For the hypothetical reaction `2A rarr3C` , the reaction rate r in terms of the rate of change of the concentration is given by

Options

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

Answer

To solve the problem regarding the reaction \(2A \rightarrow 3C\) and to express the reaction rate \(r\) in terms of the rate of change of concentration, we can follow these steps:

### Step-by-Step Solution:

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

2. **General Rate Expression**:
For a general reaction of the form \(aA \rightarrow bB\), the rate of the reaction can be expressed as:
\[ r = -\frac{1}{a} \frac{d[A]}{dt} = \frac{1}{b} \frac{d[B]}{dt} \]
Here, \(r\) is the rate of the reaction, \([A]\) is the concentration of reactant A, and \([B]\) is the concentration of product B.

3. **Apply to the Given Reaction**:
For our specific reaction \(2A \rightarrow 3C\):
- The stoichiometric coefficient for \(A\) is 2.
- The stoichiometric coefficient for \(C\) is 3.

4. **Write the Rate Expressions**:
Using the stoichiometric coefficients:
\[ r = -\frac{1}{2} \frac{d[A]}{dt} \quad \text{(for reactant A)} \]
\[ r = \frac{1}{3} \frac{d[C]}{dt} \quad \text{(for product C)} \]

5. **Focus on the Rate in Terms of A**:
Since the question asks for the rate \(r\) in terms of the change in concentration of \(A\), we use the expression derived from \(A\):
\[ r = -\frac{1}{2} \frac{d[A]}{dt} \]

6. **Conclusion**:
Therefore, the final expression for the reaction rate \(r\) in terms of the rate of change of the concentration of \(A\) is:
\[ r = -\frac{1}{2} \frac{d[A]}{dt} \]