Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 21

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CHAPTE R 14? Entropy and Free Energy

Practice Problem c o n c e p t ua l i z e? Which of the following graphs best represents the
relationship between DG and temperature for a process that is exothermic and for which DS is
negative?

?G

0

T

T

(i)

Student Annotation: The introduction of
the term ?G° enables us to write Equation
14.10 as
?G° = ?H° ? T?S°

T

(ii)

T

(iii)

(iv)

Standard Free-Energy Changes, ????G°
The standard free energy of reaction (?G° ) is the free-energy change for a reaction when it
rxn
occurs under standard-state conditions—that is, when reactants in their standard states are converted to products in their standard states. The conventions used by chemists to define the standard
states of pure substances and solutions are
• Gases
• Liquids
• Solids
• Elements
• Solutions

1 atm pressure
Pure liquid
Pure solid
The most stable allotropic form at 1 atm and 25°C
1 molar concentration

To calculate ?G° , we start with the general equation
rxn
aA + bB

cC + dD

The standard free-energy change for this reaction is given by
Equation 14.11

?G° = [c?G °(C) + d?G °(D)] ? [a?G °(A) + b?G °(B)]
rxn
f
f
f
f

Equation 14.11 can be generalized as follows:
Equation 14.12

?G° = ?n?G ° (products) ? ?m?G ° (reactants)
rxn
f
f

where m and n are stoichiometric coefficients. The term ?G° is the standard free energy of
f
formation of a compound—that is, the free-energy change that occurs when 1 mole of the compound is synthesized from its constituent elements, each in its standard state. For the combustion
of graphite,
C(graphite) + O2(g)

CO2(g)

the standard free-energy change (from Equation 14.12) is
?G° = [?G °(CO2)] ? [?G °(C, graphite) + ?G °(O2)]
rxn
f
f
f
As with standard enthalpy of formation, the standard free energy of formation of any element (in
its most stable allotropic form at 1 atm) is defined as zero. Thus,
?G °(C, graphite) = 0????and?????G °(O2) = 0
f
f
Therefore, the standard free-energy change for the reaction in this case is equal to the standard free
energy of formation of CO2:
?G° = ?G °(CO2)
rxn
f
Appendix 2 lists the values of ?G ° at 25°C for a number of compounds.
f

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9/10/13 12:01 PM