what is the Gibbs free energy change when 62 g of methane undergoes a pressure change from 0.5 bar to 5.2 bar at 298 k?

Answer 1

To calculate the change in Gibbs free energy (ΔG) when 62 g of methane (CH4) undergoes a pressure change from 0.5 bar to 5.2 bar at a temperature of 298 K, we use the formula:

ΔG = nRT ln(P2/P1)

where n is the number of moles of the gas, R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, P1 and P2 are the initial and final pressures, respectively.

1. Calculate the number of moles of methane:
2. Molar mass of CH4 = 16.04 g/mol
3. Mass of CH4 = 62 g
4. n = mass / molar mass = 62 g / 16.04 g/mol ≈ 3.866 mol
5. Using the formula for ΔG: ΔG = 3.866 mol × 8.314 J/mol·K × 298 K × ln(5.2/0.5)
6. Calculate ln(5.2/0.5) ≈ ln(10.4) ≈ 2.341
7. Then calculate ΔG: ΔG = 3.866 × 8.314 × 298 × 2.341 ≈ 19263 J

Thus, the change in Gibbs free energy for this process is approximately 19263 J (or about 19.263 kJ).