Searatons n Chemcal Engneerng Searatons (gas from a mxture of gases, lquds from a mxture of lquds, solds from a soluton of solds n lquds, dssolved gases from lquds, solvents from gases artally/comletely saturated wth solvents) are mortant n chemcal rocess ndustres because they comrse large orton (u to 90%) of catal and oeratng exendture. ll searatons nvolve ether brngng a hase (hyscally searable mass) contanng the mxture to be searated wth another hase nto whch the desred seces gets dstrbuted or creatng another hase nto whch the desred seces gets concentrated. The dstrbuton or concentraton contnues tll the two hases reach equlbrum after whch there s no net transfer of the seces. t equlbrum, the two hases get saturated wth the seces. Examles of Searatons bsorton: gas (or gases) from a mxture of gases s absorbed nto a lqud that s brought nto contact wth the mxture. Searaton deends on solublty of the gas or gases that are absorbed. Dstllaton: mxture of lqud s heated and a vaour hase s created. The vaour hase s enrched wth the seces wth low bolng ont or hgher volatlty; ths hase s cooled and condensed to obtan a lqud hase concentrated wth more volatle seces. Lqud extracton: mxture of lquds s agtated wth another mmscble or artally mscble lqud vgorously and then the two lqud hases are allowed searate. The desred seces dstrbutes between the two lqud hases. dsorton: gas or gases from a mxture of gases or a lqud (or lquds) from a mxture of lquds s bound hyscally to the surface of a sold. Crystallzaton: sold comes out of the soluton and forms crystals when the temerature of a soluton contanng the sold s lowered. Sngle Comonent hase Equlbrum ressure Sold Lqud Vaour Temerature
It s reresented by a lot between temerature (on x-axs) and ressure on y-axs. onts on red boundary ndcate vaour ressure and temerature; those on blue boundary reresent ressure and meltng ont temerature; those on black boundary are ressure and sublmaton temerature. Normal bolng ont s the temerature at whch vaour ressure becomes equal to one atmoshere (a ont on red boundary). Vaour ressure s the ressure of vaour n equlbrum wth ts own lqud or sold. Imagne an evacuated n whch a lqud s taken and a temerature s mantaned. The maxmum ressure recorded at ths temerature s the vaour ressure of the lqud at that temerature. Vaour s a strong functon of temerature rsng exonentally wth t. Vaour ressure s also the measure the volatlty; the hgher the vaour ressure the hgher s the volatlty. Vaour ressure can be estmated n the followng ways: ^ H v Clausus Claeyron equaton: ln = + RT Where s vaour ressure, H^ v s latent heat of vaourzaton, T s temerature, R s gas constant and s a constant. Knowng the values of varables and constants on RHS, we could calculate vaour ressure. ntone equaton: log 10 = T + C Where s vaour ressure, T s temerature,, and C are constants. The constants are avalable n any standard text book or n erry s Chemcal Engneerng hand book. Note the unts of and T before luggng n the values. Cox charts: ecause of mortance of vaour ressure n chemcal engneerng calculatons, lots called Cox charts have been reared. In ths grah, vaour ressure s lotted aganst temerature. gan, standard text books should have ths chart. Gas-lqud Systems: One condensable comonent When temerature of a gas contanng a solvent s lowered at constant temerature, the solvent condenses. The temerature at whch frst drolet of the solvent forms s called dew ont temerature. t ths temerature, f Raoult s s aled: = y = Where s artal ressure of the solvent, s total ressure, y s mole fracton of the solvent n the gas. ccordng to above equaton, solvent n a gas condenses whenever ts artal ressure equals vaour ressure. t temeratures hgher than dew ont temerature, artal ressure s less than vaour ressure and the vaour n the gas s called suer heated vaour. = y < The dfference between the temerature of the gas and ts dew ont temerature s called degrees of suerheat.
