Calculate the temperature at which `DeltaG=-5.2 kJ``mol^-1`,DeltaH=145.6kJ``mol^-1` and `DeltaS=216 JK^-1` `mol^-1` for a chemical reaction

Options

A. `698^@ C`
B. `425^@C`
C. `650^@`
D. `550^@C`

Explanation

To calculate the temperature at which the Gibbs free energy change (ΔG) is -5.2 kJ/mol, given ΔH = 145.6 kJ/mol and ΔS = 216 J/K·mol, we can use the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

### Step-by-step Solution:

1. **Convert Units**:
- Convert ΔG from kJ to J:
\[ \Delta G = -5.2 \text{ kJ/mol} = -5200 \text{ J/mol} \]
- ΔH is already in kJ, but we will convert it to J for consistency:
\[ \Delta H = 145.6 \text{ kJ/mol} = 145600 \text{ J/mol} \]
- ΔS is given in J/K·mol, so it remains the same:
\[ \Delta S = 216 \text{ J/K·mol} \]

2. **Substitute Values into the Gibbs Free Energy Equation**:
\[ -5200 = 145600 - T \times 216 \]

3. **Rearrange the Equation to Solve for T**:
\[ T \times 216 = 145600 + 5200 \]
\[ T \times 216 = 150800 \]

4. **Calculate T**:
\[ T = \frac{150800}{216} \]
\[ T \approx 696.3 \text{ K} \]

5. **Final Answer**:
The temperature at which the reaction occurs is approximately:
\[ T \approx 696.3 \text{ K} \]