There are two compounds A and B that react with one common reagent C following first order kinetics. Suppose 99.9% of A must React before 0.1% of B has reacted then what is the minimum ratio of their respective rate Constants?
There are two compounds $\ce{A}$ and $\ce{B}$ that react with one common reagent $\ce{C}$ following first order kinetics. Suppose 99.9% of $\ce{A}$ must react before 0.1% of $\ce{B}$ has reacted then what is the minimum ratio of their respective rate constants?
My Attempt at the question :
We know that the reactions follow first order kinetics, hence I tried to find the time at which the given percentage of A$\ce{A}$ and B$\ce{B}$ is left using the formula $$ t = \frac{2.303}{k} \cdot \log\left(\frac{C_0}{C_1}\right)$$ where -$t$ is the time, $k$ is the rate constant for each reaction and $C_0$ and $C_1$ are initial and final concentration respectively.
t = 2.303/k . log(C0/C1)
where t is the time, k is the rate constant for each reaction and C0 and C1 are initial and final concentration respectively.
After this I tried to find the ratio of rate Constantsconstants directly but couldn't arrive at the answer.
P.S.
I I derived the above formula using the integrated rate law.
