Themes > Science > Chemistry > Miscellenous > Help file Index > Spontaneity and Entropy > Computing DG at different temperatures

The Gibbs free energy is usually computed at 250C since the values of DH and DS are gotten from tables of these quantities at 250C. If you want to compute DG at a different temperature, you should correct the values of the enthalpies and entropies. Luckily, neither tends to vary much, and since both DH and DS change in the same direction the changes tend to cancel out. Therefore, to compute DG at a temperature other than 25oC, just keep the standard entropy and enthalpy values and change the temperature.

Example: Is the following reaction spontaneous at 5000C?

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 - 773K*(-0.0886 kJ/mol*K)
DG = -415 kJ/mol
The reaction is spontaneous, since DG < 0

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