Chapter 20, Problem 103SAE

Interpretation Introduction

Interpretation:

Rate of the given first order reaction should is to be calculated.

Concept introduction:

A rate law expression defines the relationship between the rate of reaction and the concentration of reactants.

Consider a reaction,

$a\text{A}+b\text{B}\to \text{Products}$

The rate law for the above equation can be defined as follows:

$r=k{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b$

As the reaction proceeds, the concentration of reactants decreases, and the concentration of products increases.

For the first order reaction, the rate law expression is as follows:

$k=\frac{1}{t}\ln \left(\frac{{\left[\text{A}\right]}_0}{{\left[\text{A}\right]}_t}\right)$

The expression for half-life for the first-order reaction is as follows:

$t_{1/2}=\frac{0.693}{k}$