \left[{\text{A}}_{\text{0}}\right]\text{= initial}\text{concentration}\\ \text{k=}\text{rate constant}\\ t=time\\ \left[\text{A}\right]=concentrationaftertimet\end{array}$

Half–life period: It is the time required for the reactant (substrate) concentration to reduce to the one-half of its initial concentration.

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{0.693}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$