# Chemical potential at equlibrium

• LalithP
In summary, there is some confusion regarding the value of chemical potential at equilibrium. According to a source, it is zero, but other sources state that it is the change in chemical potential that is zero, not the individual chemical potentials. The mathematical definition of chemical potential involves derivatives of internal energy or Helmholtz free energy at constant entropy, volume, temperature, and pressure. The most commonly used form is the partial derivative of Gibbs free energy with respect to the number of moles of a species, which is used in chemical thermodynamics to determine equilibrium.
LalithP
What is the value of chemical potential of a substance at equilibrium?
According to following article it is zero:

https://www.uni-muenster.de/Physik....hen/Forschungsschwerpunkte/mBECwatfratcp.html

But I have seen in many articles that it is the change in chemical potential (ie. stoichimetric sum of chemical potentials) is zero, not individual chemical potentials. Could somebody clarify this?

What is your understanding of the mathematical definition of "chemical potential?"

I think I know the basics like, it is the derivative of internal energy at constant entropy and volume or the partial derivative Helmholtz free energy at constant temperature and volume...

The most useful version is the partial derivative of the gibbs free energy G with respect to the number of moles of a given species at constant temperature and pressure. This is the form most extensively used in chemical thermodynamics. The equilibrium criterion for a chemical reacting mixture is that the gibbs free energy is minimized.

## 1. What is chemical potential at equilibrium?

Chemical potential at equilibrium is the potential energy of a substance in a system when it is in a state of equilibrium, meaning there is no net flow of matter or energy in or out of the system. It is a measure of the tendency of a substance to undergo a chemical reaction or physical change.

## 2. How is chemical potential at equilibrium calculated?

Chemical potential at equilibrium can be calculated using the Gibbs free energy equation: ΔG = ΔH - TΔS, where ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change. Chemical potential is equal to the partial molar Gibbs free energy, which is the change in Gibbs free energy when adding one mole of a substance to a solution at constant temperature and pressure.

## 3. What factors affect chemical potential at equilibrium?

The chemical potential at equilibrium is affected by several factors, including temperature, pressure, and the composition of the system. Changes in any of these factors can alter the equilibrium state, resulting in a change in the chemical potential.

## 4. How does chemical potential at equilibrium relate to the equilibrium constant?

The chemical potential at equilibrium is directly related to the equilibrium constant, which is a measure of the ratio of products to reactants at equilibrium. The equilibrium constant is equal to the ratio of the chemical potentials of the products to the chemical potentials of the reactants, raised to the power of their respective stoichiometric coefficients.

## 5. Why is understanding chemical potential at equilibrium important in chemistry?

Understanding chemical potential at equilibrium is crucial in chemistry because it helps predict and explain the behavior of chemical systems. It allows scientists to determine the conditions necessary for a reaction to reach equilibrium and the direction in which the reaction will proceed. Additionally, the concept of chemical potential at equilibrium is essential in thermodynamics and plays a key role in many chemical processes, such as phase transitions and chemical reactions.

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