Chemistry - Chemical Kinetics Question with Solution | TestHub

Question Explanation:

Calculate the time when reactant and product concentrations are equal in a parallel reaction.

Concept:

Kinetics of Parallel First-Order Reactions.

Solution:

In the given parallel reaction, A decays into B and C simultaneously. The total rate constant is $\mathrm{K}={\mathrm{k}}_1+{\mathrm{k}}_2$.

The problem asks when $[\mathrm{A}]=[\mathrm{B}]=[\mathrm{C}]$. Since $[\mathrm{B}]=[\mathrm{C}]$, this means $[\mathrm{A}]=[\mathrm{B}]$ and the total concentration is constant: $[\mathrm{A}{]}_0=[\mathrm{A}]+[\mathrm{B}]+[\mathrm{C}]$.

On substituting equalities: $[\mathrm{A}{]}_0=[\mathrm{A}]+[\mathrm{A}]+[\mathrm{A}]=3[\mathrm{A}]$. So, $[\mathrm{A}]=\frac{1}{3}[\mathrm{A}{]}_0$.

Using the first-order rate law: $[A]=[A{]}_0{e}^{-\left(k_1+k_2\right)t}$ Since $k_1=k_2$, the equation is $\frac{1}{3}[A{]}_0=[A{]}_0{e}^{-2k_{1}t}$.

$\frac{1}{3}=e^{-2k_{1}t}\Rightarrow 3=e^{2k_{1}t}\Rightarrow \ln 3=2k_{1}t$. Solving for $t:t=\frac{1}{2k_1}\ln 3$.

Final Answer: Option (A)