--%>
Assignment Help - homework help

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 P = 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 : Q what is the basicity of primary

    what is the basicity of primary secondary and tertiary amines in chlorobenzene

    		•
  • Q : Symmetry Elements The symmetry of the

    The symmetry of the molecules can be described in terms of electrons of symmetry and the corresponding symmetry operations.Clearly some molecules, like H2O and CH4, are symmetric. Now w

    		•
  • Q : Mole fraction of benzene Choose the

    Choose the right answer from following. In a solution of 8.7g benzene C6H6 and 46.0 gm toluene ,(C6, H5, CH3) the mole fraction of benzene in this solution is: (a)1/6 (b)1/5 (c)1/2 (d)1/3

    		•
  • Q : What is heat capacity and how to

    The temperature reliance of internal energy and enthalpy depends on the heat capacities at constant volume and constant pressure. The internal energy and enthalpy of chemical systems and the energy changes that accompany chemical reactions depend on the

    		•
  • Q : Thermodynamics I) Sulphur dioxide (SO2)

    I) Sulphur dioxide (SO2) with a volumetric flow rate 5000cm3/s at 1 bar and 1000C is mixed with a second SO2 stream flowing at 2500cm3/s at 2 bar and 200C. The process occurs at steady state. You may assume ideal gas behaviour. For SO2 take the heat capacity at constant pressure to be CP/R = 3.267

    		•
  • Q : What are homogenous catalyst? Give few

    When a catalyst mixes homogeneously with the reactants and forms a single phase, the catalyst is said to be homogeneous and this type of catalysis is called homogeneous catalysis. Some more examples of homogeneous catalysis are:    SO2

    		•
  • Q : Determining concentration in ppm A 500

    A 500 gm tooth paste sample has 0.2g fluoride concentration. Determine the concentration of F in terms of ppm level: (a) 250 (b) 200 (c) 400 (d) 1000Answer: (c) F-ions in ppm = (0.2/500) x 106 = 400

    		•
  • Q : What are biodegradable polymers?

      These are polymers that can be broken into small segments by enzyme-catalysed reactions. The required enzymes are produced by microorganism. It is a known fact that the carbon-carbon bonds of chain growth polymers are inert to enzyme-catalysed reactions, and hence they are non biod

    		•
  • Q : Explain group 15 elements. The various

    The various elements

    		•
  • Q : Explain Ionic Bond with examples. The

    The bonding in ionic molecules can be described with a coulombic attractive term.For some diatomic molecules we take quite a different approach from that used in preceding sections to describe the bonding. Ionic bonds are interpreted in terms of the coulom

    		•