Which of the following is not a disproprotionation reaction?
I. `NH_(4)NO_(3)overset(Delta)rarrN_(2)O+H_(2)O`
II. `P_(4)overset(Delta)rarrPH_(3)+HPO_(2)^(ө)`
III. `PCl_(5)overset(Delta)rarrPCl_(3)+Cl_(2)`
IV. `IO_(3)^(ө)+I^(ө)rarrI_(2)`

Options

A. `I,II`
B. `I,III,IV`
C. `II,IV`
D. `I,III`

Explanation

To determine which of the given reactions is not a disproportionation reaction, we need to analyze each reaction and check if the same element is undergoing both oxidation and reduction.

### Step-by-Step Solution:

1. **Understanding Disproportionation Reaction**:
A disproportionation reaction is a type of redox reaction where an element in a single oxidation state is simultaneously oxidized and reduced to form two different products with different oxidation states.

2. **Analyzing Reaction I**:
\[ NH_4NO_3 \overset{\Delta}{\rightarrow} N_2O + H_2O \]
- In ammonium nitrate (NH₄NO₃), nitrogen has an oxidation state of +1.
- In nitrous oxide (N₂O), the oxidation state of nitrogen is +1 as well.
- Since there is no change in the oxidation state of nitrogen, this reaction does not involve both oxidation and reduction.
- **Conclusion**: This is **not** a disproportionation reaction.

3. **Analyzing Reaction II**:
\[ P_4 \overset{\Delta}{\rightarrow} PH_3 + HPO_2^{\circ} \]
- In P₄, the oxidation state of phosphorus is 0.
- In phosphine (PH₃), the oxidation state of phosphorus is -3.
- In hypophosphorous acid (HPO₂), the oxidation state of phosphorus is +1.
- Here, phosphorus is being oxidized (from 0 to +1) and reduced (from 0 to -3).
- **Conclusion**: This is a disproportionation reaction.

4. **Analyzing Reaction III**:
\[ PCl_5 \overset{\Delta}{\rightarrow} PCl_3 + Cl_2 \]
- In phosphorus pentachloride (PCl₅), phosphorus has an oxidation state of +5.
- In phosphorus trichloride (PCl₃), phosphorus has an oxidation state of +3.
- Chlorine in Cl₂ has an oxidation state of 0.
- Here, phosphorus is reduced (from +5 to +3) but chlorine is not being oxidized and reduced simultaneously.
- **Conclusion**: This is **not** a disproportionation reaction.

5. **Analyzing Reaction IV**:
\[ IO_3^{-} + I^{-} \rightarrow I_2 \]
- In iodate (IO₃⁻), iodine has an oxidation state of +5.
- In iodide (I⁻), iodine has an oxidation state of -1.
- In I₂, the oxidation state of iodine is 0.
- Here, iodine is being reduced (from +5 to 0) and iodide is being oxidized (from -1 to 0).
- **Conclusion**: This is a disproportionation reaction.

### Final Conclusion:
The reactions that are **not** disproportionation reactions are:
- Reaction I: \( NH_4NO_3 \rightarrow N_2O + H_2O \)
- Reaction III: \( PCl_5 \rightarrow PCl_3 + Cl_2 \)

Thus, the correct answer is that the reactions that are **not** disproportionation reactions are **I and III**.