Gases part 2 (1)

Gases part 2 (1) - Real Gases - General Observations...

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Real Gases - General Observations Deviations from ideal gas law are particularly important at high pressures and low temperatures (rel. to condensation point of gas) Real gases differ from ideal gases in that there can be interactions between molecules in the gas state Repulsive forces important only when molecules are nearly in contact, i.e. very high pressures Gases at high pressures (spn small), gases less compressible Attractive forces operate at relatively long range (several molecular diameters) Gases at moderate pressures (spn few molecular dia.) are more compressible since attractive forces dominate At low pressures, neither repulsive or attractive forces dominate - ideal behavior
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Compression Factor, Z Compression factor, Z, is ratio of the actual molar volume of a gas to the molar volume of an ideal gas at the Z = V m / V m ° , where V m = V/n Using ideal gas law, p V m = RTZ The compression factor of a gas is a measure of its deviation from ideality Depends on pressure (influence of repulsive or attractive forces) z = 1, ideal behavior z < 1 attractive forces dominate, moderate pressures z > 1 repulsive forces dominate, high pressures
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Real Gases - Other Equations of State Virial Equation Consider carbon dioxide At high temperatures (>50° C) and high molar volumes (V m > 0.3 L/mol), isotherm looks close to ideal Suggests that behavior of real gases can be approximated using a power series (virial) expansion in n/V (1/V m ) {Kammerlingh-Onnes, 1911} Virial expansions common in physical chemistry CO 2 pV m = RT 1 + B V m + C V m 2 + .......
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Virial Equation (continued) C oefficients e xperimentally determined (s ee Atkins, Table 1.3 ) 3 rd coefficient less impt than 2 nd , etc. B/V m >> C/V m 2 For mixtures, coeff. depend on mole fractions B = x 1 2 B 11 + 2 x 1 x 2 B 12 + x 2 2 B 22 x 1 x 2 B 12 represents interaction between gases The compressibility factor, Z, is a function of p (see earlier figure) and T For ideal gas dZ/dp (slope of graph) = 0 Why? For real gas, dZ/dp can be determined using virial equation Substitute for Vm (V m = Z V m ° ); and V m ° =RT/p Slope = B’ + 2pC’+ …. As p 0, dZ/dP B’, not necessarily 0. Although eqn of state approaches ideal behavior as p 0, not all properties of gases do Since Z is also function of T there is a temperature at which Z 1 with zero slope - Boyle Temperature, T B At T B , B’ 0 and, since remaining terms in virial eqn are small, p V m = RT for real gas 2 nd Virial Coefficients Equimolar Mixtures of CH 4 and CF 4 K B 1 (CH 4 ) (cm 3 /mol) B 1 (CH 4 ) (cm 3 /mol) B 12 (cm 3 /mol) 273.15 -53.35 -111.00 -62.07 298.15 -42.82 -88.30 -48.48 373.15 -21.00 -43.50 -20.43
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Critical Constants Consider what happens when you compress a real gas at constant T (move to left from point A) Near A, P increases by Boyle’s Law
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This note was uploaded on 07/31/2011 for the course CHM 170 taught by Professor Lemtayo during the Spring '11 term at MIT.

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Gases part 2 (1) - Real Gases - General Observations...

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