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Parallel Reactions

Kinetics of Side/Concurrent First-Order Reactions ($A \rightarrow B$ and $A \rightarrow C$).

By chemca Team • Updated Jan 2026

In parallel or side reactions, a single reactant reacts simultaneously via two or more different pathways to form different products. The reaction with the higher rate constant forms the major product.

1. The Reaction Scheme

$$ A \xrightarrow{k_1} B \text{ (Main Product)} $$ $$ A \xrightarrow{k_2} C \text{ (Side Product)} $$

Both reactions are assumed to be First Order.
$k_1, k_2$ are the rate constants for the respective paths.

2. Rate Laws & Effective Constant

The rate of disappearance of A is the sum of rates of both paths:

$$ \frac{-d[A]}{dt} = k_1[A] + k_2[A] = (k_1 + k_2)[A] $$

Effective Rate Constant ($k_{eff}$):

$$ k_{eff} = k_1 + k_2 $$

Integrated Rate Equation: Similar to a simple first-order reaction:

$$ [A]_t = [A]_0 e^{-(k_1 + k_2)t} $$ $$ t_{1/2} = \frac{\ln 2}{k_{eff}} = \frac{0.693}{k_1 + k_2} $$

3. Product Analysis & Yield

Branching Ratio

The rates of formation of products are:

$$ \frac{d[B]}{dt} = k_1[A] \quad \text{and} \quad \frac{d[C]}{dt} = k_2[A] $$

Dividing the two rates:

$$ \frac{[B]_t}{[C]_t} = \frac{k_1}{k_2} $$

Key Insight: The ratio of products formed at any time $t$ is constant and equal to the ratio of their rate constants.

Percentage Yield

$$ \% \text{ Yield of B} = \frac{k_1}{k_1 + k_2} \times 100 $$ $$ \% \text{ Yield of C} = \frac{k_2}{k_1 + k_2} \times 100 $$

4. Activation Energy ($E_{eff}$)

Temperature Dependence

Using the Arrhenius equation $k = Ae^{-E_a/RT}$, the effective activation energy for the overall reaction is a weighted average.

$$ E_{eff} = \frac{k_1 E_1 + k_2 E_2}{k_1 + k_2} $$

Effect of Temperature on Yield:

• If $E_1 > E_2$: Increasing temperature favors product B (Higher $E_a$ path is favored at high T).
• If $E_1 < E_2$: Decreasing temperature favors product B.

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