Question

If instantaneous rate of reaction is stated as $-\frac{1}{2} \frac{d[x]}{dt} = -\frac{d[y]}{dt} = \frac{1}{2} \frac{d[z]}{dt}$, identify the reaction.

• A. $x - 2y \rightarrow 2z$
• B. $2x + y \rightarrow 2z$
• C. $x + y \rightarrow z$
• D. $2x - 2y \rightarrow z$

Hint:

Read the denominators carefully. The denominator in the rate expression fraction is always the stoichiometric coefficient. A missing fraction simply means the coefficient is 1.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The rate of reaction is expressed by dividing the rate of change of concentration of a species by its stoichiometric coefficient. Reactants have a negative sign (disappearance), and products have a positive sign (appearance).

Step 2: Formula Application:
For a general reaction $aA + bB \rightarrow cC$: Rate $= -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt}$.

Step 3: Explanation:
Given: $-\frac{1}{2} \frac{d[x]}{dt} = -\frac{1}{1} \frac{d[y]}{dt} = \frac{1}{2} \frac{d[z]}{dt}$. Comparing the denominators: - Coefficient of $x$ is 2 (Reactant). - Coefficient of $y$ is 1 (Reactant). - Coefficient of $z$ is 2 (Product). This corresponds to the reaction: $2x + y \rightarrow 2z$.

Step 4: Final Answer:
The reaction is $2x + y \rightarrow 2z$.