Free Energy

What is Free Energy in Chemistry?

Free energy in chemistry is a thermodynamics energy function that is used in various physical or chemical studies and calculations. 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. 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.

The formation of the water molecule process spontaneously. If we mix 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 as,
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 = w_nm
where w_nm = nonmechanical work

The above formula signifies that decreases of G are equal to the non-mechanical work done by the system in the reversible isothermal isobaric process.

Gibbs Free Energy Equation

From definition,
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 the 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 the 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 solids.

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 + w_max.

Since the reversible isothermal process yields maximum work.

Therefore, ΔA = ΔU − (ΔU + w_max)
or, ΔA = − w_max

The 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 in 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 contains 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.