In the reaction `3Ararr2B`, rate of reaction `+(d[B])/(dt)` is equal to :

Options

A. `(1)/(3)(d[A])/(dt)`
B. `(2)/(3)(d[A])/(dt)`
C. `+2(d[A])/(dt)`
D. `(3)/(2)(d[A])/(dt)`

Answer

To solve the problem regarding the rate of reaction for the given chemical equation \( 3A \rightarrow 2B \), we need to analyze the stoichiometry of the reaction and how it relates to the rates of change of the concentrations of the reactants and products.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction is given as:
\[ 3A \rightarrow 2B \]

2. **Write the Rate Expressions**:
The rate of reaction can be expressed in terms of the change in concentration of the reactants and products. For the reaction:
- The rate of disappearance of \( A \) is given by:
\[ -\frac{1}{3} \frac{d[A]}{dt} \]
- The rate of formation of \( B \) is given by:
\[ \frac{1}{2} \frac{d[B]}{dt} \]

3. **Relate the Rates**:
According to the stoichiometry of the reaction:
\[ -\frac{1}{3} \frac{d[A]}{dt} = \frac{1}{2} \frac{d[B]}{dt} \]

4. **Express the Rate of Formation of \( B \)**:
Rearranging the equation to find the rate of formation of \( B \):
\[ \frac{d[B]}{dt} = -\frac{3}{2} \frac{d[A]}{dt} \]

5. **Final Expression**:
Since the question asks for the rate of formation of \( B \) in terms of the rate of disappearance of \( A \), we can express it as:
\[ \frac{d[B]}{dt} = \frac{2}{3} \left(-\frac{d[A]}{dt}\right) \]
Therefore, the rate of formation of \( B \) is:
\[ \frac{d[B]}{dt} = \frac{2}{3} \text{(rate of disappearance of A)} \]

### Conclusion:
The rate of reaction \( \frac{d[B]}{dt} \) is equal to \( \frac{2}{3} \) times the rate of disappearance of \( A \).