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The Gibbs Free Energy is a thermodynamic quantity which can be used to determine if a reaction is spontaneous or not. The definition of the Gibbs free energy is

G = H- T*S
where G is the free energy, H is the enthalpy and S is the entropy. If we consider the change in G for a reaction where the temperature does not change, we have
DG = DH - TDS
DH and DS are computed from the usual procedures. Temperatures for this equation must be in Kelvin. The above equation is often known as the "Gibbs-Helmholtz equation". Since the values of DH and DS are usually gotten from tables of standard entropy and enthalpy, the Gibbs free energy change usually computed is the standard Gibbs free energy change, DG0 at 250C- for different temperatures the procedure is similar

The sign of DG determines if a reaction is spontaneous or not.

• DG < 0: the reaction is spontaneous
• DG > 0: the reaction is not spontaneous
• DG = 0: the reaction is at equilibrium
When computing DG, be careful about the units. Entropy is usually given in Joules/mol*K, whereas enthalpy is usually given in kiloJoules/mol.

Example: Is the following reaction spontaneous at 250C?

2H2(g) + O2(g) -> 2H2O(g)

Solution: We need to compute both DH and DS for the reaction, get the value of DG, and see if it is less than zero. First, look up the thermodynamic data

 Compound DHf0 (kJ/mol) DS0 (J/mol*K) H2(g) 0.0 130.6 O2(g) 0.0 205.0 H2O(g) -241.8 188.7

Next, compute both DH and DS

DH = (2*DHH2O0) - (2*DHH20 + 1*DHO20)
DH = (2* -241.8) - (2*0 + 1*0)
DH = -483.6 kJ/mol
DS = (2*DSH2O0) - (2*DSH20 + 1*DSO20)
DS = (2* 188.7) - (2*130.6 + 1*205.0)
DS = -88.6 J/mol*K = -0.0886 kJ/mol*K
Combine the two of them into DG
DG = DH - T*DS
DG = -483.6 kJ/mol - 298K*(-0.0886 kJ/mol*K)
DG = -457 kJ/mol
The reaction is spontaneous, since DG < 0

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