This is an incomplete question, here is a complete question.
The rearrangement of methyl isonitrile (CH₃NC) to acetonitrile (CH₃NC) is a first-order reaction and has a rate constant of 5.11 × 10⁻⁵ s⁻¹ at 472 K. If the initial concentration of CH₃NC is 3.00 × 10⁻² M :
How many hours will it take for the concentration of methyl isonitrile to drop to 14.0 % of its initial value?
Answer : The time taken will be, 10.7 hours
Explanation :
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]5.11\times 10^{-5}s^{-1}[/tex]
t = time passed by the sample = ?
a = let initial amount of the reactant = 100
a - x = amount left after decay process = 14 % of 100 = 14
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{5.11\times 10^{-5}}\log\frac{100}{14}[/tex]
[tex]t=38482.72s=\frac{38482.72}{3600}=10.7hr[/tex]
Therefore, the time taken will be, 10.7 hours
