Name: Methods of Determination of Order of Reactions
Uploaded: 2019-07-19
Duration: 2 min 47 s
Description: There are various methods to ascertain the order of reactions. Let’s watch the video and learn some of the important methods for the determination of the ord...

Question

State the rate equation for a first order reaction. Derive the half-life period from the rate equation. A first order reaction takes $69.3$ minutes for $50 %$ completion. How much time will be needed for $80 %$ completion ?

Accepted Answer

The rate equation, in which the concentration of only one reactant changes and the rate of reaction is proportional to the first power of the concentration of the reactant, is called first order rate equation.

Rate equation for first order reaction

$k = \frac{2.303}{t} . \log \frac{a}{(a - x)}$

Let $t_{\frac{1}{2}} =$ The time taken for the completion of half of the reaction, Then initial concentration $a$ becomes half i.e. becomes $\frac{a}{2}$ . $t_{\frac{1}{2}}$ is also called half-life period.

$At t = t_{\frac{1}{2}} and x = \frac{a}{2}$ Substituting these values in rate equation ,we get,

$k = \frac{2.303}{t_{\frac{1}{2}}} . \log \frac{a}{a - \frac{a}{2}}$

$k = \frac{2.303}{t_{\frac{1}{2}}} \log 2$

$k = \frac{2.303}{t_{\frac{1}{2}}} \times 0.301$

$t_{\frac{1}{2}} = \frac{0.693}{k}$ =Half life period of first oder reaction.

We given, $t_{\frac{1}{2}} = 69.3 \min$ .

Then, $k = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{69.3} = 0.01 .$

Now, if $a = 100, x = 80 and (a - x) = 20 .$ Substitute these values in first order rate equation, we get,

$k = \frac{2.303}{t} . \log \frac{100}{20}$

$t = \frac{2.303}{0.01} \log 5 = 230.3 \times 0.6989 = 160.96 \min .$

State the rate equation for a first order reaction. Derive the half-life period from the rate equation. A first order reaction takes $69.3$ minutes for $50 %$ completion. How much time will be needed for $80 %$ completion ?

Important Questions on Chemical Kinetics

Learn and Prepare for any exam you want !

State the rate equation for a first order reaction. Derive the half-life period from the rate equation. A first order reaction takes 69.3 minutes for 50% completion. How much time will be needed for 80% completion ?

Important Questions on Chemical Kinetics

Learn and Prepare for any exam you want !

State the rate equation for a first order reaction. Derive the half-life period from the rate equation. A first order reaction takes $69.3$ minutes for $50 %$ completion. How much time will be needed for $80 %$ completion ?