Question

in a first order reaction A gives rise to products 60% of the given sample of A is decomposed in 40 min.what is the half life of the reaction​

Answer 1

Answer:

Our formula is T=2.303/k log(product /reactant)

Explanation:

By using 1st equation we have to find k

40=2.303/k log(60/40)

put the value of k in

Half Life T=0.693÷k

Answer 2

The half life of the reaction is 30 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

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

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

$k=\frac{2.303}{40}\times 0.40$

$k=0.023min^{-1}$ 

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.

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

$t_{\frac{1}{2}}=\frac{0.693}{0.023min}=30min$

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