1. Chemistry 231 Real Gases

2. 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 (P id = P obs + constant) Real gas molecules are not point masses (V id = V obs - const.)

7. The Van der Waal's Equation of State V id = V obs - nb  b is a constant for different gases P id = P obs + a (n / V) 2  a is also different for different gases Ideal gas Law P id V id = nRT  (P obs + a (n / V) 2 ) x (V obs - nb) = nRT

8. Critical Constants Critical temperature (T c ) - the temperature above which a gas cannot be liquefied Critical pressure (P c ) – the minimum pressure that needs to be applied at T c to bring about liquefaction

9. Compression Factor The compression factor

10. The Boyle Temperature Boyle temperature - for a van der Waal's gas, the Boyle temperature (T B ) is written

11. The Boyle Temperature #2 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.

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

13. Reduced Variables The reduced state variables are defined

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