Chemistry - Chemical Kinetics Question with Solution | TestHub

Reaction:

$A(g)\to 2B(g)$

Given:

$$\frac{d[B]}{dt}=6\times 10^{-4}[A]=0.1M$$

$$\frac{d[B]}{dt}=2.4\times 10^{-3}[A]=0.4M$$

Rate of reaction:

$$Rate=\frac{1}{2}\frac{d[B]}{dt}=k[A{]}^n$$

Taking ratio:

$$\frac{2.4\times 10^{-3}}{6\times 10^{-4}}={\left(\frac{0.4}{0.1}\right)}^n$$

$$4=4^n\Rightarrow n=1$$

So, the reaction is **first order**.

For first order:

$$t=\frac{2.303}{k}\log \frac{[A{]}_0}{[A]}$$

Find $k$:

$$3\times 10^{-4}=k(0.1)$$

$$k=3\times 10^{-3}{s}^{-1}$$

$$t=\frac{2.303}{3\times 10^{-3}}\log \frac{0.6}{0.15}$$

$$t=\frac{2.303}{0.003}\log 4$$

$$t=461s=7.68min$$

$$\boxed{t\approx 7.7min}$$