Themes > Science > Chemistry > Miscellenous > Help file Index > Spontaneity and Entropy > Temperature, the Gibbs free energy and spontaneity

The sign of the change in the Gibbs free energy for a reaction determines the spontaneity of that reaction. Since DG is computed from the change in enthalpy and entropy in the reaction, we can look at the signs of both DH and DS and consider how these affect the value of DG for a reaction.

 DH - DH + DS+ Spontaneous at all temperatures Spontaneous at high T DS- Spontaneous at low T Never spontaneous

When DH is negative and DS is positive, the Gibbs free energy change DG = DH - T*DS is always negative and thus the reaction is always spontaneous.

When DH is positive and DS is negative, the Gibbs free energy change DG is always positive and thus the reaction is never spontaneous.

When the signs of DH and DS are the same, the entropy and enthalpy parts of the Gibbs free energy oppose each other. When this occurs, the temperature decides when the reaction is spontaneous or not. You can compute this temperature by figuring out the temperature at which DG is zero: this is where it changes sign and thus the reaction changes its spontaneity.

Example: At what temperature does the following reaction become spontaneous?

2SO3(g) -> 2SO2(g) + O2(g)

Solution: We need to compute the parts of DG, so first look up the thermodynamic data from a table

 Compound DHf0 (kJ/mol) DS0 (J/mol*K) SO3(g) -395.7 +256.7 SO2(g) -296.8 +248.1 O2(g) 0.0 +205.0

Next, compute DH and DS

DH = (2*DHSO20 + 1*DHO20) - (2*DHSO30)
DH = (2* -296.8 + 1*0) - (2*395.7)
DH = +197.8 kJ/mol
DS = (2*DSSO20 + 1*DSO20) - (2*DSSO30)
DS = (2* 248.1 + 1*205) -(2*256.7)
DS = +187.8 J/mol*K = 0.1878 kJ/mol*K
Since both DH and DS are positive, this reaction will be spontaneous at high temperature. If we set DG equal to zero we can compute this temperature
DG = DH - T*DS
0 = 197.8 kJ/mol - T*0.1878 kJ/mol*K
T = 1053 K

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