Question

The half life for a first order reaction is "4minute" the time after which 99.9% reactions gets completed

Answer 1

The time after which 99.9% reactions gets completed is 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.

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

$k=\frac{0.693}{4min}=0.173min^{-1}$

b) for completion of 99.9 % of reaction  

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

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

$t=\frac{2.303}{0.173}\times 3$

$t_{99.9}=40min$

The time after which 99.9% reactions gets completed is 40 minutes

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Answer 2

Answer:

Explanation:

Half life of a first order reaction is 0.693/k,where k is the rate constant.Time taken for first order reaction is 2.303/k*log(Ao/A),

where Ao is the initial concentration and A is the remaining concentration after time t.After applying these,we get time as 39.87min.