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# 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. Free energy can be described by two 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 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. Since 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. Hence G = 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 and 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. Therefore, ΔG = ΔU + PΔV – ΔU – w = PΔV – w.

From the above equation, – ΔG = w – PΔV = wnm, where wnm = nonmechanical work. This 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. Therefore the combined form of these two equations, dG = VdP – SdT. It is another basic thermodynamic Gibbs free energy equation. Two cases of the equation are,

### For isothermal process

For an isothermal process, dT = 0. Hence, dG = VdP. For n moles ideal gas, dG = nRTdP/P. Therefore, G = nRTlnP + G0 (integration constant). Dividing by n, μ = μ0 + RTlnP, where μ = G/n = free energy per mole substances = chemical potential.

### For isobaric process

For reversible isobaric process, dP = 0, and dG = – SdT. Since the entropy (S) of the system is always positive. Therefore, free energy decreases with increasing the temperature of the system at constant pressure. The rate of decreasing 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 as, 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 and TΔS = q = ΔU + wmax. Since reversible isothermal process yields maximum work. Therefore, ΔA = ΔU – (ΔU + wmax) = – wmax. This 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. Therefore, dA = – PdV – SdT. It is the basic thermodynamic work function formula. Two cases for the above formula are,

### 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 = nRTln(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. Therefore, dA = – SdT. Since entropy is always a positive quantity. It implies that work function A decreases with the increasing temperature of the isochoric process.