Question

If decomposition of hydrogen peroxide is a first order reaction, it's rate law equation can be represented as

• A. $r = k [\mathrm{H_2O_2}]^2$
• B. $r = k [\mathrm{H_2O_2}]$
• C. $r = k [\mathrm{H_2O}][\mathrm{O_2}]^{1/2} / [\mathrm{H_2O_2}]$
• D. $r = k [\mathrm{H_2O_2}][\mathrm{H_2O_2}][\mathrm{O_2}]^{1/2}$

Hint:

Never rely blindly on balanced stoichiometric coefficients to write a rate law unless the reaction is explicitly stated to be elementary. Always use the experimental order given in the text of the problem!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question specifies that the chemical decomposition of hydrogen peroxide ($\mathrm{H_2O_2}$) is a first-order kinetic reaction and asks for its corresponding mathematical rate law expression.

Step 2: Key Formula or Approach:
By definition, the rate law equation for any chemical reaction expresses the reaction rate ($r$) as a function of the rate constant ($k$) and the concentrations of the reactants raised to a power equal to their partial order of reaction. For a general reaction component $\mathrm{A}$ that is first-order, the rate expression is: $$r = k [\mathrm{A}]^1$$

Step 3: Detailed Explanation:
The chemical equation for the decomposition of hydrogen peroxide is: $$\mathrm{2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)}$$ Though the stoichiometric coefficient of $\mathrm{H_2O_2}$ in the balanced equation is 2, the question explicitly states that the mechanism follows

first-order kinetics. This means the rate depends on the concentration of hydrogen peroxide raised to the power of 1.
Substituting $\mathrm{H_2O_2}$ into the first-order rate template gives: $$r = k [\mathrm{H_2O_2}]$$ This perfectly matches the expression provided in option (B).

Step 4: Final Answer:
The rate law equation is represented by $r = k [\mathrm{H_2O_2}]$, which matches option (B).