For a particular reaction (A `rightarrow` B) the rate constant is 0.693 `min^-1` If the initial concentration of the reactant, A is 1 M, then the rate of reaction after 1 minute will be

Options

A. 0.35 M `min^(-1)`
B. 0.14 M `min^(-1)`
C. 0.693 M `min^(-1)`
D. 0.30 M `min^(-1)`

Answer

To solve the problem, we need to determine the rate of the reaction \( A \rightarrow B \) after 1 minute, given that the rate constant \( k \) is 0.693 min\(^{-1}\) and the initial concentration of \( A \) is 1 M.

### Step-by-Step Solution:

1. **Identify the Order of the Reaction:**
The unit of the rate constant \( k \) is min\(^{-1}\), which indicates that this is a first-order reaction. For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant.

2. **Write the Rate Law Expression:**
For a first-order reaction, the rate of reaction can be expressed as:
\[ \text{Rate} = k \cdot [A]^1 \]
where \( [A] \) is the concentration of reactant \( A \).

3. **Substitute the Given Values:**
We know that:
- \( k = 0.693 \, \text{min}^{-1} \)
- \( [A] = 1 \, \text{M} \)

Substituting these values into the rate law expression gives:
\[ \text{Rate} = 0.693 \, \text{min}^{-1} \cdot 1 \, \text{M} \]

4. **Calculate the Rate:**
\[ \text{Rate} = 0.693 \, \text{mol} \, \text{min}^{-1} \]

5. **Conclusion:**
Therefore, the rate of the reaction after 1 minute is \( 0.693 \, \text{mol} \, \text{min}^{-1} \).

### Final Answer:
The rate of reaction after 1 minute is \( 0.693 \, \text{mol} \, \text{min}^{-1} \).

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