Chapter 6, Problem 6C.4ST

Interpretation Introduction

Interpretation:

The half-life time when the concentration is lowered to $0.50mmold{m}^{-3}$ has to be calculated.

Concept Introduction:

Integrated rate law for second order reactions:

Taking in the example of following reaction,

    $\text{aA}\to \text{products}$

And the reaction follows second order rate law,

Then the relationship between the concentration of $\text{A}$ and time can be mathematically expressed as,

    $\frac{\text{1}}{{\left[\text{A}\right]}_{\text{t}}}\text{=kt+}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}$

The above expression is called as integrated rate for second order reactions.

Half-life period:

Half-life is defined as the time taken for amount of the sample to reduce to half of its starting value.  The symbol is ${\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}$.

$t_{\frac{1}{2}}=\frac{\ln \left(2\right)}{k}$

Half-life for a first order reaction is, $t_{\frac{1}{2}}=\frac{0.693}{k}$