1.1 What is Chemistry?

http://www.ck12.org Chapter 20. Entropy and Free Energy

Standard Free Energy Change

Much like the corresponding equations for∆H°rxnand∆S°rxn,∆G°rxnfor a given reaction can be calculated from
the corresponding∆G°fvalues, which are tabulated for a wide variety of substances.

∆G°rxn=Σn∆G°f(products) –Σn∆G°f(reactants)

As with the standard enthalpy of formation values, there is no absolute zero for Gibbs free energy, so each∆G°f
value is the change in free energy for a compound when prepared from its constituent elements in their standard
states. Also like the enthalpy of formation values,∆G°ffor any element in its most stable form at 25°C is zero.

Example 20.3

Calculate the value of∆G°rxnfor the combustion of methane:

CH 4 (g) + 2O 2 (g)→CO 2 (g) + 2H 2 O(l)

∆G°fvalues can be found at the following website: http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/T
he-Free-Energy-629.html

Answer:

Multiply each∆G°fvalue by the coefficient from the balanced equation, and subtract the free energy of the reactants
from that of the products. Note that water is present as a liquid, so make sure to use the∆G°fvalue for the correct
state. Because O 2 (g) is the standard form of oxygen, it has a∆G°fvalue of zero.

∆G°rxn=Σn∆G°f(products) –Σn∆G°f(reactants)

∆G°rxn= [(-394.36 kJ/mol) + 2(-237.13 kJ/mol)] –[(-50.72 kJ/mol + 2(0 kJ/mol)]

∆G°rxn= -868.62 kJ/mol –(-50.72 kJ/mol)

∆G°rxn= -817.90 kJ/mol

The large negative value for∆G°rxnindicates that the forward reaction is heavily favored under standard conditions.
This reaction proceeds spontaneously in the forward direction.

20.3 Free Energy and Equilibrium

The sign of∆G° predicts the behavior of a chemical reaction at the standard conditions of 25°C and 1 atm of pressure.
If∆G° is negative, the reaction will proceed spontaneously, if∆G° is zero, the reaction is at equilibrium, and if∆G°
is positive, the reaction will proceed spontaneously in thereversedirection. However, this does not tell us what will
happen with a given reaction under non-standard conditions.

Consider the following reaction between ammonia and hydrogen chloride gas:

NH 3 (g) + HCl(g)→NH 4 Cl(s)

We could calculate∆G°rxnfor this reaction using∆G°fvalues, as we did in the previous example problem, but that
would only tell us the value of∆G at 25°C. Alternatively, we could calculate∆G at other temperatures using the
following equation:

∆Grxn=∆Hrxn- T∆Srxn