Answer: 85 minutes
Explanation:
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
Half life for second order kinetics is given by:
[tex]t_{\frac{1}{2}=\frac{1}{k\times a_0}[/tex]
[tex]t_{\frac{1}{2}[/tex] = half life = 15 min
k = rate constant =?
[tex]a_0[/tex] = initial concentration = 100 (say)
[tex]15min=\frac{1}{k\times 100}[/tex]
[tex]k=\frac{1}{1500}[/tex]
Integrated rate law for second order kinetics is given by:
[tex]\frac{1}{a}=kt+\frac{1}{a_0}[/tex]
a= concentration left after time t = [tex]100-\farc{85}{100}\times 100=15[/tex]
[tex]\frac{1}{15}=\frac{1}{1500}\times t+\frac{1}{100}[/tex]
[tex]t=85min[/tex]
Thus after 85 minutes after the start of the reaction, it will be 85% complete.
