Certainly! Let's solve for \(\Delta G_{\text{system}}\) using the provided data and the formula:
[tex]\[
\Delta G_{\text{system}} = \Delta H_{\text{system}} - T \Delta S_{\text{system}}
\][/tex]
Here is the step-by-step process:
1. Given Data:
- \(\Delta H_{\text{system}} = -232 \text{ kJ}\)
- \(T = 293 \text{ K}\)
- \(\Delta S_{\text{system}} = 195 \text{ J/K}\)
2. Convert \(\Delta S_{\text{system}}\) to kJ/K:
Since the entropy \(\Delta S_{\text{system}}\) is given in J/K and we need it in kJ/K to match the units of \(\Delta H_{\text{system}}\), we divide it by 1000.
[tex]\[
\Delta S_{\text{system}} = \frac{195 \text{ J/K}}{1000} = 0.195 \text{ kJ/K}
\][/tex]
3. Plug in the values into the formula:
[tex]\[
\Delta G_{\text{system}} = \Delta H_{\text{system}} - T \Delta S_{\text{system}}
\][/tex]
Substitute the values:
[tex]\[
\Delta G_{\text{system}} = (-232 \text{ kJ}) - (293 \text{ K}) \cdot (0.195 \text{ kJ/K})
\][/tex]
4. Calculate \( T \Delta S_{\text{system}} \):
[tex]\[
293 \text{ K} \cdot 0.195 \text{ kJ/K} = 57.135 \text{ kJ}
\][/tex]
5. Finish the calculation:
[tex]\[
\Delta G_{\text{system}} = -232 \text{ kJ} - 57.135 \text{ kJ} = -289.135 \text{ kJ}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\Delta G_{\text{system}} = -289.135 \text{ kJ}
\][/tex]
Among the given options, the closest and correct answer is:
[tex]\[
\boxed{-289 \text{ kJ}}
\][/tex]
