Question

Half-life period of a first-order reaction is 1386 seconds. The specific rate constant of the reaction is:

• A. $5.0\times {10}^{-2}{s}^{-1}$
• B. $5.0\times {10}^{-3}{s}^{-1}$
• C. $0.5\times {10}^{-2}{s}^{-1}$
• D. $0.5\times {10}^{-3}{s}^{-1}$

Answer 1

The correct option is D $0.5\times {10}^{-3}{s}^{-1}$

Half-life of a first-order reaction = $\frac{0.693}{K}$

where,

$K$ is the rate constant or the specific rate constant.

Given half-life = 1386 sec.

$\frac{0.693}{K}=1386$

$\Rightarrow$ $K=\frac{693}{1386}\times {10}^{-3}\Rightarrow 0.5\times {10}^{-3}{s}^{-1}$

Hence, option D is correct.