Question

For the reaction \(2\text{A}⟶3\text{C}+\text{D}\), the rate of reaction is represented by

• A. \(-\text{d}[A]/\text{dt} = -\text{d}[D]/\text{dt}\)
• B. \(-\text{d}[C]/\text{dt} = -2\text{d}[A]/\text{dt}\)
• C. \(-\text{d}[A]/\text{dt} = -\text{d}[D]/\text{dt}\)
• D. \(-\frac{1}{2}\frac{\text{d}[A]}{\text{dt}} = +\frac{1}{3}\frac{\text{d}[C]}{\text{dt}}\)

Hint:

Divide each rate by its stoichiometric coefficient; reactant rates carry a minus sign, products a plus sign.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For \(a\text{A} \rightarrow b\text{C} + c\text{D}\), the reaction rate is \(-\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[C]}{dt} = \frac{1}{c}\frac{d[D]}{dt}\). The reactant concentration falls (negative sign) and products rise (positive sign).

Step 2: Detailed Explanation
Here \(a = 2\), \(b = 3\), \(c = 1\):
\[ \text{Rate} = -\frac{1}{2}\frac{d[A]}{dt} = +\frac{1}{3}\frac{d[C]}{dt} = +\frac{d[D]}{dt} \]
Option (D) states exactly the first equality. In options (A) and (C), \(-d[A]/dt\) is a positive number but \(-d[D]/dt\) is negative because D is formed, and the coefficient 2 is also missing. In option (B), \(-d[C]/dt\) is negative while \(-2\,d[A]/dt\) is positive, and the ratio of coefficients is also wrong.

Final Answer:
Option (D) is the correct form of the rate expression. \[ \boxed{-\frac{1}{2}\frac{d[A]}{dt} = +\frac{1}{3}\frac{d[C]}{dt}} \]