Question

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 Vm, for which these values are obtained? (20 pts)

Answer 1

Imole gas (ideal) the equation is PV=RT . Luo volume of the gas rpm Preessure of the gas Rt Universal gas constant Tt Temparature] for 1 mole real gas , van der Waals . equation is (P+ ) (w-b) = RT Pas preesswee correction constant by volume correction constant] ... The deviation of the real gases from the ideal states can be clearly displayed by plotting the ratio of observed inolar volume (Vm) to the ideal molar volume (vi) as a function of pressure at constant temparature. This reatio is called the compressibility factor (2)

Case-Io- . 2<1 when vi > vm Then the gas will be more compressible than theoretical expectation. The deviation will be negative. . It will happen when molar volume of ideal gas is greates than the molar volume of real gas. It will cause when the attreactive force among the gas molecules will be very high and the gas can be easily liquifiable putting the value of tovi (= RT) we get . ui yum : on RT ) Um :-) | RT Yump] - Р This es 2.61 is the relating condition to become t with Vem

Case-I 281 when wom) Wi The gas will be less compressible. . than the all theoretical explanation. The deviation will be positive.. . It will happen when molar volume of real gas is greates than the molar volume of ideal. gas. It will cause when the rabuloi w #m a va Hu 8, molecules will be greater than the attreactive force. Hence the gas will not be easily liquifiable putting the value of Ni (= RT) we get Vad vi . or. umy RT or lump >RT . This is the condition to become 2) 1 relating T with Wm