`{:("Column-I (F.R.Favourable)","COlumn-II"),((A) H_(2(g)) + I_(2(g)) hArr 2HI_((g)) + Q,(P)"High temperature"),((B) 2SO_(2(g)) + O_(2(g)) hArr 2SO_(3(g)) + Q,(Q)"Low temperature "),((C) 2NH_(3(g)) hArr N_(2(g)) + 3H_(2(g)) - Q,(R)"High pressure"),((D) PCl_(5(g)) hArr PCl_(3(g)) + Cl_(2(g)) - Q,(S)"Low pressure"):}`

Answer

To solve the problem, we will analyze each reaction in Column-I and determine the conditions from Column-II that favor the forward reaction. We will consider the effects of temperature and pressure based on the nature of the reaction (exothermic or endothermic) and the change in the number of moles of reactants and products.

### Step-by-Step Solution:

1. **Reaction A: \( H_2(g) + I_2(g) \rightleftharpoons 2HI(g) + Q \)**
- **Nature of Reaction**: This reaction is exothermic (releases heat).
- **Change in Moles**: There is no change in the number of moles (2 moles of reactants and 2 moles of products).
- **Temperature Effect**: For exothermic reactions, low temperature favors the forward reaction.
- **Pressure Effect**: Since there is no change in moles, pressure has no effect.
- **Conclusion**: The favorable condition is **(Q) Low temperature**.

2. **Reaction B: \( 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) + Q \)**
- **Nature of Reaction**: This reaction is exothermic.
- **Change in Moles**: There are 3 moles of reactants (2 SO₂ + 1 O₂) and 2 moles of products (2 SO₃).
- **Temperature Effect**: For exothermic reactions, low temperature favors the forward reaction.
- **Pressure Effect**: Increasing pressure favors the direction with fewer moles (from 3 moles to 2 moles).
- **Conclusion**: The favorable conditions are **(R) High pressure** and **(Q) Low temperature**.

3. **Reaction C: \( 2NH_3(g) \rightleftharpoons N_2(g) + 3H_2(g) - Q \)**
- **Nature of Reaction**: This reaction is endothermic (absorbs heat).
- **Change in Moles**: There are 2 moles of reactants (2 NH₃) and 4 moles of products (1 N₂ + 3 H₂).
- **Temperature Effect**: For endothermic reactions, high temperature favors the forward reaction.
- **Pressure Effect**: Increasing pressure favors the direction with fewer moles (from 4 moles to 2 moles), thus low pressure favors the forward reaction.
- **Conclusion**: The favorable conditions are **(S) Low pressure** and **(P) High temperature**.

4. **Reaction D: \( PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) - Q \)**
- **Nature of Reaction**: This reaction is endothermic.
- **Change in Moles**: There is a change from 1 mole of reactant (PCl₅) to 2 moles of products (PCl₃ + Cl₂).
- **Temperature Effect**: For endothermic reactions, high temperature favors the forward reaction.
- **Pressure Effect**: Increasing pressure favors the direction with fewer moles (from 2 moles to 1 mole), thus low pressure favors the forward reaction.
- **Conclusion**: The favorable conditions are **(S) Low pressure** and **(P) High temperature**.

### Final Matching:
- A → Q (Low temperature)
- B → R (High pressure) and Q (Low temperature)
- C → S (Low pressure) and P (High temperature)
- D → S (Low pressure) and P (High temperature)