This question involves analyzing a set of parallel and sequential equilibrium reactions to determine the correct product distribution. The reactions show a compound undergoing two possible pathways with different rate constants.

Step 1: Understand the Reaction System
We have a reactant $A$ that can react via two parallel paths:

Path 1: $A \overset{k_{1}}{\to} B$ with rate constant $k_{1}$
Path 2: $A \overset{k_{2}}{\to} C$ with rate constant $k_{2}$

Product

B

then further reacts:

B \overset{k_{3}}{\to} D

with rate constant

k_{3}

.

Step 2: Apply Steady State Approximation
For intermediate $B$ , we apply the steady state approximation: $\frac{d [B]}{d t} = k_{1} [A] - k_{3} [B] = 0$ Solving for $[B]$ : $k_{1} [A] = k_{3} [B]$ $[B] = \frac{k_{1} [A]}{k_{3}}$

Step 3: Determine Product Distribution
The rate of formation of final products:

For $D$ : $\frac{d [D]}{d t} = k_{3} [B] = k_{1} [A]$
For $C$ : $\frac{d [C]}{d t} = k_{2} [A]$

The ratio of products formed is:

\frac{[D]}{[C]} = \frac{k_{1}}{k_{2}}

This means the product distribution depends only on the ratio of the rate constants for the initial parallel reactions, not on the subsequent reaction of B.

Step 4: Analyze the Options
Looking at the options, we need to find which one shows the correct product distribution based on the rate constants. The correct option should reflect that the ratio of final products D and C is determined by k₁/k₂, regardless of k₃.

Final Answer: Based on the steady state analysis, the correct option is the one where the product distribution follows the ratio k₁/k₂.

Related Topics

Parallel Reactions: When a reactant can undergo two or more different reactions simultaneously. The product distribution depends on the relative rates of the parallel pathways.

Sequential Reactions: Reactions where products of one step become reactants for subsequent steps. The steady state approximation is often used for intermediates.

Important Formulae

Steady state approximation for intermediate B: $\frac{d [B]}{d t} = 0$

Product ratio for parallel reactions with sequential steps: $\frac{[D]}{[C]} = \frac{k_{1}}{k_{2}}$