For the reaction `2A+B to 2C+D` which of the following does not express reaction rate?

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the Reaction**: The reaction is \(2A + B \rightarrow 2C + D\). Here, \(A\) and \(B\) are the reactants, while \(C\) and \(D\) are the products.

2. **Define Reaction Rate**: 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:
\[ \text{Rate} = -\frac{d[A]}{dt} = -\frac{1}{2}\frac{d[B]}{dt} = \frac{1}{2}\frac{d[C]}{dt} = \frac{d[D]}{dt} \]
Here, the negative sign indicates the decrease in concentration of reactants, while the positive sign indicates the increase in concentration of products.

3. **Analyze Each Option**:
- **Option 1**: \(-\frac{dD}{dt}\) - This represents the rate of disappearance of product \(D\). Since \(D\) is a product, its concentration increases over time, thus this expression does not correctly represent the rate of the reaction.
- **Option 2**: \(-\frac{dC}{dt}\) - This represents the rate of disappearance of product \(C\). Since \(C\) is a product, its concentration also increases, making this expression incorrect for the rate of reaction.
- **Option 3**: \(-\frac{dB}{dt}\) - This represents the rate of disappearance of reactant \(B\). This is a valid expression for the rate of the reaction as \(B\) is a reactant.
- **Option 4**: \(\frac{dD}{dt}\) - This represents the rate of appearance of product \(D\). This is a valid expression for the rate of the reaction as \(D\) is a product.

4. **Conclusion**: The expressions that do not correctly express the reaction rate are \(-\frac{dC}{dt}\) and \(-\frac{dD}{dt}\). However, since the question asks for one option, the most appropriate answer is \(-\frac{dC}{dt}\) since it directly relates to a product.

### Final Answer:
The expression that does not express the reaction rate is **\(-\frac{dC}{dt}\)**.