Question

Please answer the following question completely and correctly. Please write neatly and show all work.

1. Show that the van der Waals equation leads to values of Z (compressibility factor) < 1 and Z > 1, and identify the conditions, t is, how the temperature T is related to the molar volume V_m, for which these values are obtained?

Answer 1

PV = RT ideal gas equation followed by real gases high temperature and low pressure .

=) Van-der waals egna (P + 9 ) (Vm-b) =RT case when Pressure is high then 9 (attraction) is ng. There are two cases :- theni- e fum-b) = RT Pvm - Pb=RT when Pressure is low ! - then um ssb (pt a ) Vm = RT - Pum + 9 =RT Pvm + a = 1 RTVm Pvm 1 - Pb = 1 4 RT RT w RT Z - Pum RT m = [2 + 1 is greater RTVm This shows z than one , le; [ 21] one Here, z is less than de zz zz11 Hence at nigh pressure [231] at low pressure [241] & The molar volume is directly related to Temperature of the Temperature is high , volume becomes so large to make (2) neglegibly small at nigh Temperature & D also be neglected with vm. at this case Vander waals gas equ follows Real Ideal gas egh