The concept of `t_(1/2)` is useful for the reactions of

Options

A. zero order
B. first order
C. second order
D. all orders

Answer

To solve the question regarding the usefulness of the concept of half-life (t_(1/2)) in chemical kinetics, we will analyze the half-life expressions for different orders of reactions.

### Step-by-Step Solution:

1. **Understanding Half-Life (t_(1/2))**:
- The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. It is a crucial concept in kinetics as it helps in understanding the rate of reaction.

2. **Half-Life for Different Orders of Reactions**:
- **Zero-Order Reactions**:
- The half-life is given by the formula:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
- Here, [A]_0 is the initial concentration and k is the rate constant. The half-life depends on the initial concentration.

- **First-Order Reactions**:
- The half-life is constant and given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
- This indicates that the half-life does not depend on the initial concentration, making it a key feature of first-order kinetics.

- **Second-Order Reactions**:
- The half-life is given by:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
- This shows that the half-life is inversely proportional to the initial concentration.

- **Higher-Order Reactions**:
- For reactions of order n (where n > 2), the half-life expressions become more complex and generally depend on the initial concentration.

3. **Conclusion**:
- The concept of half-life is useful for all types of reactions (zero, first, second, and higher orders). However, it is particularly significant for first-order reactions because the half-life is independent of the initial concentration, making it a constant value.

### Final Answer:
The concept of t_(1/2) is useful for all types of reactions, but it is especially useful for first-order reactions due to its constant nature.

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