(a) To calculate the AS at 298 K, we can use the Gibbs-Helmholtz equation:
ΔG = ΔH - TΔS
Rearranging this equation to solve for ΔS, we get:
ΔS = (ΔH - ΔG) / T
Substituting the given values, we get:
ΔS = (-220 kJ/mol - (-206 kJ/mol)) / (298 K) = -0.47 kJ/(mol K)
Therefore, the AS at 298 K is -0.47 kJ/(mol K).
(b) Assuming that AS and AH change little with temperature, we can use the equation:
ΔG = ΔH - TΔS
To calculate the AG at 450 K.
Substituting the given values, we get:
ΔG = -220 kJ/mol - (450 K)(-0.47 kJ/(mol K)) = -2.2 kJ/mol
Therefore, the AG at 450 K is -2.2 kJ/mol.