At 298K, Go = -141.8 kJ for the reaction
2 SO2 + O2 in equilibrium with 2 SO3
Calculate the change in Gibbs free energy (in kJ) at the same temperature when P (SO2) = 0.505 bar, P (O2) = 0.80 bar and P (SO3) = 1.317 bar. (R = 8.314 J/K mol)
2. An aluminum bar is 2 m long at a temperature of 20° C. What will be the length of the bar at a temperature of 100 C
To calculate the change in Gibbs free energy at the given temperature and pressure conditions, we can use the equation:
ΔG = ΔGo + RT ln(Q)
Where:
- ΔG is the change in Gibbs free energy
- ΔGo is the standard Gibbs free energy change at standard conditions (298K)
- R is the gas constant (8.314 J/K mol)
- T is the temperature in Kelvin
- Q is the reaction quotient
First, we need to calculate the reaction quotient, Q, using the given partial pressures of the reactants and products. But before we do that, let's convert the given temperatures to Kelvin:
298K = 298 + 273 = 571K
Now, let's calculate Q:
Q = (P(SO3)^2) / (P(SO2)^2 * P(O2))
= (1.317 bar)^2 / ((0.505 bar)^2 * (0.80 bar))
= (1.738229 bar^2) / (0.202025 bar^2)
= 8.598
Now, we can use the equation ΔG = ΔGo + RT ln(Q) to calculate the change in Gibbs free energy.
ΔG = (-141.8 kJ) + (8.314 J/mol K * 571 K * ln(8.598))
Let's solve this using the given values:
ΔG ≈ -141.8 kJ + (8.314 J/mol K * 571 K * ln(8.598))
≈ -141.8 kJ + (8.314 * 571 * 2.152)
≈ -141.8 kJ + 8004.179 kJ
≈ 7862.379 kJ
Therefore, the change in Gibbs free energy at the given temperature and pressure conditions is approximately 7862.379 kJ.