Question

In a first order reaction, R → Q, if ‘k’ is the rate constant and initial concentration of the reactant R is 0.5 M, then the half-life is

• A. $\frac{log\,2}{k}$
• B. $\frac{log\,2}{k\sqrt{0.5}}$
• C. $\frac{In\,2}{k}$
• D. $\frac{0.693}{0.5 k}$

Answer 1

Answer: (C)

For a first order reaction,
$k=\frac{2.303}{t} log_{10} \frac{a}{a-x}; when \, t=t_{1 /2}, x=0.5/2$
$\therefore \, k=\frac{2.303}{t_{1 /2}} log_{10} \frac{0.5}{\left(0.5/ 2\right)}$
$\Rightarrow \, t_{1 /2}=\frac{2.303}{k} log_{10} \, 2=\frac{in \, 2}{k}$