Fugacity - Definition in Terms of Chemical Potential

Definition in Terms of Chemical Potential

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.

In general, the chemical potential (μ) is defined as the partial molar Gibbs free energy. However for any pure substance, it is equal to the molar Gibbs free energy, and its variation with temperature (T) and pressure (P) is given by . At constant temperature, this expression can be integrated as a function of . We must also set a reference state. For an ideal gas the reference state depends only on pressure, and we set = 1 bar so that

Now, for an ideal gas

\mu - \mu ^\circ = \int_{P^\circ }^P {\frac{{RT}} {P}dP} = RT\ln \frac{P} {{P^\circ }}

Reordering, we get

\mu = \mu ^\circ + RT\ln \frac{P} {{P^\circ }}

This gives the chemical potential for an ideal gas in an isothermal process, with a reference state is = 1 bar.

For a real gas, we cannot calculate because we do not have a simple expression for a real gas’ molar volume. Even if using an approximate expression such as the van der Waals equation, the Redlich-Kwong or any other equation of state, it would depend on the substance being studied and would be 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.

We would like the expression for a real gas’ chemical potential to be similar to the one for an ideal gas. We therefore define a magnitude, called fugacity, so that the chemical potential for a real gas becomes

\mu = \mu ^\circ + RT\ln \frac{f} {{f^\circ }}

with a given reference state to be discussed later. This is the usual form of the definition, but it may be solved for f to obtain the equivalent explicit form

Read more about this topic:  Fugacity

Famous quotes containing the words definition, terms, chemical and/or potential:

    “Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
    —The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)

    “It must be a peace without victory.... Victory would mean peace forced upon the losers, a victor’s terms imposed upon the vanquished. It would be accepted in humiliation, under duress, at an intolerable sacrifice, and would leave a sting, a resentment, a bitter memory upon which the terms of peace would rest, not permanently, but only as upon quicksand.”
    —Woodrow Wilson (1856–1924)

    “We are close to dead. There are faces and bodies like gorged maggots on the dance floor, on the highway, in the city, in the stadium; they are a host of chemical machines who swallow the product of chemical factories, aspirin, preservatives, stimulant, relaxant, and breathe out their chemical wastes into a polluted air. The sense of a long last night over civilization is back again.”
    —Norman Mailer (b. 1923)

    “Laughing at someone else is an excellent way of learning how to laugh at oneself; and questioning what seem to be the absurd beliefs of another group is a good way of recognizing the potential absurdity of many of one’s own cherished beliefs.”
    —Gore Vidal (b. 1925)