Question

A vessel contains 1 mol of gas A and 2 mol of gas B at 2 bar and 25°C. The gas mixture is compressed such that the final pressure becomes 3 bar without any change in temperature. Considering ideal gas behaviour, the change in Gibbs free energy (in kJ) during the compression is closest to

• A. 1
• B. 3
• C. 6
• D. 9

Hint:

The Gibbs free energy change for an ideal gas during an isothermal compression or expansion can be calculated using the formula involving pressure and temperature.

Answer 1

The Correct Option is B

Step 1: Using the Gibbs free energy formula.
The change in Gibbs free energy for an ideal gas during an isothermal process is given by: \[ \Delta G = nRT \ln \frac{P_f}{P_i} \] where \( n \) is the total number of moles, \( R \) is the gas constant, \( T \) is the temperature, \( P_f \) is the final pressure, and \( P_i \) is the initial pressure.
Step 2: Given data.
- Initial pressure, \( P_i = 2 \, \text{bar} \)
- Final pressure, \( P_f = 3 \, \text{bar} \)
- Total moles, \( n = 1 + 2 = 3 \, \text{mol} \)
- \( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \)
- Temperature, \( T = 25^\circ \text{C} = 298 \, \text{K} \)
Step 3: Calculation.
Now we can substitute the values into the equation: \[ \Delta G = 3 \times 8.314 \times 298 \times \ln \left( \frac{3}{2} \right) \] \[ \Delta G \approx 3 \times 8.314 \times 298 \times 0.4055 \approx 3 \times 8.314 \times 120.5 \approx 3000 \, \text{J} = 3 \, \text{kJ} \] Step 4: Conclusion.
The change in Gibbs free energy during the compression is closest to 3 kJ. Final Answer: \[ \boxed{3 \, \text{kJ}} \]