Which of these changes with time for a first-order reaction
A Rate of reaction B . Rate constant
C . Half-life

Options

A. A only
B. C only
C. A and B only
D. B and C only

Answer

To solve the question of which of the following changes with time for a first-order reaction, we will analyze each option one by one.

### Step-by-Step Solution:

1. **Understanding Rate of Reaction (Option A)**:
- For a first-order reaction, the rate of reaction (R) is given by the equation:
\[ R = k[A] \]
where \( k \) is the rate constant and \([A]\) is the concentration of the reactant.
- As the reaction proceeds, the concentration of the reactant \([A]\) decreases over time. Therefore, the rate of reaction also decreases as time progresses.
- Hence, the rate of reaction changes with time.

2. **Understanding Rate Constant (Option B)**:
- The rate constant \( k \) for a reaction is a value that is specific to the reaction at a given temperature. It does not change with time.
- The rate constant is only affected by changes in temperature or the presence of a catalyst, but not by the progression of the reaction.
- Therefore, the rate constant does not change with time.

3. **Understanding Half-Life (Option C)**:
- The half-life (\( t_{1/2} \)) for a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
- For first-order reactions, the half-life is independent of the initial concentration of the reactant and remains constant as long as the rate constant \( k \) does not change.
- Thus, the half-life does not change with time.

### Conclusion:
From the analysis above, we can conclude that:
- **Rate of Reaction (Option A)** changes with time.
- **Rate Constant (Option B)** does not change with time.
- **Half-Life (Option C)** does not change with time.

Thus, the correct answer is **A. Rate of Reaction**.