Which of the statement is/are true about the reactivity of halogenation of alkanes ? The reactivity ordar is `F_(2) gt C1_(2) gt Br_(2) gt I_(2)` .
I. Lower the activation energy for the chain initiation step, more reactive is the halogen.
II. Lower the activation energy for the first chain propagation step, more reactive is the halogen.
III. More negative is the overall heat of the reaction `(Delta H_(r)^(@))` of halogenation ofg alkane, more reactive is the halogen.
IV. Lower the activation energy for the second chain-propagation step, more reactives is the halogen.

Options

A. (a) (I), (II)
B. (b) (I), (II), (III)
C. (c) (II),(III)
D. (d) (II), (III), (IV)

Explanation

To determine which statements about the reactivity of halogenation of alkanes are true, we will analyze each statement based on the principles of the free radical mechanism of halogenation.

### Step-by-Step Solution:

1. **Understanding the Reactivity Order**:
The reactivity order for halogenation of alkanes is given as \( F_2 > Cl_2 > Br_2 > I_2 \). This indicates that fluorine is the most reactive halogen, while iodine is the least reactive.

2. **Analyzing Statement I**:
**Statement**: "Lower the activation energy for the chain initiation step, more reactive is the halogen."
- **Analysis**: The chain initiation step requires energy input (heat or light) to initiate the reaction. The activation energy for this step does not affect the reactivity of the halogen because we are supplying energy. Therefore, this statement is **false**.

3. **Analyzing Statement II**:
**Statement**: "Lower the activation energy for the first chain propagation step, more reactive is the halogen."
- **Analysis**: The first chain propagation step is the rate-determining step (RDS) of the reaction. A lower activation energy in this step means that the reaction can proceed more readily, making the halogen more reactive. Thus, this statement is **true**.

4. **Analyzing Statement III**:
**Statement**: "More negative is the overall heat of the reaction \((\Delta H_r^{(@)})\) of halogenation of alkane, more reactive is the halogen."
- **Analysis**: A more negative \(\Delta H_r\) indicates that the reaction is more exothermic, which generally correlates with higher reactivity. Therefore, this statement is **true**.

5. **Analyzing Statement IV**:
**Statement**: "Lower the activation energy for the second chain propagation step, more reactive is the halogen."
- **Analysis**: The second chain propagation step does not determine the overall reactivity of the halogen. The first propagation step is the critical one for determining reactivity. Thus, this statement is **false**.

### Conclusion:
Based on the analysis:
- **True Statements**: II and III
- **False Statements**: I and IV

Thus, the correct answer is that statements II and III are true.