Answer to Question #207926 in General Chemistry for Earl

Question

1. For the reaction, H2O(l) --> H2O (g), calculate ∆G at a) 20°C b) 100°C c) 150°C

2. Calculate the standards-free energy changes for the reaction 2MgO(s) + 2Mg(s) + O2(g) at 25°C

Answer 1

∆G = ∆H -T∆S

The change in the molar heat capacity at constant pressure for the reaction is as shown.

ΔCP = Cp​(H₂O,g)−CP(H₂O,l)=33.305−75.312=−42.007J/Kmole

The entropy change at 293 K is as shown.

ΔrS293=T∆H​=293

40639

​=138.7J/Kmole

The relationship between the entropy change and the change in molar heat capacity at constant pressure is as shown.

d(ΔrS)=T

Δr​CPdt

​

Δr

​S293​−ΔrS293​=Δr​CP

​lnT1

​T2

​​Δr∆S29=138.7−(−42.007ln293 293)

=147.7J/Kmole

The relationship between the enthalpy change and the change in molar heat capacity at constant pressure is as shown.

d(Δr​H)=Δr​CPdTΔr​H293​−Δr​H293

​=42.007(50)ΔrH293

​=42739.35J/mole

The relationship between Gibbs free energy change, the entropy change and the enthalpy change is as shown.

Δr​G293=Δr

​H293−TΔrS293

​

ΔrG293 = 42739.35-293(147.7)

= 5594.35

= 5.59KJ/m

Hence, the Gibbs free energy change for the reaction is 5.59kJ/mol.

2.) The reaction's free energy change is a state function. We can express the free energy change in the thermodynamic standard state from known standard free energy change of formation values in the literature. Both reactants are omitted because they are the pure elements in their respective standard states:

ΔG=2ΔG of,MgO,sΔGo

=2×(−567.0 kJ/mol)ΔGo

=−1134.0 kJ/mol