For a relatively fast reaction, the rate constant is relatively………….and half-change time is relatively…………. .

Answer

To solve the question, we need to understand the relationship between the rate constant (k), the rate of reaction, and the half-life (t_half) of a reaction.

### Step-by-Step Solution:

1. **Understanding Reaction Rate**:
- The rate of a chemical reaction is often expressed in terms of the rate constant (k). For a reaction to be classified as "fast," it means that the reaction proceeds quickly, which implies a high rate.

2. **Relationship Between Rate and Rate Constant**:
- The rate of a reaction is directly proportional to the rate constant (k). Therefore, for a relatively fast reaction, the rate constant (k) must be relatively **large**.

3. **Understanding Half-Life**:
- The half-life (t_half) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration.

4. **Relationship Between Rate and Half-Life**:
- The half-life is inversely proportional to the rate of reaction. This means that as the rate of reaction increases (for a fast reaction), the half-life decreases. Therefore, for a relatively fast reaction, the half-life (t_half) must be relatively **small**.

5. **Final Answer**:
- For a relatively fast reaction, the rate constant is relatively **large** and the half-life is relatively **small**.

### Summary of the Answer:
- Rate constant (k): **Large**
- Half-life (t_half): **Small**