Gibb’s Free Energy
As we said earlier, the two driving forces for chemical
reactions are enthalpy and entropy. If a chemical reaction is endothermic,
it must result in an increase in entropy, and if a reaction results
in a decrease in entropy, it must be exothermic. For the SAT II
Chemistry test, you will be expected to know how to use given entropy
(S) and enthalpy (H) values to
calculate if a reaction will be spontaneous or not, and you can
do so by using the Gibb’s free energy (G) equation:
DG = DH - TDS
The Gibb’s free energy equation combines all the information
that we have learned thus far. But what does the Gibb’s free energy
value tell us about a reaction? It tells us the following:
-
If G is negative, the reaction is
spontaneous in the forward direction.
- If G is
equal to zero, the reaction is at equilibrium.
- If G is
positive, then the reaction is nonspontaneous in the forward direction, but
the reverse reaction will be spontaneous.
for elements at standard state (pure elements
at 25ºC and 1 atm are assigned a value of zero).
The Gibb’s free energy equation can be used to calculate
the phase change temperature of a substance. During a phase change,
equilibrium exists between phases, so if the G is
zero, we know that the reaction is in equilibrium.
Example
Find the thermodynamic boiling point of
H2O(l)
H2O(g)
given the following information:
Hvap =
+44 kJ Svap =
118.8 J/K
Explanation
You would solve this problem by setting the equation equal
to zero since in equilibrium, G has a value of
0.
0 = (44,000 J ) - (T )(118.8
J/K)
Now solve for T: the answer is 370K,
the boiling point of water.
Here’s a handy reference table for interpreting what enthalpy
and entropy values say about chemical reactions:
| DH |
DS |
Result |
| Negative |
Positive |
Spontaneous at all temperatures |
| Positive |
Positive |
Spontaneous at high temperatures |
| Negative |
Negative |
Spontaneous at low temperatures |
| Positive |
Positive |
Never spontaneous |
Much as is the case with both enthalpy and entropy, you
can calculate DG using the following equation:
The units for DG are the same as the units as for enthalpy:
J/K.
Now try using the above equation in a problem.
Example
Find the free energy of formation for the oxidation of
water to produce hydrogen peroxide.
2H2O(l) +
O2(g)
2H2O2(l)
given the following information:
|
∆Gf˚ |
| H2O(l) |
-56.7 kcal/mol |
| O2(g) |
0 kcal/mol |
| H2O2(l) |
-27.2 kcal/mol |
Explanation
Plugging all of the values you were given into the equation
(remember that elements have a DGf˚
of 0), you get
[2(-27.2)] - [2(-56.7) + 1(0)] = 59.0 kcal/mol
