Question

the half life of a substance in first order reaction is 25 minutes calculate the rate constant

Answer 1

Given :

• Half life of first order reaction = 25minutes

To find :

Rate constant

Formula used :

$\sf \: k \times t_{ \frac{1}{2} } \: \: = \: ln(2)$

Here,

$\sf \bullet \: \: k \: = \: rate \: constant \\ \sf \bullet \: \: t_{ \frac{1}{2} }\: = \:half \: life \\ \sf \bullet \: \: ln \: = \:natural \: logarithm \:$

Solution :

$\sf \: k \times t_{ \frac{1}{2} } \: \: = \: ln(2) \\ \\ \sf \implies \: k \: \times 25min \: = \: 2.303 \times log(2) \\ \\ \sf \implies \: k \: = \: \dfrac{2.303}{25min} \times (0.3010) \\ \\ \sf \implies \: k \: = \: \dfrac{0.693}{25min} \\ \\ \sf \implies \: k \: = \: 0.0277 \: per \: min$

ANSWER :

Rate constant = 0.0277 per minute