Question

Half - life of the reaction :$H_2{O}_{2\left(aq\right)}\to H_2{O}_{\ell }+\frac{1}{2}{O}_{2\left(g\right)}$ is independent of initial concentration of $H_2{O}_2$. Volume of $O_2$ gas after 20 minutes is 5L at 1 atm and ${27}^{\circ }C$, and after completion of the reaction 50 L. The rate constant is :

• A. $\frac{1}{20}log10mi{n}^{-1}$
• B. $\frac{2.303}{20}log10mi{n}^{-1}$
• C. $\frac{2.303}{20}log\frac{50}{45}mi{n}^{-1}$
• D. $\frac{2.303}{20}log\frac{45}{50}mi{n}^{-1}$

Answer 1

The correct option is C

$\frac{2.303}{20}log\frac{50}{45}mi{n}^{-1}$

$t_{12}$ is independent of initial concentration, a, for first order reaction.
$x\alpha V_t(=5Latt=20minutes)a\alpha V_{\infty }(=50Latcompletion)\frac{2.303}{20}log\frac{a}{a-x}=\frac{2.303}{20}log\frac{50}{45}$