Determine which of the following reactions taking place at constant pressure represents system that do work on the surrounding environment
(I)`Ag^(+)(aq)+Cl^(-)(aq)rarrAgCl(s)" (II) ``NH_(4)Cl(s)rarrNH_(3)(g)+HCl(g) "
(III) 2NH_(3)(g)rarrN_(2)(g)+3H_(2)(g)`

Options

A. I
B. III
C. II and III
D. I and II

Explanation

To determine which of the given reactions at constant pressure represents a system that does work on the surrounding environment, we need to analyze the change in the number of gaseous moles (Δn_g) for each reaction. The work done by the system can be expressed as:

\[ W = -P \Delta V \]

At constant pressure, this can also be related to the change in the number of moles of gas:

\[ W = -\Delta n_g RT \]

Where:
- \( W \) = work done by the system
- \( P \) = pressure (constant)
- \( \Delta V \) = change in volume
- \( R \) = universal gas constant
- \( T \) = temperature
- \( \Delta n_g \) = change in the number of gaseous moles (moles of products - moles of reactants)

Now, let's analyze each reaction one by one.

### Reaction I:
\[ \text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s) \]

- **Reactants:** 0 moles of gas (both are aqueous)
- **Products:** 0 moles of gas (solid)
- **Δn_g = 0 - 0 = 0**

Since there is no change in the number of gaseous moles, the work done \( W = -\Delta n_g RT = 0 \). Therefore, this reaction does not do work on the surroundings.

### Reaction II:
\[ \text{NH}_4\text{Cl}(s) \rightarrow \text{NH}_3(g) + \text{HCl}(g) \]

- **Reactants:** 0 moles of gas (solid)
- **Products:** 2 moles of gas (1 mole of NH₃ and 1 mole of HCl)
- **Δn_g = 2 - 0 = 2**

Since there is a change in the number of gaseous moles, the work done \( W = -\Delta n_g RT = -2RT \). Thus, this reaction does work on the surroundings.

### Reaction III:
\[ 2\text{NH}_3(g) \rightarrow \text{N}_2(g) + 3\text{H}_2(g) \]

- **Reactants:** 2 moles of gas (2 moles of NH₃)
- **Products:** 4 moles of gas (1 mole of N₂ and 3 moles of H₂)
- **Δn_g = 4 - 2 = 2**

Again, there is a change in the number of gaseous moles, so the work done \( W = -\Delta n_g RT = -2RT \). Thus, this reaction also does work on the surroundings.

### Conclusion:
From the analysis, we find that:
- Reaction I does not do work (Δn_g = 0).
- Reaction II does work (Δn_g = 2).
- Reaction III does work (Δn_g = 2).

Thus, the reactions that do work on the surrounding environment are **II and III**.

### Final Answer:
The reactions that do work on the surrounding environment are:
**II and III.**