In chemical thermodynamicsthe fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant.
It is equal to the pressure of an ideal gas which has the same chemical potential as the real gas. Ideal-gas nitrogen at Fugacities are determined experimentally or estimated from various models such as a Van der Waals gas that are closer to reality than an ideal gas.
The fugacity is closely related How To Write Hydrogen Gas the thermodynamic activity. For a gas, the activity is simply the fugacity divided by a reference pressure to give a dimensionless quantity. Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. The thermodynamic condition for chemical equilibrium is that the total chemical potential of reactants is equal to that of products.
If the chemical potential of each gas is expressed as a function of fugacity, the equilibrium condition may be transformed into the familiar reaction quotient form or law of mass action except that the pressures are replaced by fugacities. For a condensed phase liquid or solid in equilibrium with its vapor phase, the chemical potential is equal to that of the vapor, and therefore the fugacity is equal to the fugacity of the vapor.
This fugacity is approximately equal to the vapor pressure when the vapor pressure is not too high. The word fugacity is derived from the Latin for "fleetness", which is often interpreted as "the tendency to flee or escape". The concept of fugacity was introduced by American chemist Gilbert N.
The fugacity of a real gas is formally defined by an equation analogous to the relation between the chemical potential and the pressure of an ideal gas. However, for any pure substance it is equal to the molar Gibbs energy, and its variation with temperature T and pressure P is given by. At constant temperature, this expression can be integrated as a read more of P.
We must also set a reference state. Even if using an approximate expression such as the van der Waals equationthe Redlich—Kwong or any other equation of stateit would depend on the substance being studied and would How To Write Hydrogen Gas therefore of very limited utility.
Additionally, chemical potential is not mathematically well behaved.
It approaches negative infinity as pressure approaches zero and this creates problems in doing real calculations. It is desirable that the expression for a real gas's chemical potential to be similar to the one for an ideal gas. Therefore, one can define a quantity, called fugacityso that the chemical potential for a real gas becomes.
This is the usual form of the definition, but it may be solved for f to obtain the equivalent explicit form. Fugacity is used to better approximate the chemical potential of real gases than estimations made using the ideal gas law.
Yet fugacity allows the use of many of the relationships developed for an idealized system. How To Write Hydrogen Gas the real world, gases approach ideal gas behavior at low pressures and high temperatures; under such conditions the value of fugacity approaches the value of pressure. Yet no substance is truly ideal. At moderate pressures real gases have attractive interactions read article at high pressures intermolecular repulsions become important.
Both interactions result in a deviation from "ideal" behavior for which interactions between gas atoms or molecules are ignored. For a given temperature Tthe fugacity f satisfies the following differential relation:. Thus, for any two physical states at the same temperature, represented by subscripts 1 and 2, the ratio of the two fugacities is as follows:. Therefore, fugacity must obey the limit equation. We can then write. Since in the reference state the gas is considered to be ideal it is an hypothetical reference statewe can write that for the real gas.
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For a gas obeying the van der Waals equationthe explicit formula  for the fugacity is. This formula is difficult to use, since the pressure depends on the molar volume V [ p ]; so one must choose here volume, calculate the pressure, and then use these two values on the right-hand side of the equation.
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For a pure fluid in vapor—liquid equilibrium, the vapor phase fugacity is equal to the liquid phase fugacity. At pressures above the saturation pressure, the liquid phase fugacity is: The exponential term represents the Poynting correction factor and is usually near 1 unless pressures are very high.
Frequently, the fugacity of the pure liquid is used as a reference state when defining and using mixture activity coefficients. From Wikipedia, the free encyclopedia. Atkins' Physical Chemistry 8th ed. Atkins' Physical Chemistry 7th ed.
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Proceedings of the American Academy of Arts and Sciences. The fugacity of a "hard-sphere" semi-ideal gas and the van der Waals gas".
Molecular Thermodynamics of Fluid Phase Equilibria 3rd ed. Retrieved from " https: Physical chemistry Chemical thermodynamics Thermodynamic properties State functions. Views Read Edit View history.