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What is [tex]\Delta G_{\text{system}}[/tex] for the system described by the following data?

[tex]\[
\begin{array}{l}
\Delta H_{\text{system}} = -232 \text{ kJ} \\
T = 293 \text{ K} \\
\Delta S_{\text{system}} = 195 \text{ J/K} \\
\Delta G_{\text{system}} = \Delta H_{\text{system}} - T \Delta S_{\text{system}}
\end{array}
\][/tex]

A. \(-289 \text{ kJ}\)
B. \(-175 \text{ kJ}\)
C. \(256 \text{ kJ}\)
D. [tex]\(56,903 \text{ kJ}\)[/tex]



Answer :

GinnyAnswer
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]

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