For the precipitation of AgCl by `Ag^(+)` ions and HCl

Options

A. `Delta H = 0`
B. `Delta G = 0`
C. `Delta G = -ve`
D. `Delta H = Delta G`

Explanation

To solve the problem of determining the conditions under which AgCl can be precipitated from Ag⁺ ions and HCl, we need to analyze the thermodynamics of the reaction. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Reaction
The precipitation of silver chloride (AgCl) occurs when silver ions (Ag⁺) react with chloride ions (Cl⁻) from HCl. The reaction can be represented as:
\[ \text{Ag}^+ + \text{Cl}^- \rightarrow \text{AgCl (s)} \]

### Step 2: Determine Spontaneity
For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative:
\[ \Delta G < 0 \]

### Step 3: Use the Gibbs Free Energy Equation
The Gibbs free energy change is related to the enthalpy change (ΔH) and the entropy change (ΔS) by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step 4: Analyze the Options
1. **Option A: ΔH = 0**
If ΔH = 0, then ΔG = -TΔS. For ΔG to be negative, ΔS must be positive. This means the reaction can be spontaneous if ΔS is positive.

2. **Option B: ΔG = 0**
If ΔG = 0, the reaction is at equilibrium, meaning no net precipitation occurs. This option is not favorable for precipitation.

3. **Option C: ΔG < 0**
This is the condition for spontaneity. If ΔG is negative, the reaction is favorable for precipitation.

4. **Option D: ΔH = ΔG**
If ΔH = ΔG, then ΔS must be zero (since ΔG = ΔH - TΔS). This means there is no change in entropy, which is not favorable for precipitation.

### Conclusion
The correct option for the precipitation of AgCl in the presence of Ag⁺ ions and HCl is **Option C: ΔG < 0**, indicating that the reaction is spontaneous.