# Gibbs Free Energy Gibbs Free Energy

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Gibbs Free Energy

Recall:

•   A decrease in enthalpy, ∆H = (-), favours a spontaneous reaction (i.e. a reaction is more
likely to occur if the products formed are more stable than the reactants)
•   An increase in entropy, ∆S = (+), favours a spontaneous reaction (i.e. if the products
formed are more random or disorganized than the reactants were, then the reaction is
more likely to happen)
•   Therefore it easy to see that reactions in which ∆H = (-) and ∆S = (+) should always be
spontaneous
•   But what about if ∆H = (-) and ∆S = (-), or ∆H = (+) and ∆S = (-), or ∆H = (+) and ∆S =
(+)? Will these reactions occur?
•   We need to consider another factor: temperature. For example, the melting of ice is a
spontaneous reaction, but only at temperatures less than 0oC
•   To more accurately predict whether a reaction will occur, we need to look at a third
value, Gibb’s Free Energy (G)

Gibbs Free Energy
•   Is energy that becomes “free” or available to do useful work
•   Any reaction that is accompanied by a decrease in free energy, i.e. ∆G = (-), is a
spontaneous reaction
•   If ∆G >0, then that reaction will NOT be spontaneous and if ∆G = 0, we say that the
reaction is at equilibrium (we will study this in a later unit)
•   The following equation can be used to determine whether ∆G is negative at a given
temperature, and therefore whether that reaction will be spontaneous at a that
temperature:

∆G = ∆Ho – T∆So, where T is measures in Kelvin (K)
Predict under what temperature conditions that the following conditions will produce a
spontaneous reaction: i.e. ∆G < 0
OR
∆Ho – T∆So < 0

∆H
+                                       -
∆S    +

-

** Remember that ∆Ho is measured in kJ and ∆So is measured in J, therefore ∆Ho will always
make a greater contribution to ∆G.
Calculations using ∆G

For any temperature:    ∆G = ∆Ho – T∆So, where T is measures in Kelvin (K)*

*To convert from Celsius to Kelvin, just add 273 to the Celsius temperature

Example 1:

Determine ∆Go for the reaction: 4Fe(s) + 3O2(g)      2Fe2O3(s). Is the reaction spontaneous?

•   To calculate ∆Go, you will first have to calculate ∆Ho and ∆So using Hess’s Law
•   Since you are asked to calculate standard ∆G, T = 25oC which, when converted to Kelvin =
298K
Example 2:

Under what temperature range will the reaction be spontaneous?
3NO2(g) + H2O(l)      2HNO3(l) + NO(g)

•   You will need to calculate ∆Ho and ∆So using Hess’s Law
•   You will need to solve the inequality ∆Ho – T∆So < 0
Example 3:

At what temperature will steam decompose?

•   You will need to write out the balanced equation for the reaction
•   You will need to calculate ∆Ho and ∆So using Hess’s Law
•   You will need to solve the inequality ∆Ho – T∆So < 0

**∆G can also be calculated using Hess’s Law:

∆G = Σn∆Gproducts – Σn∆Greactants

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