Science  People  Locations  Timeline
Index: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Home > Gibbs free energy


 Contents
In thermodynamics the Gibbs free energy is a state function of any system defined as
G = H - TS

where

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.

1 Useful identities

and rearranging gives

which relates the electrical potential of a reaction to the equilibrium coefficient for that reaction.

where

ΔG = change in Gibbs free energy

ΔH = change in enthalpy

T = temperature

ΔS = change in entropy

R = gas constant

ln = natural logarithm

K = equilibrium constant

n = number of electrons/ moleThe mole (symbol: mol) is one of the seven SI base units and is commonly used in chemistry. It measures the amount of substance of a system and is defined as the amount of substance that contains as many elementary entities as there are atoms in exactly 0 product

F = Faraday constantIn physics and chemistry, the Faraday constant is the amount of electric charge of one mole of electrons. It has the symbol F, and is given by :, where N is Avogadro's number (approximately 6. 02 x 1023) and q is the charge on an electron. The value of F ( coulombs/ mole)

ΔE = electrical potential of the reaction

2 Derivation of Gibbs Free Energy

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

and if then the process is reversible.

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

.

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

(1)

Notice that it is not defined in terms of any external state functions, such as ΔSext or ΔStot. Then the second law becomes:

irreversible reaction
reversible reaction
impossible reaction

Gibbs free energy G itself is defined as

(2)

but notice that to obtain equation (2) from equation (1) we must assume that T is constant.

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.



Read more »

Non User