The `Delta G` in the process of melting of Ice at `-15^(@) C` is

Options

A. `Delta G lt 0`
B. `Delta G gt 0`
C. `Delta G = 0`
D. All of these

Answer

To determine the change in Gibbs free energy (ΔG) for the melting of ice at -15°C, we can follow these steps:

### Step 1: Understand the Gibbs Free Energy Equation
The Gibbs free energy change (ΔG) is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step 2: Convert Temperature to Kelvin
The temperature given is -15°C. To convert this to Kelvin:
\[ T(K) = -15 + 273.15 = 258.15 \, K \]

### Step 3: Analyze the Process of Melting Ice
Melting ice is an endothermic process, meaning it requires heat. Therefore, the change in enthalpy (ΔH) for melting ice is positive.

### Step 4: Consider the Change in Entropy
When ice melts, the entropy (ΔS) increases because the solid structure of ice becomes the more disordered liquid water. Thus, ΔS is also positive.

### Step 5: Evaluate the Dominance of Terms in the ΔG Equation
At low temperatures (like -15°C or 258.15 K), the term \( T \Delta S \) may not be large enough to offset the positive ΔH. Since ΔH is positive and dominates, we can expect that ΔG will also be positive.

### Step 6: Conclusion about ΔG
Since ΔG is positive, the process of melting ice at -15°C is non-spontaneous. Therefore, we conclude:
\[ \Delta G > 0 \]

### Final Answer
The change in Gibbs free energy (ΔG) for the melting of ice at -15°C is positive, indicating that the process is non-spontaneous.

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