Name: Effect of Surface Area and Catalyst on Reaction Rate
Uploaded: 2019-07-19
Duration: 5 min 20 s
Description: This video introduces two factors that influence the rate of a chemical reaction. Surface area and catalysts affect the speed of a chemical reaction enormous...

Question

Derive an integrated rate equation for rate constant of a first order reaction.

Accepted Answer

Derivation of integrated rate equation for first order reactions :

Reaction, $A \to B$ , is of first order.

So, rate for the reaction can be expressed as : $- \frac{d [A]}{dt} = k [A]$ , where $k$ is rate constant.

Integrating both sides : $- \int \frac{d [A]}{[A]} = \int kt$ .

$- \ln [A] = kt + c$ .

At $t = 0; {[A]}_{t} = {[A]}_{\circ}$ . Therefore, $c = - \ln {[A]}_{\circ}$ , where, ${[A]}_{\circ}$ is the initial molar concentration of reactant $A$ .

$- \ln {[A]}_{t} = kt - \ln {[A]}_{\circ} \ln {[A]}_{t} = \ln {[A]}_{\circ} - kt \ln \frac{{[A]}_{\circ}}{{[A]}_{t}} = kt 2.303 \log_{10} \frac{{[A]}_{\circ}}{{[A]}_{t}} = kt k = \frac{2.303}{t} \log_{10} \frac{{[A]}_{\circ}}{{[A]}_{t}}$

The integrated rate equation for fist order reactions is $k = \frac{2.303}{t} \log_{10} \frac{{[A]}_{\circ}}{{[A]}_{t}}$ .

Derive an integrated rate equation for rate constant of a first order reaction.

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