Question

For the reaction \(2A \rightarrow 3B\), the rate of reaction \(\frac{d[B]}{dt}\) is equal to :

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

Hint:

For \(aA \rightarrow bB\), \[ -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt} \] Always divide the rate of change by the stoichiometric coefficient first.

Answer 1

The Correct Option is A

Concept: For a general reaction: \[ aA \rightarrow bB \] the rate of reaction is defined as: \[ -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt} \] This definition ensures that the numerical value of the reaction rate remains the same regardless of the species chosen.

Step 1: Write the given reaction. \[ 2A \rightarrow 3B \] Here, \[ a=2,\qquad b=3 \]

Step 2: Apply rate expression. \[ -\frac{1}{2}\frac{d[A]}{dt} = \frac{1}{3}\frac{d[B]}{dt} \]

Step 3: Rearranging. Multiplying both sides by 3: \[ -\frac{3}{2}\frac{d[A]}{dt} = \frac{d[B]}{dt} \]

Step 4: Final answer. \[ \boxed{\frac{d[B]}{dt} = -\frac{3}{2}\frac{d[A]}{dt}} \] Hence option (A) is correct.