Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited from idel behvior t high pressure nd low temperture. 3. Compressibility fctor (Z): The extent to which rel gs devited from idel behvior my be expressed in terms of Compressibility fctor (Z). Z= Molr volume of given gs ( P ) Molr volume of idel gs ( RT ) i. For n idel gs, Z=1 nd it is independent of temperture nd pressure. ii. iii. The devition from idel behvior of rel gs will be determined by the vlue of Z being grter or less thn one. The difference between unity nd the vlue of Z of gs is mesure of degree of non-idelity of the gs. For rel gs the devition from idel behvior depends on pressure nd temperture. This my be illustrted by exmining the compressibility curves of some gses. z=p/nrt 1.8 1.6 1.4 1. 1.0 0.8 0.6 0.4 N HO CH 4 CO O 00 400 600 800 1000 p/br

iv. At very low pressure, for ll these gses Z is pproximtely equl to one this indictes tht t low pressures, rel gses exhibit nerly idel behvior. v. As the pressure is incresed H shows continuous increse in Z. Thus H curve lies bove the idel gs curve (positively devited) t ll pressures. In this cse the repulsive forces dominnt. vi. For N, CO, Z first decreses (Z<1).It psses through minimum nd then increses continuously with pressure (Z>1). In this cse the forces of ttrction re dominnt. 4. Effect of temperture on devitions It is cler from the shpe of the curves tht thedevitions from idel gs behvior becomesless nd less with increse of temp. At low tempertures Z<1. While t high tempertures Z>1. At prticulr temperture, P/RT is lmost unity nd the Boyles lw is obeyed for n pprecible rnge of pressure is clled Boyles temperture. The Boyles temperture of ech gs is chrcteristic for exmple for N it is 33K. 5. Explntion for devition from idel gs behvior: The devition of rel gses from the idel behvior is minly due to two fulty ssumptions of kinetic theory of gses. i. The molecules is gs re point msses nd posses no volume. ii. There re no intermoleculr ttrctions in gs. There fore idel gs eqution P=nRT derived from kinetic theory could not hold for rel gs. 6. Eqution of stte for rel gs nder wlls pointed out tht both the pressure (P) nd volume () fctors re the idel gs eqution needed correction in order to more it pplicble to rel gses. i. The volume of rel gs =volume of idel gs volume occupied by gs molecules Thus corrected volume = (-b) Here b is co-volume or excluded volume or prohibited volume.

For n mole of gs, Co-volume is (-nb) Excluded volume is four times the ctul volume of molecules (b=4v). ii. Corrected pressure P P for one mole. v n For n mole of gs P= P.. iii. n der Wls eqution for one mole of Rel gs is ( p+ ) (v-b)=rt For n mole of gs is n P nb =nrt Here nd b re constnts known s n der Wls constnts, which vry from gs to gs. iv. Units of & b The vlue of is given by the reltion. = pv n = pressure( volume) mole The excluded volume b= tm lit. mole volume litre litre 1 n mole mole * is mesure to the mgnitude of ttrctive forces, greter the vlue of. more is the ese of liquifiction of gs. 7. Interprettion of devitions from n der Wls equtions: i. Cse 1: At extremity low pressure volume becomes very lrge hence b nd cn be neglected. Therefore the nder Wls equtions reduces to P=RT ii. Cse : At low pressure volume will be lrge; b cn be neglected, hence P RT ( or) P RT, dividing both sides with RT, we get P/RT =1- /RT, Z= 1-/RT i.e. Z<1

