Technology & Engineering
Chemical Potential Ideal Gas
The chemical potential of an ideal gas is a measure of the potential energy per particle in the gas. It represents the tendency of the gas to move or react in a particular direction. In an ideal gas, the chemical potential is directly related to the pressure, temperature, and composition of the gas.
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5 Key excerpts on "Chemical Potential Ideal Gas"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 Chemical Potential Chemical potential , symbolized by μ , is a quantity first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. In simplest terms, it is an analogue to electric potential and gravitational potential, utilizing the same idea of force fields as being the cause of things moving, be they charges, masses, or, in this case, chemicals. He defined it as follows: If to any homogeneous mass in a state of hydrostatic stress we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered. Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a substance, whether capable or not of existing by itself as a homogeneous body. Chemical potential is also referred to as partial molar Gibbs energy . Chemical potential is measured in units of energy/particle or, equivalently, energy/mole. The chemical potential is used in thermodynamics, physics and chemistry. In modern statistical physics the chemical potential is the Lagrange multiplier for the average particle constraint, when maximizing the entropy, divided by the temperature. This is the precise and abstract scientific definition, just like the temperature is defined in terms of the Lagrange multiplier for the average energy constraint. In some fields (particularly electrochemistry), the term chemical potential is used to describe a fundamentally different (but related) concept, namely the internal chemical potential. The chemical potential of a system of electrons is also called the Fermi level.
eBook - PDF- Hubert H. Girault(Author)
- 2002(Publication Date)
- EPFL PRESS(Publisher)
These deviations of the behaviour of a real gas with respect to an ideal gas are taken into account by adding a correcting factor to the expression (1.9) for the chemical potential: Fig. 1.1 Variation of chemical potential with pressure. Repulsion Attractions between the molecules o ln(p/p o ) 4 Analytical and Physical Electrochemistry µ µ ϕ µ ( ) ( ) ln ln ( ) ln T T RT p p RT T RT f p = + + = + o o o o (1.10) where is called the fugacity coefficient (dimensionless) and f = p is the fugacity. The term RTln represents the energy of interaction between the molecules. Given that gases tend towards behaving ideally at low pressures, we can see that Æ 1 when p Æ 0 . The reasoning developed above for a pure gas can be applied equally to ideal mixtures of ideal gases. The chemical potential of the constituent i of an ideal mixture of gases is therefore given by µ µ µ i i i i i T T RT p p T RT p p RT y ( ) ( ) ln ( ) ln ln = + = + + o o o o (1.11) with p i being the partial pressure of the constituent i and y i the mole fraction. The standard state of a constituent i corresponds to the pure gas i considered as ideal and at the standard pressure of 1 bar. Chemical potential in the liquid phase In a liquid phase, the molecules are too close to one another to allow the hypothesis used in the case of ideal gases, i.e. that the intermolecular forces can be neglected. We define an ideal solution as a solution in which the molecules of the various constituents are so similar that a molecule of one constituent may be replaced by a molecule of another without altering the spatial structure of the solution (e.g. the volume) or the average interaction energy. In the case of a binary mixture A and B, this means that A and B have approximately the same size, and that the energy of the interactions A-A, A-B and B-B are almost equal (for example a benzene-toluene mixture).
eBook - PDFStatistical and Thermal Physics
With Computer Applications, Second Edition
- Harvey Gould, Jan Tobochnik(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
7 ........................................... The Chemical Potential and Phase Equilibria W e discuss some simple models and simulations to illustrate the nature of the chemical potential and then discuss its role in understanding phase transitions, with an emphasis on the van der Waals equation of state. We also discuss chemical reac-tions and the law of mass action. 7.1 Meaning of the Chemical Potential We know that, if two systems are at different temperatures and are then placed in thermal contact, there will be a net transfer of energy from one system to the other until the temperatures of the two systems become equal. We also know that if there is a movable wall between two systems at different pressures, then the wall will move so as to change the volume of each system to make the pressures equal. Hence we expect that, if two systems are initially at different chemical potentials and are then allowed to exchange particles, there will be a net transfer of particles from the system at the higher chemical potential to the one at the lower chemical potential until the chemical potentials become equal. You are asked to derive this result in Problem 7.1. Problem 7.1. Diffusive equilibrium Assume that two systems A and B are initially in thermal and mechanical equilibrium, but not in diffusive equilibrium, that is, T A = T B , P A = P B , but μ A = μ B . Use reasoning similar to that used in Section 2.13 to show that particles will be transferred from the system at the higher chemical potential to the system at the lower chemical potential. (An easy way to remember the various thermodynamic relations for μ is to start from the fundamental thermodynamic relation in the form dE = TdS − PdV + μ dN .) 7.1 MEANING OF THE CHEMICAL POTENTIAL • 341 TABLE 7.1 The number of states of subsystems A and B such that the composite Einstein solid has a total number of particles N = N A + N B = 10 with E A = 8 and E B = 5.
