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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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