Consider the following conversions:
(i) `O_((g))+e^(-) to O_((g))^(-),DeltaH_(1)`
(ii) `F_((g))+e^(-) to F_((g))^(-),DeltaH_(2)`
(iii) `Cl_((g))+e^(-) to Cl_((g))^(-),DeltaH_(3)`
(iv) `O_((g))^(-) +e^(-) to O_((g))^(2-),DeltaH_(4)`
the according to given information the incorrect statement is :

Options

A. `DeltaH_(3)` is more negative than `DeltaH_(1) and DeltaH_(2)`
B. `DeltaH_(1)` is less negative than `DeltaH_(2)`
C. `DeltaH_(1),DeltaH_(2) and DeltaH_(3)` are negative whereas `DeltaH_(4)` is positive
D. `DeltaH_(1) and DeltaH_(3)` are negative whereas `DeltaH_(2) and DeltaH_(4)` positive

Explanation

To solve the problem, we need to analyze the given conversions and their corresponding electron gain enthalpies (ΔH). The conversions are as follows:

1. \( O(g) + e^- \rightarrow O(g)^- \) with ΔH1
2. \( F(g) + e^- \rightarrow F(g)^- \) with ΔH2
3. \( Cl(g) + e^- \rightarrow Cl(g)^- \) with ΔH3
4. \( O(g)^- + e^- \rightarrow O(g)^{2-} \) with ΔH4

### Step-by-Step Solution:

**Step 1: Understand Electron Gain Enthalpy**
- Electron gain enthalpy is the energy change when an electron is added to a neutral atom in the gas phase. It is usually negative because energy is released when an electron is added.

**Step 2: Analyze the Given Reactions**
- For reactions (i), (ii), and (iii), we are adding an electron to neutral atoms (O, F, Cl) to form anions (O^-, F^-, Cl^-). These processes release energy, hence ΔH1, ΔH2, and ΔH3 are negative.
- For reaction (iv), we are adding an electron to an anion (O^-) to form O^{2-}. This process requires energy to overcome electron-electron repulsion, making ΔH4 positive.

**Step 3: Compare the Electron Gain Enthalpies**
- The general trend for electron gain enthalpy is that it becomes more negative as we move from left to right across a period. However, there are exceptions due to atomic size and electron repulsion.
- The order of electron gain enthalpies based on the elements is:
- ΔH3 (Cl) < ΔH2 (F) < ΔH1 (O)
- This means ΔH3 is more negative than ΔH2 and ΔH1.

**Step 4: Summarize the Key Points**
- ΔH1, ΔH2, and ΔH3 are negative.
- ΔH4 is positive.
- The order of negativity for ΔH is: ΔH3 < ΔH2 < ΔH1.

**Step 5: Identify the Incorrect Statement**
- The statements to analyze are:
1. ΔH3 is more negative than ΔH1 and ΔH2. (Correct)
2. ΔH1 is less negative than ΔH2. (Correct)
3. ΔH1, ΔH2, and ΔH3 are negative, while ΔH4 is positive. (Correct)
4. ΔH1 and ΔH3 are negative, and ΔH4 is positive. (Incorrect, as ΔH4 is the only positive one.)

### Conclusion:
The incorrect statement is option 4.