`A+ 2B rarr C+D." If "-(d[A])/(dt)=5xx10^(-4)" mol L"^(-1) s^(-1)," then "-(d[B])/(dt)` is :

Options

A. `2.5xx10^(-4)" mol L"^(-1) s^(-1)`
B. `5.0xx10^(-4)" mol L"^(-1) s^(-1)`
C. `2.5xx10^(-3)" mol L"^(-1) s^(-1)`
D. `1.0xx10^(-3)" mol L"^(-1) s^(-1)`

Explanation

To solve the problem, we need to analyze the given reaction and apply the concepts of chemical kinetics.

### Step-by-Step Solution:

1. **Understand the Reaction**: The reaction is given as:
\[ A + 2B \rightarrow C + D \]
This indicates that for every 1 mole of A that reacts, 2 moles of B are consumed.

2. **Identify the Rate of Disappearance of A**: We are given that the rate of disappearance of A is:
\[ -\frac{d[A]}{dt} = 5 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

3. **Relate the Rates of Disappearance**: From the stoichiometry of the reaction, we can relate the rates of disappearance of A and B. The relationship can be expressed as:
\[ -\frac{d[B]}{dt} = \frac{2}{1} \left(-\frac{d[A]}{dt}\right) \]
This means that for every mole of A that disappears, 2 moles of B disappear.

4. **Substitute the Known Rate**: Now, substituting the known rate of disappearance of A into the equation:
\[ -\frac{d[B]}{dt} = 2 \left(5 \times 10^{-4}\right) \]

5. **Calculate the Rate of Disappearance of B**:
\[ -\frac{d[B]}{dt} = 10 \times 10^{-4} = 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \]

6. **Final Answer**: Therefore, the rate of disappearance of B is:
\[ -\frac{d[B]}{dt} = 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \]