Prepared By: Bhadka Ravi H. Guided By: Mr. P. L. Koradiya Van der waals Equation Prepared By: Bhadka Ravi H. Guided By: Mr. P. L. Koradiya

The Ideal Gas Law Extensive vs. intensive properties Units of pressure Units of temperature Triple point of water occurs at 273.16 K (0.01oC)

Deviations from Ideal Gas Law Real molecules have volume. The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves. There are intermolecular forces. An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions. Otherwise a gas could not condense to become a liquid.

Van der Waals equation At fixed P and T, V is the solution of a cubic equation. There may be one or three real-valued solutions. The set of parameters Pc, Vc, Tc for which the number of solutions changes from one to three, is called the critical point. The van der Waals equation has an inflection point at Tc.

Critical Point of van der Waals Equation

Deviations from Ideal Gas Behavior T=300K “compressibility factor” Ideal gas: z = 1 z < 1: attractive intermolecular forces dominate z > 1: repulsive intermolecular forces dominate

According to van der Waals, the theorem of corresponding states (or principle of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree

The law of corresponding states All gases behave the same way under similar conditions relative to their critical point. (This is approximately true.)

Limitations of Van Der Waals Equation are given below 1.     The values of constant ‘a’ and ‘b’ obtained by different methods differ considerably. Although Van Der Waals theory assumes them to be constant. The value of ‘a’ is found to depend on the temperature. At very high temperatures, it tends to zero. 2.     According to theory, Vc=3b, but it is found to depend on the nature of gas. Experimentally, it is found that Vc≈2b. 3.     The theoretical value of critical coefficient RTc∕ PcVc is 2.667 for all gases. However, it varies from gas to gas with an average value of 3.7 for most of the gases. This constant appears to depend on the molecular structure of the gas. Thus no gas obeys Van Der Waals equation closely in the vicinity of the critical point.