Question

For a first order reaction with rate constant k and initial concentration a, the half-life period is given by:

• A. $\frac{ln2}{k}$
• B. $\frac{1}{ka}$
• C. $\frac{0.693}{k}$
• D. $\frac{2.303}{k}log2$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\frac{ln2}{k}$
C $\frac{0.693}{k}$
D $\frac{2.303}{k}log2$

For first order reaction, $t=\frac{1}{k}ln\frac{a}{a-x}.$
When $t=t_{1/2},x=a/2$

Hence, the expression for the half-life period of first-order reaction is as shown below:
$t_{1/2}=\frac{ln2}{k}.$

$t_{1/2}=\frac{2.303}{k}log2.$

and $t_{1/2}=\frac{2.303}{k}log2$.

Hence, the options A, C and D are correct.