Free Energy and Chemical Reactions

In this section we will show you how to calculate standard free energy.  Standard free energy
(G°) is the change in free energy that will occur if the reactants in their standadrd states are converted to the products in their standard states.  For example, the reaction

C(s) + O2(g) --> CO2(g)

H° = -393.5 kJ, S° = 3.05 J/K, and the temperature is at 298 K.

G° = H° - TS°
= -3.935 * 105 J - (298 K)(3.05 J/K)
= -3.944 * 105 J
= -394.4 kJ (per mole of CO
2)

It is very important to convert everything to joules first.  The answer will not be correct if S° is in kilojoules and H° is in joules.
A second way of calculating G° is similar to calculating the H° by using Hess' law.  For example, using this method to find the G° of

2CO(g) + O2(g) --> 2CO2(g)

We are given

2CH4(g) + 3O2(g) --> 2CO(g) + 4H2O(g)             G° = -1088 kJ
CH4(g) + 2O2(g) --> CO2(g) + 2H2O(g)              G° = -801 kJ

The first equation needs to be reversed and the second equation needs to be multiplied by two.

2CO(g) + 4H2O(g) --> 2CH4(g) + 3O2(g)             G° = -(-1088 kJ)
2CH4(g) + 4O2(g) --> 2CO2(g) + 4H2O(g)          G° = 2(-801 kJ)

2CO(g) + O2 --> 2CO2(g)                             G° = -514 kJ