For the reaction A + H2O → products, find the rate of the reaction when [A] = 0.75 M, k= 0.02.

Options

A. `0.077 S^(-1)`
B. `0.085 S^(-1)`
C. `0.015 S^(-1)`
D. `0.045 S^(-1)`

Answer

To solve the problem, we need to calculate the rate of the reaction given the concentration of reactant A and the rate constant k. The reaction is given as:

\[ A + H_2O \rightarrow \text{products} \]

### Step-by-Step Solution:

1. **Identify the Rate Law**:
For the reaction, the rate can be expressed using the rate law for a first-order reaction:
\[ \text{Rate} = k \cdot [A] \]
where \( k \) is the rate constant and \([A]\) is the concentration of reactant A.

2. **Substitute the Given Values**:
We are given:
- \([A] = 0.75 \, \text{M}\)
- \(k = 0.02 \, \text{s}^{-1}\)

Now, substitute these values into the rate equation:
\[ \text{Rate} = 0.02 \, \text{s}^{-1} \cdot 0.75 \, \text{M} \]

3. **Calculate the Rate**:
Multiply the values:
\[ \text{Rate} = 0.02 \times 0.75 = 0.015 \, \text{M/s} \]

4. **Final Answer**:
The rate of the reaction is:
\[ \text{Rate} = 0.015 \, \text{M/s} \]