Rate constant in case of first order reaction is

Options

A. inversely proportional to the concentration units
B. independent of concentration units
C. directly proportional to concentration units
D. inversely proportional to the square of concentration units.

Answer

To find the rate constant in the case of a first-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Rate Constant**:
The rate constant (k) is a proportionality constant that relates the rate of a chemical reaction to the concentration of the reactants. For a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant.

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

3. **Identify the Units of Rate and Concentration**:
- The unit of rate is typically expressed in terms of concentration change over time, which is:
\[ \text{Rate} = \frac{\text{mol}}{\text{L} \cdot \text{s}} \]
- The unit of concentration [A] is:
\[ \text{mol/L} \]

4. **Rearrange the Rate Law to Solve for k**:
From the rate law, we can rearrange it to find k:
\[ k = \frac{\text{Rate}}{[A]} \]

5. **Substitute the Units into the Equation**:
Substituting the units into the equation gives:
\[ k = \frac{\frac{\text{mol}}{\text{L} \cdot \text{s}}}{\frac{\text{mol}}{\text{L}}} \]

6. **Simplify the Units**:
When we simplify the units, we find:
\[ k = \frac{\text{mol}}{\text{L} \cdot \text{s}} \times \frac{\text{L}}{\text{mol}} = \frac{1}{\text{s}} \]
Therefore, the unit of the rate constant (k) for a first-order reaction is:
\[ k = \text{s}^{-1} \]

7. **Conclusion**:
The rate constant for a first-order reaction is independent of the concentration units and only depends on the time factor.

### Final Answer:
The rate constant in the case of a first-order reaction is independent of concentration units and has the unit of \( \text{s}^{-1} \).

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