Answer: 360 minutes are required for 20 percent of a sample of cyclopropane to isomerize topropane.
Explanation:
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
As the units of rate constant is [tex]min^{-1}[/tex] , the reaction follows first order kinetics.
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant =[tex]6.2\times 10^{-4}min^{-1}[/tex]
t = time for decomposition = ?
a = let initial amount of the reactant = 100
x = amount decayed = [tex]\frac{20}{100}\times 100=20[/tex]
a - x = amount left after decay process = 100-20= 80
[tex]t=\frac{2.303}{6.2\times 10^{-4}min^{-1}}\log\frac{100}{100-20}[/tex]
[tex]t=360min[/tex]
Thus 360 minutes are requiredfor 20 percent of a sample of cyclopropane to isomerize topropane.
