Question

In a first order reaction $A\to B,$ $k$ is rate constant and initial concentration of the reactant $A$ is $0.5\text{M}$, then the half-life is:

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

Answer 1

The correct option is C $\frac{\ln 2}{k}$

For a $1^{st}$ order reaction,
$k=\frac{1}{t}\ln \frac{a}{a-x}$

At $t_{1/2},x=\frac{a}{2}$
$\therefore k=\frac{1}{t_{1/2}}\ln \frac{a}{a-\frac{a}{2}}\Rightarrow t_{1/2}=\frac{\ln 2}{k}$
So, half life period $\left(t_{1/2}\right)$ of $1^{st}$ order reaction is independent of initial concentration.