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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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