To find the value of ΔG (Gibbs free energy) at 141.0°C for the formation of phosphorus trichloride (PCI3) from its constituent elements (P2 and Cl2), you can use the equation:
ΔG = ΔH - TΔS
Where:
ΔH = Enthalpy change
ΔS = Entropy change
T = Temperature in Kelvin
Given the values at 25.0°C (298.15 K):
ΔH = -720.5 kJ/mol
ΔG° = -642.9 kJ/mol
ΔS° = -263.7 J/K
First, convert ΔH and ΔS to J/mol to match the units of ΔS°:
ΔH = -720.5 kJ/mol = -720,500 J/mol
Now, calculate ΔG at 141.0°C (141.0°C + 273.15 K = 414.15 K):
ΔG = ΔH - TΔS
ΔG = (-720,500 J/mol) - (414.15 K)(-263.7 J/K)
ΔG = -720,500 J/mol + 109,427.755 J
ΔG ≈ -611,072.245 J/mol
Now, convert the result back to kJ/mol:
ΔG ≈ -611.072245 kJ/mol
So, at 141.0°C, the value of ΔG for the formation of phosphorus trichloride from its constituent elements is approximately -611.1 kJ/mol.