What is free energy in chemistry?
Free energy can be described by two types of energy functions,
- Helmholtz’s free energy or work function (A).
- Gibbs free energy or thermodynamics potential or Gibbs function.
What is standard free energy?
The standard free energy of a reaction is the energy change that occurs when one mole of a molecule is formed from its constituent elements at the standard state.
The formation of the water molecule process spontaneously. If we mixing hydrogen and oxygen at 25 °C, the hydrogen and oxygen molecule does not react appreciably due to the extremely slow rate of reaction. If the reaction rate is accelerated by an electric spark, the chemical equilibrium is established easily.
What is Gibbs free energy?
Gibbs free energy is a thermodynamic property defined,
G = H − TS
Here H and TS are energy terms. Hence G is also an energy term.
Specific heat (H), temperature (T), and entropy (S) are state functions. Therefore, G is also a state function.
TS is a measure of unavailable energy for doing useful work. Therefore, G is the part of the enthalpy that is available for doing work.
Physical significance of Gibbs free energy
Let us consider a reversible isothermal and isobaric change of the system,
ΔG = ΔH − TΔS
Again, ΔH = ΔU + PΔV
Therefore, ΔG = ΔU + PdV − TΔS
Again, TΔS = q (heat) = ΔU + w. This work may be partially mechanical and partially non-mechanical or fully mechanical or fully non-mechanical.
∴ ΔG = ΔU + PΔV − ΔU − w
= PΔV − w
From the above equation, − ΔG = w − PΔV = wnm
where wnm = nonmechanical work
Above formula signifies that decreases of G equal to the non-mechanical work done by the system in the reversible isothermal isobaric process.
Gibbs free energy equation
G = H − TS = U + PV − TS
or, dG = dU + PdV + VdP − TdS − SdT
TdS = q = dU + PdV, when the work is mechanical work only.
Combining above two equations,
dG = dU + PdV + VdP − dU − PdV − SdT
∴ dG = VdP − SdT
It is another basic thermodynamic Gibbs free energy equation.
For isothermal process
For an isothermal process,
dT = 0
∴ dG = VdP
For n moles ideal gas, V = nRT/P
∴ dG = nRTdP/P
Integrating the above equation,
G = nRTlnP + G0 (integration constant)
Dividing by n,
μ = μ0 + RTlnP
where μ = G/n = free energy per mole = chemical potential
For isobaric process
For reversible isobaric process,
dP = 0
∴ dG = − SdT
Since the entropy of the system is always positive. Therefore, free energy decreases with increasing the temperature of the system at constant pressure. The rate of decrease of G with temperature is highest for gases and lowest for solid.
What is work function?
Helmholtz free energy or work function is a thermodynamic property defined,
A = U − TS
Here, U = internal energy and TS is also an energy term. Therefore, A is also an energy term.
Further internal energy, temperature, and entropy are state functions and perfectly differential quantities. Therefore, A also a state function and perfectly differential quantity.
Significance of Helmholtz free energy
If we consider an isothermal reversible process, the work function,
ΔA = ΔU − TΔS
Again, TΔS = q = ΔU + wmax. Since reversible isothermal process yields maximum work.
Therefore, ΔA = ΔU − (ΔU + wmax)
or, ΔA = − wmax
Above formula signifies that decreases in work function are equal to the maximum work done by the system. Therefore, the work function measures the workability of a system. When the system works, A values decrease.
Work function formula
From the definition of work function,
A = U – TS
For a small change of the system,
dA = dU − TdS − SdT
When the work is mechanical,
TdS = q (heat) = dU + PdV
∴ dA = − PdV − SdT
It is the basic thermodynamic work function formula.
For reversible isothermal process
For the reversible isothermal process,
dT = 0
Therefore, dA = − PdV
If the system contain ideal gas,
dA = − nRT/V
Integrating within the limits,
ΔA = nRT ln(V1/V2)
Therefore, with the increase of the volume of the system, work function decreases.
For isochoric process
For the reversible isochoric system,
dV = 0
∴ dA = − SdT
Since entropy is always a positive quantity. It implies that Helmholtz’s free energy or work function A decreases with the increasing temperature of the isochoric process.