May 2011 - Career Point

KEY CONCEPTPhysicalChemistryFundamentalsGASEOUS STATEReal Gases :Deviation from Ideal Behaviour :Real gases do not obey the ideal gas laws exactlyunder all conditions of temperature and pressure.Experiments show that at low pressures andmoderately high temperatures, gases obey the laws ofBoyle, Charles and Avogadro approximately, but asthe pressure is increased or the temperature isdecreased, a marked departure from ideal behaviouris observed.Ideal gaspVPlot of p versus V of hydrogen, ascompared to that of an ideal gasThe curve for the real gas has a tendency to coincidewith that of an ideal gas at low pressures when thevolume is large. At higher pressures, however,deviations are observed.Compressibility Factor :The deviations can be displayed more clearly, byplotting the ratio of the observed molar volume V m tothe ideal molar volume V m,ideal (= RT/p) as a functionof pressure at constant temperature. This ratio iscalled the compressibility factor Z and can beexpressed asZ =VVmm,idealp= RTVmPlots of Compressibility Factor versus Pressure :For an ideal gas Z = 1 and is independent of pressureand temperature. For a real gas, Z = f(T, p), afunction of both temperature and pressure.A graph between Z and p for some gases at 273.15 K,the pressure range in this graph is very large. It canbe noted that:(1) Z is always greater than 1 for H 2 .(2) For N 2 , Z < 1 in the lower pressure range and isgreater than 1 at higher pressures. It decreases withincrease of pressure in the lower pressure region,passes through a minimum at some pressure and thenH 2increases continuously with pressure in the higherpressure region.(3) For CO 2 , there is a large dip in the beginning. Infact, for gases which are easily liquefied, Z dipssharply below the ideal line in the low pressureregion.1.0t = 0ºCH 2N 2CH 4ideal gasCO 2Z0 100 200 300p/101.325 barPlots of Z versus p of a few gasesThis graph gives an impression that the nature of thedeviations depend upon the nature of the gas. In fact,it is not so. The determining factor is the temperaturerelative to the critical temperature of the particulargas; near the critical temperature, the pV curves arelike those for CO 2 , but when far away, the curves arelike those for H 2 (below fig.)Z1.0T 1 >T 2 >T 3 >T 4ideal gas0 200 400 600p/101.325 kPaT 4T 3T 2Plots of Z versus p of a single gasat various temperaturesProvided the pressure is of the order of 1 bar or less,and the temperature is not too near the point ofliquefaction, the observed deviations from the idealgas laws are not more than a few percent. Underthese conditions, therefore, the equation pV = nRTand related expressions may be used.Van der Waals Equation of state for a Real gasCauses of Deviations from Ideal Behaviour :The ideal gas laws can be derived from the kinetictheory of gases which is based on the following twoimportant assumptions:T 1XtraEdge for IIT-JEE 30 MAY 2011