116.

(i) Define specific reaction rate.
(ii) Define Half-life period of a chemical reaction. Also obtain the expression for half-life period.

Or

Derive the general for of the expression for the half-life of a first order reaction.

(i) Specific reaction rate. This is also called rate constant or velocity constant. Specific reaction rate may be defined as the rate of reaction under specific conditions, when the product of concentration of the reactants is unity.

(ii) Half-life period of a chemical reaction in which the concentration of reactant is reduced to half of the intial value of concentration.
It is denoted by t_l/2 or t_0.5.

The rate equation for a reaction of first order is expressed as:
                 $\mathrm{k}= \frac{2.303}{\mathrm{t}}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}$


or               $\mathrm{t}=\frac{2.303}{\mathrm{k}}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}$


   When      $\mathrm{t}=\frac{1}{2}, \mathrm{x} = 0.5 \mathrm{a} \mathrm{or} \frac{\mathrm{a}}{2}$

   On substituting these values, we get

          $$\begin{gathered} {\mathrm{t}}_{1/2} \frac{2.303}{\mathrm{k}}\log \frac{\mathrm{a}}{\mathrm{a}-0.5\mathrm{a}}=\frac{2.303}{\mathrm{k}}\log 2. \\ \mathrm{or} {\mathrm{t}}_{1/2} = \frac{0.693}{\mathrm{k}} ...\left(\mathrm{i}\right) \end{gathered}$$

The relation (i) is the required expression for half-life period of first order reaction.