Answer:
[tex]\large\boxed{\large\boxed{k=6.68\times 10^{-4}s^{-1}}}[/tex]
Explanation:
The first-order rate law is:
[tex]\dfrac{d[CH_3NC]}{[CH_3NC]}=-kt[/tex]
The solution of that differential equation is:
[tex][CH_3NC]=[CH_3NC]_0e^{-kt}[/tex]
You are given:
[tex]\dfrac{CH_3NC]}{[CH_3NC]_0}=0.72[/tex]
[tex]t=492s[/tex]
And you want to determine k.
Substitute into the solution of the differential equation and solve for t:
[tex]0.72=e^{-k\times 492s}[/tex]
[tex]k=-ln(0.72)/492s\\\\k=6.6769\times10^{-4}s^{-1}\approx6.68\times 10^{-4}s^{-1}[/tex]
