Thermodynamics: ideal gas chemical potential

The discussion then goes on to explain that this equation is used to define a perfect mixture and how the partial pressure of a component in the mixture is equal to the pressure of the pure component in equilibrium. To prove this equation, the gas in the mixture and the free gas on the other side of the semipermeable membrane must be in equilibrium with equal partial and total pressures. This information can be found in Chapter 10 of Introduction to Chemical Engineering Thermodynamics by Smith and Van Ness. In summary, the conversation discusses the equation for the chemical potential of a component in a perfect mixture and explains
  • #1
Lordgraver
2
0
Can someone explain me why we could put pi, μi and μiο in
this equation:
upload_2015-1-4_16-8-29.png

and we get this:
potencjal_chemiczny.jpg

(this is The chemical potential of a component in a perfect mixture of ideal gases wher pi is
partial pressure)
 
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  • #2
Basically, this is the definition of a perfect mixture, i.e. the partial pressure of a component in the mixture is equal to the pressure of the pure component being in equilibrium contact via a semipermeable membrane being permeable only for this component.
 
  • #3
ok... Can you enlighten me as to prove this equation? How to start it?
 
  • #4
If the gas in the mixture and the free gas on the other side of the semipermeable membrane are in equilibrium when the partial respective total pressures are equal then also the chemical potentials must be equal and have the same dependence on the respective pressures.
 
  • #5
See Chapter 10 of Introduction to Chemical Engineering Thermodynamics by Smith and Van Ness.

Chet
 

1. What is thermodynamics?

Thermodynamics is a branch of physics that deals with the study of heat and its relationship with other forms of energy, such as work. It also involves the study of how heat and energy flow through systems and how they affect the properties of matter.

2. What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law, which describes the relationship between pressure, volume, and temperature. It is assumed to have no intermolecular forces and the particles are considered to be point masses.

3. What is chemical potential in thermodynamics?

Chemical potential is a measure of the energy required to add or remove a particle from a system at constant temperature and pressure. It is a thermodynamic property that is used to describe the tendency of a substance to undergo a chemical reaction.

4. How is chemical potential related to ideal gases?

In ideal gases, the chemical potential is directly proportional to the temperature. This means that as the temperature of an ideal gas increases, the chemical potential also increases. Additionally, the chemical potential of an ideal gas is equal to its molar enthalpy.

5. What are some real-world applications of ideal gas chemical potential?

Ideal gas chemical potential has many practical applications, such as in the design of chemical reactions, the production of industrial gases, and the study of gas mixtures in engines. It is also used in the development of new materials and in the analysis of biological systems.

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