2 H2O2(aq) → 2 H2O(l) + O2(g) ΔH° = −196 kJ/mol_rxn The decomposition of H2O2(aq) is represented by — Kinetics Chemistry Question

STEPS:

1. Understand chemical kinetics and reaction order: The order of a reaction cannot be determined simply by looking at the stoichiometric coefficients of a balanced overall chemical equation. Instead, it must be determined experimentally by analyzing how the concentration of the reactant changes over time.
2. Recall the graphical representations of integrated rate laws:
* First^-Order Reaction: The integrated rate law is mathematically represented as:
$$\ln[\text{A}]_t - \ln[\text{A}]_0 = -kt \implies \ln[\text{A}]_t = -kt + \ln[\text{A}]_0\ \text{}$$
This equation matches the equation of a straight line ($y = mx + b$), where $y = \ln[\text{A}]$, $x = t$, and the slope ($m$) is equal to $-k$. Therefore, a plot of $\ln[\text{H}_2\text{O}_2]$ versus time will yield a straight line if the reaction is first order.
* Second^-Order Reaction: The integrated rate law is:
$$\frac{1}{[\text{A}]_t} - \frac{1}{[\text{A}]_0} = kt \implies \frac{1}{[\text{A}]_t} = kt + \frac{1}{[\text{A}]_0}\ \text{}$$
This also matches the equation of a straight line, but with $y = \frac{1}{[\text{A}]}$. Therefore, a plot of $\frac{1}{[\text{H}_2\text{O}_2]}$ versus time will yield a straight line if the reaction is second order.
* Zero^-Order Reaction: A plot of the concentration $[\text{H}_2\text{O}_2]$ versus time will yield a straight line.
3. Identify the correct experimental test: To determine if the decomposition of hydrogen peroxide is first order, a student would plot $\ln[\text{H}_2\text{O}_2]$ versus time. If this plot is linear, it mathematically confirms first-order kinetics. This directly matches the statement in Option B.

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WHY_OTHERS_WRONG:

• Option A is incorrect: The number of reactant species in the overall equation does not dictate the reaction order. Many reactions with a single reactant proceed through a complex, multi-step mechanism that is not first order.
• Option C is incorrect: A straight line for a plot of $\frac{1}{[\text{H}_2\text{O}_2]}$ versus time is the distinct graphical proof for a second-order reaction, not a first-order reaction.
• Option D is incorrect: This is a common trap that assumes the reaction order is equal to the stoichiometric coefficient (2) from the balanced equation. Because the overall reaction is often the result of multiple elementary steps, the rate law and reaction orders must be determined experimentally, not from overall coefficients.