Fugacity - Definition in Terms of Chemical Potential | Definition Terms 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

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

“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)

“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)

“Ethical and cultural desegregation. It is a contradiction in terms to scream race pride and equality while at the same time spurning Negro teachers and self-association.”
—Zora Neale Hurston (1891–1960)

“If Thought is capable of being classed with Electricity, or Will with chemical affinity, as a mode of motion, it seems necessary to fall at once under the second law of thermodynamics as one of the energies which most easily degrades itself, and, if not carefully guarded, returns bodily to the cheaper form called Heat. Of all possible theories, this is likely to prove the most fatal to Professors of History.”
—Henry Brooks Adams (1838–1918)

“Not many appreciate the ultimate power and potential usefulness of basic knowledge accumulated by obscure, unseen investigators who, in a lifetime of intensive study, may never see any practical use for their findings but who go on seeking answers to the unknown without thought of financial or practical gain.”
—Eugenie Clark (b. 1922)