For the first order reaction half-life time is ………….. on the initial concentration.

Answer

### Step-by-Step Solution:

1. **Understanding Half-Life in Chemical Kinetics**:
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.

2. **General Formula for Half-Life**:
For a reaction of order n, the half-life can be expressed as:
\[ T_{half} \propto \frac{1}{[A]^{n-1}} \]
where [A] is the initial concentration of the reactant.

3. **Applying to First Order Reactions**:
For a first-order reaction, n = 1. Substituting this value into the formula gives:
\[ T_{half} \propto \frac{1}{[A]^{1-1}} = \frac{1}{[A]^0} = 1 \]
Since any number raised to the power of 0 is 1, this indicates that the half-life is independent of the initial concentration.

4. **Mathematical Expression for First Order Half-Life**:
The specific mathematical expression for the half-life of a first-order reaction is:
\[ T_{half} = \frac{0.693}{k} \]
where k is the rate constant of the reaction. Notice that there is no concentration term in this expression.

5. **Conclusion**:
Therefore, we conclude that the half-life of a first-order reaction is independent of the initial concentration of the reactant.

### Final Answer:
For a first-order reaction, the half-life time is independent of the initial concentration.

---