Free Energy

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Free Energy

• Also called Gibbs Free Energy
• Thermodynamic function also related to
  spontaneity and is useful dealing with the
  temperature dependence of spontaneity.
• Symbolized by G and for a process that occurs
  at constant temperature, the change in free
  energy is given by
• ?G ?H - T?S

2

• Processes carried out at constant temperature and
  pressure are spontaneous only if ?G is negative.
• That is, a process (at constant T and P) is
  spontaneous in the direction in which the free
  energy decreases (-?G means ?Suniv).

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?H, ?S, ?G and Spontaneity

• ?G ?H - T?S
• H is enthalpy, T is Kelvin temperature

Value of ?H Value of T?S Value of ?G Spontaneity
Negative Positive Negative Spontaneous
Positive Negative Positive Nonspontaneous
Negative Negative ??? Spontaneous if the absolute value of ?H is greater than the absolute value of T?S (low temperature)
Positive Positive ??? Spontaneous if the absolute value of T?S is greater than the absolute value of ?H (high temperature)
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Free Energy and Chemical Reactions

• Standard Free Energy Change (?Go)
• ?Go is the change in free energy that will occur
  if the reactants in their standard states are
  converted to the products in their standard
  states.
• ?Go cannot be measured directly.
• Knowing ?Go values for reactions can help predict
  the relative tendency of reactions to occur
• The more negative the value for ?Go, the farther
  to the right the reaction will proceed in order
  to achieve equilibrium.
• Equilibrium is the lowest possible free energy
  position for a reaction.

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Calculating Free Energy Change

• There are several ways to calculate ?Go.
• Method 1

For reactions at constant temperature ?G0 ?H0
- T?S0
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Calculating Free Energy Method 2
An adaptation of Hess's Law
Cdiamond(s) O2(g) ? CO2(g) ?G0 -397 kJ
Cgraphite(s) O2(g) ? CO2(g) ?G0 -394 kJ
Cdiamond(s) O2(g) ? CO2(g) ?G0 -397 kJ
CO2(g) ? Cgraphite(s) O2(g) ?G0 394
kJ
Cdiamond(s) ? Cgraphite(s)
?G0
-3 kJ
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Calculating Free Energy Method 3
Using standard free energy of formation (?Gf0)
?Gf0 of an element in its standard state is zero