Question

In a first-order reaction, $A⟶B$, if $k$ is rate constant and initial concentration of the reactant $A$ is $0.5$ $M$ then 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 1st order reaction, $k=\frac{1}{t}ln\left(\frac{a_0}{a_t}\right)$

where $a_0$= initial concentrattion,

$a_t$= concentration at time t.

For half-life, $a_t=\frac{a_0}{2}$

$k{t}_{1/2}=ln\left(\frac{a_0}{a_0/2}\right)=ln\left(2\right)$

half-life = $t_{1/2}$ = $\frac{ln\left(2\right)}{k}$