Which of the following is/are correct about the first order reaction ?

Options

A.
B.
C. Half life depends on temperature.
D. Rate constant is directly proportional to temperature.

Answer

To determine which statements are correct about first-order reactions, we can analyze each option based on the principles of chemical kinetics.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
- A first-order reaction is characterized by a rate that is directly proportional to the concentration of one reactant. The rate law can be expressed as:
\[ \text{Rate} = k[A] \]
where \( k \) is the rate constant and \([A]\) is the concentration of the reactant.

2. **Analyzing Option A**:
- **Statement**: "The rate of reaction decreases with time."
- As the reaction proceeds, the concentration of the reactant decreases, leading to a decrease in the rate of reaction. Thus, this statement is **correct**.

3. **Analyzing Option B**:
- **Statement**: "Concentration of the reactant decreases with time."
- In a first-order reaction, the concentration of the reactant decreases over time as it is converted into products. Therefore, this statement is also **correct**.

4. **Analyzing Option C**:
- **Statement**: "Half-life depends on temperature."
- The half-life (\( t_{1/2} \)) for a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
Since the rate constant \( k \) depends on temperature (as described by the Arrhenius equation), the half-life also depends on temperature. Thus, this statement is **correct**.

5. **Analyzing Option D**:
- **Statement**: "Rate constant is directly proportional to temperature."
- The rate constant \( k \) is related to temperature through the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
This indicates that \( k \) is not directly proportional to temperature; rather, it is exponentially related to temperature. Therefore, this statement is **incorrect**.

### Conclusion:
The correct options regarding first-order reactions are **A, B, and C**. Option D is incorrect.

### Final Answer:
- Correct options: **A, B, C**.