Hence the gs shows negtive devition from idel behviour. iii. Cse 3.At high pressure volume will be smll, therefore Hence cn be neglected. P(-b ) =RT or P=RT+ Pb or P/RT =1+ Pb/RT i.e Z>1The gs shows positive devition from idel behviour iv. Cse 4.At high temperture volume will be lrge nd pressure will be smll, the stte eqution becomes P=RT 8. In cse of H nd He ttrction between the molecules is negligible becuse of smll mss. So cn be neglected, the stte of eqution becomes P (-b) = RT or P=RT+Pb, dividing both sides with RT, we get Z=1+Pb/RT i.e Z>1 Hence both hydrogen nd helium lwys show positive devition from idel behvior Liquefction of Gses nd Criticl Point A gs cn be liquefied by lowering the temperture nd incresing pressure (or) rpid evportion nd doing mechnicl work in dibtic conditions. 9. Isotherms The grph drwn between pressure nd olume t constnt temperture is clled isotherm. The perfect gs isotherms re obtined from n der Wls eqution t high temperture nd low pressure. Andrews plotted isotherms of crbon dioxide t vrious tempertures s shown in the following

E P P c D C c T c Fig.5. Isotherms of crbondioxide t vrious tempertures B 50 0 C 31.1 0 C 30 0 C 0 0 C A It ws noticed tht t high tempertures isotherms look like tht of n idel gs. The gs cn not be liquified even t very high pressure. As the temperture is lowered, shpe of the curve chnges nd shows considerble devition from idel behviour. In the isotherm of CO t 00C, t point A it is gs. When the gs is compressed, the pressure increses upto point B. The piston cn be pushed in from point B to D through C without ny further increse in pressure. The gs begins to condense from point B nd condenstion completes t point D. At point C the vessel contins both the liquid nd gs. At point D the molecules re in liquid stte. A very lrge pressure is required to decrese the volume from D to E. It is becuse when the pressure is incresed from D the repulsive forces between the molecules increses. So the decrese in volume is less from D to E even though the pressure increse is very high. At 31.10C, crbondioxide remins s gs up to 73 tm pressure. At 73 tm, liquid crbondioxide ppers for the first time. 31.10C is clled criticl temperture of crbondioxide.

The temperture bove which the gs cn t be liquified by the ppliction of pressure is clled criticl temperture (Tc). olume of one mole of gs t criticl temperture (Tc) is clled criticl volume (c) nd pressure t this temperture is clled criticl pressure (Pc). Tc, Pc nd c re clled criticl constnts nd re obtined using the n der Wls constnts nd b. Criticl temperture Tc = Criticl volume, c = 3b Criticl pressure, Pc = 7b 8 7Rb At criticl condition, the compressibility fctor for one mole of gs, z = P P c c 3 RT RT 8 Liquefction of Gses c All rel gses upon compression t constnt temperture show the sme behviour s shown by crbon dioxide. Gses cooled only below their criticl tempertures, cn be liquified esily. This is becuse gses devites much from idel gs behviour nd intermoleculr ttrctions re considerbly high. A gs liquefies if it is cooled below its boiling point t given pressure. At 1 tm chlorine cn be liquefied by cooling it to 340C in dry ice bth. To liquify gses like nitrogen nd oxygen simple cooling to bring down temperture to 1960C nd 1830C is not possible. To liquify such type of gses the technique bsed on intermoleculr forces clled Joule Thomson effect is used.

When gs is llowed to expnd from high pressure to low pressure dibticlly through nrrow opening, the cooling effect of gs tkes plce. It is clled Joule - Thomson effect. In Joule - Thomson effect, the gs is llowed to expnd from high pressure to low pressure through nrrow opening (throttle), without supplying het from outside. In expnding, the molecules require certin energy to overcome the ttrctions of their neighbouring molecules. For this some of their kinetic energy converted into potentil energy. So the verge velocity of molecules decreses nd hence the temperture of the gs decreses nd the gs gets cooling effect. Under norml conditions when hydrogen is subjected to Joule - Thomson effect it wrms up. Becuse it s Z is greter thn 1. It cn be condensed to liquid only when the temperture of gs is below the inversion temperture. The temperture bove which gses get heted up nd below which gses get cooled due to Joule Thomson experiment is clled inversion temperture, Ti. Where Ti = /Rb Liquefction of gses like helium nd hydrogen is difficult. They re clled permnent gses. Liquefction of permnent gses requires cooling s well s compression.