Non-ideal Gases Fugacity

The fugacity is a pressure like quantity that is used to treat the free energy of nonideal gases.

Now we begin the steps that allow us to relate free energy changes to the equilibrium constant of real, nonideal gases. The thermodynamic reaction (∂G/∂P) t = V is used with the ideal gas relation PV = RT, or V = RT/P, to obtain G = G° = R in P. it was this equation that led to the familiar equilibrium constant expression. If the ideal gas relation PV = RT is not satisfactory, some other quality equations, that of van der Waals, for example, could be used to express the pressure dependence of V. if that were done, the integration of (∂G/∂P)T = V would produce an awkward expression for the equilibrium constant. Thus a route that preserves the simple form of the equilibrium constant expression is preferable.

A satisfactory procedure is the introduction of a function called the fugacy ƒ.  This procedure insists on the free energy equation having the convenient form of the nonideal complications are hidden in the fugacy term. A number of manipulations are necessary; we begin with the thermodynamic equation for mol 1 of gas at constant temperature.

G2 - G1 = V dP

The quantity RT/P can be added to and subtracted from the integrand to give

G2 - G1 = [RT/P + (V - RT/P0] dP

= RT/P dP = (V - RT/P dP

= RTY in P2/P1 + (V - RT/P) dP


Thus the ratio f/P can be calculated at any temperature for which viral coefficient data are available and for any pressure in the range in which these data are applicable. If the real gas behavior is expressed by any other equation of state, the integration can be carried out graphically or with the help of a computer.

Fugacity and the law of corresponding states: for gases for which molar volume measurements have not been made and an equation of state is not available, the law of corresponding states can be used to estimate the fugacities at various reduced variables PR, VR and TR all gases follow the same imperfection and therefore the same nonideality. Furthermore, the variation of the compressibility factor Z with the reduced pressure has been represented for various values TR. These data are all that is necessary for the integration values of:

Z = PV/RT

From which we obtain:

V = RT/P × Z

With this relation eq. can be written as:

RT In ƒ/P = ∫PO (RT/P × Z - RT/P) dP = RT  ∫PO (Z - 1) dP/P

Or, In ƒ/P = 
 ∫PO (Z - 1) dP/P =  ∫PO (Z - 1) d PR/PR

The data of Z as a function of PR for a given value of TR then allow graphical integrations to be performed to give curves.

Example: estimate the fugacity of methane at 200 bar and 25°C, but use the correlation that is based on the law of corresponding states. The critical data give = 46.3 bar and T = 190.6 K for methane.

Solution: at 200 bar the reduced pressure is 200 bar/46.3 bar = 4.32. At 25°C the reduced temperature is 298.15/190.6 K = 1.56. From the value of ƒ/P is estimated at about 0.8, given ƒ = 160 bar.

   Related Questions in Chemistry

  • Q : Problem on distribution law The

    The distribution law is exerted for the distribution of basic acid among: (i) Water and ethyl alcohol (ii) Water and amyl alcohol (iii) Water and sulphuric acid (iv) Water and liquor ammonia What is the right answer.

  • Q : Calculating molarity of a solution

    Select the right answer of the question .The molarity of a 0.2 N N2Co3 solution will be: (a) 0.05 M (b) 0.2 M (c) 0.1 M (d)0.4 M

  • Q : What do you mean by the term alum What

    What do you mean by the term alum? Also illustrate its uses?

  • Q : Calculating density of water using

    What is the percent error in calculating the density of water using the ideal gas law for the following conditions:  a. 110 oC, 1 bar   b. 210 oC 10 bar  c. 374 o

  • Q : Vander Waals forces Wax is an example

    Wax is an example of: (a) Ionic crystal  (b) Covalent crystal  (c) Metallic crystal  (d) Molecular crystalAnswer: (d) Iodine crystals are molecular crystals, in which constituent particles are molecules having inter particle

  • Q : Lowering of vapour pressure Help me to

    Help me to go through this problem. Lowering of vapour pressure is highest for: (a) urea (b) 0.1 M glucose (c) 0.1M MgSo4 (d) 0.1M BaCl2

  • Q : Problems related to entropy change A)

    A) Two compartments each of 1 m3 capacity are joined by a valve and insulated from the surroundings and from one another. One compartment has saturated steam at 683.6 kPa and the other contains steam at the same temperature but at a pressure of 101.3 kPa. T

  • Q : Strength of any solution Give me answer

    Give me answer of this question. A solution contains 1.2046 x 1024 hydrochloric acid molecules in one dm3 of the solution. The strength of the solution is: (a) 6 N (b) 2 N (c) 4 N (d) 8 N

  • Q : Direction of dipole moment expected

    Illustrate the direction of the dipole moment expected for hydrogen bromide?

  • Q : M ive me answer of this question. When

    ive me answer of this question. When mercuric iodide is added to the aqueous solution of potassium iodide, the: (a) Freezing point is raised (b) Freezing point is lowered (c) Freezing point does not change (d) Boiling point does not change

©TutorsGlobe All rights reserved 2022-2023.