X + 2 Y → Z + 3 Q For the reaction represented above, the initial rate of decrease in [X] was 2.8 × — Kinetics Chemistry Question

STEPS:

1. Analyze the Balanced Equation: Identify the stoichiometric coefficients for the reactants in the given reaction: $X + 2 Y \rightarrow Z + 3 Q$. The coefficients indicate that for every 1 mole of $X$ that is consumed, 2 moles of $Y$ must be consumed simultaneously.
2. Understand the Concept of Relative Rates: The rate of a reaction can be expressed in terms of the disappearance of reactants. These rates are proportional to their stoichiometric coefficients. Therefore, the rate of decrease in $[Y]$ is twice as fast as the rate of decrease in $[X]$.
3. Set Up the Relationship: Mathematically, this relationship is expressed as:
$$\text{Rate of decrease in } [Y] = 2 \times (\text{Rate of decrease in } [X])$$
4. Substitute and Calculate: Plug in the provided initial rate of decrease for $[X]$ ($2.8 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$):
$$\text{Rate of decrease in } [Y] = 2 \times (2.8 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1})$$
$$\text{Rate of decrease in } [Y] = \mathbf{5.6 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}}$$
5. Match with the Options: The calculated value of $5.6 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$ corresponds to option D.

WHY_OTHERS_WRONG:

• A) $7.0 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$: This value is one-fourth the rate of $X$, which does not match any stoichiometric relationship in the balanced equation.
• B) $1.4 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$: This is half the rate of $X$. A student might arrive at this if they incorrectly divided by the coefficient of 2 instead of multiplying by it.
• C) $2.8 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$: This assumes a 1:1 molar ratio between $X$ and $Y$, failing to account for the coefficient of 2 for $Y$ in the balanced equation.
• E) $1.1 \times 10^{-2} \text{ mol L}^{-1} \text{ s}^{-1}$: This is four times the rate of $X$ ($4 \times 2.8 \times 10^{-3} = 1.12 \times 10^{-2}$), which is mathematically incorrect for the 1:2 stoichiometric ratio provided.