The rate constant of a first order reaction is `3 xx 10^(-6)` per second. If the initial concentration is `0.10 M`, the initial rate of reaction is

Options

A. `3 times 10^-5 Ms^-1`
B. `3 times 10^-6 Ms^-1`
C. `3 times 10^-7 Ms^-1`
D. `3 times 10^-8 Ms^-1`

Answer

To find the initial rate of a first-order reaction given the rate constant and the initial concentration, we can use the following formula:

**Step 1: Understand the formula for the rate of a first-order reaction.**
The rate of a first-order reaction can be expressed as:
\[ \text{Rate} = k[A] \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of the reactant.

**Step 2: Identify the given values.**
From the question, we have:
- Rate constant, \( k = 3 \times 10^{-6} \, \text{s}^{-1} \)
- Initial concentration, \( [A] = 0.10 \, \text{M} \)

**Step 3: Substitute the values into the formula.**
Now, we can substitute the values into the rate equation:
\[ \text{Rate} = (3 \times 10^{-6} \, \text{s}^{-1}) \times (0.10 \, \text{M}) \]

**Step 4: Perform the multiplication.**
Calculating the above expression:
\[ \text{Rate} = 3 \times 10^{-6} \times 0.10 = 3 \times 10^{-7} \, \text{M/s} \]

**Step 5: State the final answer.**
Thus, the initial rate of the reaction is:
\[ \text{Rate} = 3 \times 10^{-7} \, \text{M/s} \]

**Conclusion:**
The correct answer is \( 3 \times 10^{-7} \, \text{M/s} \), which corresponds to option 3.

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