Question

In first order reaction A–>B, 60% of the given sample of compound deciposess in 45 min. what is the half life of the reaction

Answer 1

Half life of the reaction is 35 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 60 % of reaction  

$45min=\frac{2.303}{k}\log\frac{100}{100-60}$

$k=\frac{2.303}{45}\log\frac{100}{40}$

$k=0.02min^{-1}$

b) 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.

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

$k=\frac{0.693}{0.02min^{-1}}=35min$

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