Question

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

• A. $\frac{ln2}{k}$
• B. $\frac{0.693}{0.5k}$
• C. $\frac{log2}{k}$
• D. $\frac{log2}{k\sqrt{0.5}}$

Answer 1

Answer: (A)

$\frac{ln2}{k}$

For a first-order reaction,

$A\to B$

Rate = $k\left[A\right]$

Initial concentration$=0.5M$

We know that the rate constant of a first order reaction has only time unit. It has no concentration unit, which means that numerical value of k for a first order reaction is independent of concentration unit.

$\therefore t_{\frac{1}{2}}=\frac{\ln 2}{k}\approx \frac{0.693}{k}$ or $\frac{2.303}{k\log 2}$

Hence, option A is correct.