Question

the rate constant for a first order reaction which has half life 480 sec will be?

Answer 1

rate constant = 0.693/480 = 0.0014

Answer 2

The rate constant for a first order reaction which has half life 480 sec will be $1.4\times 10^{-3}sec^{-1}$

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  

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.

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

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

$k=\frac{0.69}{480s}=1.4\times 10^{-3}sec^{-1}$

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