Question

The first order reaction,so2cl2 to so2+cl2,has a half life of 8.75 hours at 593k.How long will it take for the concentration of so2cl2 to fall to 12.5% of its initial value? 6.24hours 26.2hours 16.2hours 22.6hours

Answer 1

Answer: The time after which the concentration of $SO_2Cl_2$ fall to 12.5% of its initial value is 26.2 hours

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  = 100

a - x = amount left after decay process  = 12.5

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.

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

$k=\frac{0.693}{8.75hour}=0.0792hour^{-1}$

b) for concentration to fall to 12.5 % of initial value  

$t=\frac{2.303}{0.0792}\log\frac{100}{12.5}$

$t=26.2hours$

The time after which the concentration of $SO_2Cl_2$ fall to 12.5% of its initial value is 26.2 hours