Question

The half life for a first order reaction is 4 min. , The time after which 99.9% reaction gets completed in ?​

Answer 1

thus the required answer is 39.88 min

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Answer 2

The time after which 99.9% reaction gets completed in 40 minutes.

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  

a) for completion of half life:  

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

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$4min=\frac{0.69}{k}$

$k=0.1725min^{-1}$

b) for completion of 99.9 % of reaction  

$t=\frac{2.303}{k}\log\frac{100}{100-99.9}$

$t=\frac{2.303}{k}\log\frac{100}{100-99.9}$

$t=\frac{2.303}{k}\times 3$

$t_{99.9}=\frac{6.90}{k}$

$t_{99.9}=\frac{6.90}{0.1725}=40min$

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