eBook - PDF- Lyle Albright(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
An ideal gas is defined as one that is free of intermolecular potential energy at finite pressures. For the ideal gas, the pv product equals RT at all pressures, and is called the ideal-gas equation, pv = RT (4.4) This equation is an approximation of real gas behavior at high temperatures or low pressures. The approximation remains good at lower temperatures at progressively lower pressures. Where the degree of approximation is acceptable, the equation is in common use for its simplicity. A real gas or real liquid is said to be in the ideal-gas state when its intermolecular potential is ignored. The properties of the fluid in the ideal-gas state can be calculated with ease using Equation (4.4). One simple universal equation applies to all substances, requiring no substance-specific parameters. However, for most real states, the ideal-gas equation is inadequate, and real-fluid properties are obtained by adding to the ideal-gas equation the contribution of intermolecular potential in the form of deviation functions, also called residual functions. A major objective of Section 4.2 is to derive the deviation functions from the equation of state of the substance. Because the ideal-gas properties are known, to find the deviation function is as good as finding the state function of a real substance. In this way the ideal-gas equation is used universally in all equation-of-state calculations of thermodynamic functions. 4.1.3 F IRST L AW OF T HERMODYNAMICS AND I NTERNAL E NERGY The first law of thermodynamics states that energy can be converted from one form to another or transported from one system to another, but the sum of the energies involved—kinetic energy, T = − 100 β β β / ( ) S I lim p pv T → = 0 κ lim p pv RT → = 0 Thermodynamics of Fluid Phase and Chemical Equilibria 259 potential energy, electric energy, internal energy (which is a state function), and other forms—is always conserved and remains constant.
eBook - PDFThermodynamics
From Concepts to Applications, Second Edition
- Arthur Shavit, Chaim Gutfinger(Authors)
- 2008(Publication Date)
- CRC Press(Publisher)
83 5 Ideal Gas In this chapter we introduce the idea of an ideal gas, which is defined by a simple equa-tion of state. Such a definition has the advantage that all the properties may be calculated mathematically in a closed form without the need to resort to tables. Moreover, quasistatic processes may also be evaluated in a closed form. Although the concept of the ideal gas is just a mathematical idea, which does not neces-sarily have to describe real gas behavior, still for many situations the ideal gas assumption renders reasonable approximations. The concept of the ideal gas is combined with the first law of thermodynamics to solve problems. 5.1 Definition of an Ideal Gas It is an experimental fact that for simple substances the property pv / T approaches a fixed limit lim lim 0 → → pv T pv T R v (5.1) where R is a constant characteristic of the substance, independent of temperature. Equation 5.1 is rewritten in terms of molar specific volume v – as lim v pv T R →∞ (5.2) where R – is the universal gas constant, which is independent of the substance. R 8.31434 8.31434 J/mol K or kJ/kmol K (5.3) As v = v – / M it follows that R R M (5.4) An ideal gas is defined as one for which the following equation of state holds pv RT (5.5) It follows from Equation 5.1 that all substances approach ideal gas behavior at low densi-ties. Equation 5.5 may be rewritten in several alternative useful forms. pv RT (5.6) 84 Thermodynamics: From Concepts to Applications pV mRT (5.7) pV nRT (5.8) where n = m / M is the number of moles of the substance. There is no real substance that satisfies the ideal gas definition for the entire range of states. Therefore, the ideal gas is a concept rather than a reality.
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