Question

first order reaction, half life period is 100 min.then the rate constant is ​

Answer 1

Answer:  ​$0.00693min^{-1}$

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{2.303}{k}\log\frac{100}{50}$

$t_{\frac{1}{2}}=\frac{0.693}{k}$

Given : half life, $t_{\frac{1}{2}}=100min$

$100=\frac{0.693}{k}$

$k=0.00693min^{-1}$

Thus  the rate constant is ​$0.00693min^{-1}$