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Real Gases

Real Gases. Deviation from ideal gas Law:. Gas particles have volume Attraction exists between gas particles ( liquefication ). Ideal gas law applies only at low gas density: high T, low p. isotherm. Van der Waal’s Equation. Ideal gas law needs modification:.

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Real Gases

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  1. Real Gases Deviation from ideal gas Law: • Gas particles have volume • Attraction exists between gas particles (liquefication) Ideal gas law applies only at low gas density: high T, low p

  2. isotherm

  3. Van der Waal’s Equation Ideal gas law needs modification: • Let’s consider the molecular volume: • b: size of 1 mole of gas molecules • For 1 mole of gas: Vm,total= Vm,space + b

  4. Let’s consider the attraction forces between molecules: • Due to attraction: • -velocity decreased, • - colliding less with wall, • - pressure drops

  5. How big is this drop in pressure? • attraction force • 1f • 2f • 3f • attraction force • 1f • 2f • 3f

  6. How big is this drop in pressure?

  7. How big is this drop in pressure? • drop in pressureproportional to attraction force • drop in pressure indirectly proportional to square of Vm

  8. VdW Equation of state

  9. b: volume of 1 mole of gas molecules. • a: represents strength of attraction.

  10. Maxwell construction • a1 = a2

  11. Many other equations of state Mostly empirical Virial Equation to correct, develop in a series (additional correction terms: B,C, …: second, third, … virial coefficients: exp. determined

  12. Compression factor z • describes deviation from ideal gas behavior. • For ideal gas, z=1

  13. At a given temperature, z depends on the nature of gas • Why?

  14. Let’s find for a VdW gas at p → 0 • The slope of the curve z=f(p) in the previous diagram.

  15. slope at p → 0

  16. > 0 • = 0 • < 0

  17. Size effect > attraction • Size effect = attraction • Size effect < attraction • b: volume of 1 mole of gas molecules. • represents repulsive forces • a: represents strength of attraction

  18. Explain the trend!

  19. Critical Point • Vm range in which L and G phases coexist shrink to a single point • Above Tc, L and G phases can not be distinguished from each other: • Density (L) = Density (G) No Interface

  20. Experimental measurements of pc and Tc are more accurate than that of Vc, a and b are calculated from the experimental values of pc and Tc.

  21. The law of corresponding states • Is it possible to find an equation of state that doesn’t contain material specific constants? • Reduced properties:

  22. Two gases at the same Tr and pr have the same Vr. • These two gases are in “corresponding states’’. • Ar (302 K and 16 atm) ↔ ethylene (381 K and 18 atm)

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