Unformatted text preview: More Gas Laws!
PTEC 3302 September 20th Homework Problem 2-6 (spreadsheet) uses the Clausius-Clapeyron equation in linear form equation 2-5 in the text Problem 2-6 (spreadsheet) involves a density-temperature diagram similar to figure 2-11and the property that the densities of the liquid and gas are identical at the critical point Gas Laws, Equations of State Dalton's Law of Partial Pressure:
The total pressure exerted by a mixture of gasses is equal to the sum of the pressures exerted by its components Law of Additive pressures Assume the following gas is at a pressure of 750 psia. What is the partial pressure exerted by the methane?
Component Methane Ethane Propane Mol fraction 0.85 0.10 0.05 Apparent Molecular Weight Multiply the molecular weight of each component by the mol fraction of that component in the mixture, then sum to get the apparent molecular weight of the mixture. To find specific gravity of a mixture, divide the apparent molecular weight by 29 (molecular weight of air) Z-factors and specific gravity Example 3-8 Example 3-9 (also find mass in lbs) When there is a heptanes+: Example 3-10 When the composition is unknown: Use specific gravity and Fig 3-1: Example 3-11 When H2S and CO2 are present: Example 3-12 Equation of van der Waals Considers the attractive force between molecules (which he defined as a/v2)
a ( p + 2 )(VM - b) = RT VM a,b are constants characteristic of the particular gas, Vm = v/n) is the molar volume, R is the universal gas constant Modifications and Improvements Clausius (1880) Berthelot (1889) Dieterici (1899) Wohl (1927) Lorentz (1881) a p+ 2 VM bVM VM - = RT VM + b In the spirit of van der Waals Beattie - Bridgeman EOS RT p= 2 VM c b 1 - V - B0 1 - 3 M V T V M M A0 (1 - a / VM ) - 2 VM "When two slowly moving molecules encounter one another, there is a tendency for them to move under the influence of each other for an appreciable length of time due to the intermolecular forces between them." B&B Current EOS Soave-Redlich and Kwong (SRK) Equation of State: aT temperature dependent term is the Pitzer acentric factor aT p+ (VM - b ) = RT VM (VM + b ) aT = ac RTc b = 0.08664 pc ac ( RTc ) 2 = 0.42747 = 1 + m(1 - Tr ) ( pc ) 2 m = 0.48 + 1.574 - 0.176 2 Peng-Robinson EOS aT p+ (VM - b ) = RT VM (VM + b ) + b(VM - b ) aT = ac RTc b = 0.0778 pc ac ( RTc ) 2 = 0.45724 = 1 + m(1 - Tr ) ( pc ) 2 m = 0.37464 +1.54226 -0.269922 Mixing rules for SRK and PR ...and it gets worse! How do you deal with a j multiple component mixture? aT = yi y j aTij i j ij are binary interaction coefficients values aTij = 1 - ij aTi aTj have to be given for each pair b = y jb j ( ) SRK example
C1 0.65 VM=1.2 cu ft/lb mol Calculate pressure if T=709.6R
8687 acentric factor
5317 C2 0.25 549.5 706.5 0.7232 21042 0.0979 0.6324 0.8349 17569 nC4 0.10 765.2 550.6 1.2922 52358 0.1995 0.787 1.0591 55453 b=0.6210, (use .02 bic C1&C4, .01 C2 and C4, 0 C1 and C2) aT=10773 p=8223 psia ...
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- RT VM