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Chemistry 231

Chemistry 231. Real Gases. Real Gases. The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. Most real gases depart from ideal behaviour at deviation from low temperature high pressure. Deviations from Ideal Gas Behaviour .

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Chemistry 231

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  1. Chemistry 231 Real Gases

  2. Real Gases • The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. • Most real gases depart from ideal behaviour at deviation from • low temperature • high pressure

  3. Deviations from Ideal Gas Behaviour Low Temperatures

  4. Attractive Forces in Real Gases The variation of the potential energy of two molecules on their separation. High positive potential energy (little separation) Repulsive interactions Intermediate separations attractive interactions dominate Large separations (on the right) the potential energy is zero and there is no interaction between the molecules.

  5. Deviations from Ideal Gas Behaviour (cont’d) High Pressures

  6. Deviations from Ideal Behaviour Real gas molecules do attract one another (Pid = Pobs + constant) Real gas molecules are not point masses (Vid = Vobs - const.)

  7. The Van der Waal's Equation of State • Vid = Vobs - nb • b is a constant for different gases • Pid = Pobs + a (n / V)2 • a is also different for different gases • Ideal gas Law Pid Vid = nRT

  8. Critical Constants Critical temperature (Tc) - the temperature above whicha gas cannot be liquefied Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction

  9. Compression Factor The compression factor

  10. The Boyle Temperature For a perfect gas, the slope is zero Boyle temperature the slope is zero and the gas behaves perfectly over a wider range of conditions than at other temperatures.

  11. Critical Constants for Van der Waals’s Gases At the critical point

  12. The Boyle Temperature Boyle temperature - for a van der Waal's gas, the Boyle temperature (TB) is written

  13. Reduced Variables The reduced state variables are defined

  14. The Van der Waal’s Equation Re-write the Van der Waal’s in terms of reduced variables

  15. The Law of Corresponding States All substances obey the same equation of state in terms of the reduced variables. Degree of generality.

  16. Activities in Gaseous Systems The chemical potential of a real gas is written in terms of its fugacity

  17. Define the Activity Coefficient The activity coefficient (J) relates the activity to the concentration terms of interest. In gaseous systems, we relate the fugacity (or activity) to the ideal pressure of the gas via

  18. The Chemical Potential for Real Gases The fugacity (f) represents the chemical potential of a real gas. Define the fugacity coefficient   = f / P For a real gas

  19. Obtaining Fugacity Coefficients Comparing the chemical potential of the real gas to the chemical potential of an ideal gas at the same pressure

  20. Calculating Fugacity Coefficients The fugacity coefficients are obtained from the compression factors (Z) as shown below

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