for the reaction, `2A + B rarr 3C + D`, which of the following does not express the reaction rate

Options

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

Answer

To determine which option does not express the reaction rate for the reaction \(2A + B \rightarrow 3C + D\), we need to analyze the rate expressions based on the stoichiometry of the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction Components**:
The reaction is given as:
\[ 2A + B \rightarrow 3C + D \]
Here, \(A\) and \(B\) are reactants, and \(C\) and \(D\) are products.

2. **Understand the Stoichiometric Coefficients**:
- The stoichiometric coefficient of \(A\) is 2.
- The stoichiometric coefficient of \(B\) is 1.
- The stoichiometric coefficient of \(C\) is 3.
- The stoichiometric coefficient of \(D\) is 1.

3. **Write the Rate Expressions**:
The rate of a reaction can be expressed in terms of the change in concentration of reactants and products over time. The general form is:
\[ \text{Rate} = -\frac{1}{\text{coefficient}} \frac{d[\text{reactant}]}{dt} = \frac{1}{\text{coefficient}} \frac{d[\text{product}]}{dt} \]

- For \(A\):
\[ \text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} \]
- For \(B\):
\[ \text{Rate} = -\frac{1}{1} \frac{d[B]}{dt} = -\frac{d[B]}{dt} \]
- For \(C\):
\[ \text{Rate} = \frac{1}{3} \frac{d[C]}{dt} \]
- For \(D\):
\[ \text{Rate} = \frac{1}{1} \frac{d[D]}{dt} = \frac{d[D]}{dt} \]

4. **Evaluate Each Option**:
- **Option D**: \(-\frac{dA}{2dt}\) - This is correct for \(A\).
- **Option C**: \(\frac{dD}{dt}\) - This is correct for \(D\).
- **Option B**: \(-\frac{dB}{dt}\) - This is correct for \(B\).
- **Option A**: \(-\frac{dC}{3dt}\) - This is incorrect because \(C\) is a product and should have a positive sign.

5. **Conclusion**:
The option that does not express the reaction rate correctly is:
\[ \text{Answer: Option A: } -\frac{dC}{3dt} \]