Gibbs free energy Guide, Meaning , Facts, Information and Description
In thermodynamics the Gibbs free energy is a state function of any system defined as
- G = H - TS
G is the Gibbs free energy, measured in joules
H is the enthalpy, measured in joules
T is the temperature, measured in kelvin
S is the entropy, measured in joule per kelvin
The Gibbs free energy is one of the most important thermodynamic functions for the characterisation of a system.
The Gibbs free energy determines outcomes such as the voltage of an electrochemical cell, and the equilibrium constant for a reversible reaction. Any natural process occurs if and only if the associated change in G for the system is negative or zero, i.e. the energy of the system decreases or remains the same. It is named after American chemist Willard Gibbs.
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2 Derivation of Gibbs Free Energy 3 See also |
where
ΔG = change in Gibbs free energy
ΔH = change in enthalpy
T = temperature
ΔS = change in entropy
R = gas constant
ln = natural logarithm
n = number of electrons/mole product
F = Faraday constant (coulombs/mole)
ΔE = electrical potential of the reaction
Let Stot be the total entropy of a thermally closed system. A closed system cannot exchange heat with its surroundings. Total entropy is only defined for a closed system, an open system has internal entropy instead.
The second law of thermodynamics states that if a process is possible, then
Since the heat transfer ΔQ vanishes for a closed system, then any reversible process will be adiabatic, and an adiabatic process is also isentropic .
Now consider an open system. It has internal entropy Sint, and the system is thermally connected to its surroundings, which have entropy Sext.
The entropy form of the second law does not apply directly to the open system, it only applies to the closed system formed by both the system and its surroundings. Therefore a process is possible iff
Thus, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes do not seem to move on a P-V diagram; they do not seem to be dynamic at all. However, chemical reactions do undergo changes in chemical potential, which is a state function. Thus, thermodynamic processes are not confined to the two dimensional P-V diagram. There is at least a third dimension for n, the quantity of gas.Useful identities
and rearranging gives
which relates the electrical potential of a reaction to the equilibrium coefficient for that reaction.Derivation of Gibbs Free Energy
and if then the process is reversible.
We will try to express the left side of this inequation entirely in terms of internal state functions. ΔSext is defined as:
Temperature T is the same both internally and externally, since the system is thermally connected to its surroundings. Also, ΔQ is heat transferred to the system, so -ΔQ is heat transferred to the surroundings, and -ΔQ/T is entropy gained by the surroundings. We now have:
Multiply both sides by T:
ΔQ is heat transferred to the system; if the process is now assumed to be isobaric, then ΔQ = ΔH:
ΔH is the enthalpy change of reaction (for a chemical reaction at constant pressure and temperature). Then
for a possible process. Let the change ΔG in Gibbs free energy be defined as
Notice that it is not defined in terms of any external state functions, such as ΔSext or ΔStot. Then the second law becomes:
Gibbs free energy G itself is defined as
but notice that to obtain equation (2) from equation (1) we must assume that T is constant.