Answer:
The concentration of methyl isonitrile will become 15% of the initial value after 10.31 hrs.
Explanation:
As the data the rate constant is not given in this description, However from observing the complete question the rate constant is given as a rate constant of 5.11x10-5s-1 at 472k .
Now the ratio of two concentrations is given as
[tex]ln (\frac{C}{C_0})=-kt[/tex]
Here C/C_0 is the ratio of concentration which is given as 15% or 0.15.
k is the rate constant which is given as [tex]5.11 \times 10^{-5} \, s^{-1}[/tex]
So time t is given as
[tex]ln (\frac{C}{C_0})=-kt\\ln(0.15)=-5.11 \times 10^{-5} \times t\\t=\frac{ln(0.15)}{-5.11 \times 10^{-5} }\\t=37125.6 s\\t=37125.6/3600 \\t= 10.31 \, hrs[/tex]
So the concentration will become 15% of the initial value after 10.31 hrs.
Complete question:
The rearrangement of methyl isonitrile (CH3NC) to acetonitrile (CH3NC) is a first-order reaction and has a rate constant of 5.11x10-5s-1 at 472k . If the initial concentration of CH3NC is 3.00×10-2M. How many hours will it take for the concentration of methyl isonitrile to drop to 15.0 % of its initial value?
Answer:
The time taken for the concentration of methyl isonitrile to drop to 15.0 % of its initial value is 10.3 hours
Explanation:
The initial concentration of CH3NC is 3.00 X 10⁻²M =0.03M
The rate constant K= 5.11 X 10⁻⁵s⁻¹
If the concentration of methyl isonitrile to drop to 15.0 %;
The new concentration of methyl isonitrile becomes 0.15 X 0.03 = 0.0045 M
The time taken to drop to 0.0045 M, can be calculated as follows:
[tex]t = -ln[\frac{(CH_3NC)}{(CH_3NC)_0}]/K[/tex]
[tex]t = (-ln[\frac{0.0045}{0.03}]/5.11 X 10^{-5})X(\frac{1 min}{60 s}) = 618.8 mins[/tex]
→ 618.8 mins X 1hr/60mins = 10.3 hours
Therefore, the time taken for the concentration of methyl isonitrile to drop to 15.0 % of its initial value is 10.3 hours
