What is the concentration of the reactant in a first order reaction when the rate of the reaction is 0.6 s-1 and the rate constant is 0.035?

Options

A. 26.667 M
B. 17.143 M
C. 26.183 M
D. 17.667 M

Answer

To find the concentration of the reactant in a first-order reaction given the rate of the reaction and the rate constant, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Rate of the reaction (r) = 0.6 s⁻¹
- Rate constant (k) = 0.035 s⁻¹

2. **Write the Rate Law for a First-Order Reaction**:
For a first-order reaction, the rate law is given by:
\[ \text{Rate} = k \times [A] \]
where [A] is the concentration of the reactant.

3. **Rearrange the Rate Law to Solve for Concentration**:
We can rearrange the equation to find the concentration of the reactant:
\[ [A] = \frac{\text{Rate}}{k} \]

4. **Substitute the Given Values into the Equation**:
Now, substitute the values of the rate and the rate constant into the equation:
\[ [A] = \frac{0.6 \, \text{s}^{-1}}{0.035 \, \text{s}^{-1}} \]

5. **Calculate the Concentration**:
Performing the calculation:
\[ [A] = \frac{0.6}{0.035} \approx 17.143 \, \text{M} \]

6. **Conclusion**:
The concentration of the reactant is approximately 17.143 M.

### Final Answer:
The concentration of the reactant is **17.143 M**.