Few terms are useful n makng materal balance calculatons nvolvng condensable seces. They are: Relatve humdty = x100 Molal humdty = = M bsolute humdty = = moles of vaour moles of vaour - free (dry) gas mass of vaour ( ) M mass of vaour - free (dry) gas dry ercentage humdty = x 100 The nformaton on saturaton of a gas could be obtaned from values of any of the four terms defned above. For examle, f relatve humdty s 90% at 30 o C at 1 atm, t means the artal ressure s 0.9 tmes the vaour ressure at 30 o C. Ths ece of nformaton could be used to fnd mole fracton of the solvent, whch could be calculated by estmatng the vaour ressure at 30 o C usng, say ntone s equaton. Henry s law Ths law descrbes the equlbrum between a non-condensable gas and a lqud n whch the gas s sarngly soluble (mole fracton of the gas n lqud s close to zero). Examles of some sarngly soluble gases: CO 2, O 2, N 2, CH 4, C 2 H 6 = Hx s artal ressure of the gas above lqud, H s Henry s law constant and x s mole fracton of the gas n the lqud. Unts of H are atm/mole fracton; of course other unts for ressure could be used. Vaour Lqud Equlbrum When a mxture of lquds (lqud, lqud, lqud C and so on) s heated at a constant ressure, at a certan temerature frst bubble of vaour forms; ths temerature s called bubble ont temerature. The mole fractons of all comonents,, C and so on n the bubble add u to unty. Usng Raoult s law, we have: x x + xc + C +... = 1 Where x s mole fracton and s vaour ressure and s total ressure. You could magne, lowerng the ressure of the lqud keeng the temerature constant, the ressure at whch frst bubble of vaour forms s called bubble ont ressure. The above equaton could be used to fnd ressure for a gven temerature.
If a vaour contans more than one condensable comonent (say,, C etc.) and when the temerature s lowered, at a certan temerature frst drolet of lqud forms; ths temerature s called dew ont temerature. When ths haens, the mole fractons of all comonents n the dro should add u to unty. lyng Raoult s law and summng u the mole fractons n the dro, we have: y y yc + + +... = 1 Smlar to bubble ont ressure, dew ont ressure s the ressure to whch the vaour must be subjected at a constant temerature so that frst dro of lqud forms. bove equaton could be used to estmate the dew ont ressure for a gven temerature C Lqud Extracton To searate a seces from a lqud, another lqud, whch s mmscble or artally mscble wth the mxture s added to the mxture and mxed vgorously. fter mxng, when allowed to settle, two hases form and the seces to be searated dstrbutes between the hases. One of the hases would be rch n and the other rch n. If and are mmscble, they do not dstrbute. We wll consder only mmscble lquds. The dstrbuton of the seces between the two hases s determned by a dstrbuton coeffcent, K, defned as the rato of mass fracton of seces n one hase to ts mass fracton n other hase. dsorton mass fracton of the seces n one hase K = mass fracton of seces n other hase Ths s a rocess n whch a gas or gases from a mxture of gases adsorb on the surface of a sold. It ales to a mxture of lquds also. The seces that gets attracted to the sold s called adsorbate and the sold s called adsorbent. n adsorbent has an affnty for an adsorbate. dsorton s not used extensvely but nevertheless an mortant oeraton. X, g of adsorbate g of adsorbent artal ressure of the adsorbed seces n the gas hase
When a mxture of gases s brought n contact wth an adsorbent and f we wat for long tme, the system reaches equlbrum. That s the gas hase s n equlbrum wth the sold hase. Ths equlbrum s reresented by lottng artal ressure of the seces n the gas hase aganst rato of the amount of seces absorbed to the amount of adsorbent. The lot s generated by makng an exerment n whch a certan artal ressure of the adsorbate n the gas hase s mantaned and then X s measured. We could reeat ths exerment for several values of the artal ressure and generate the comlete curve. ll the exerments are done at a temerature and therefore the curve s called an sotherm. These curves are called Langmur-adsorton sotherms. Engneers are always nterested n fttng equatons to exermental data n order to reduce exermentaton. Langmur-adsorton sotherms can be reresented by the followng equaton: L ak L X = 1+ K where a and K L are constants obtaned by fttng exermental data to the above equaton. Knowng one quantty, ether X or, other quantty can be found f the equaton for adsorton s gven. Test Your Understandng 1. r contans 7.0 mole% water at 35 o C and 755 mm Hg. What s the dew ont temerature? What ressure ar must be subjected to at 35 o C to condense water? 2. How can you condense a solvent n artally saturated gas? 3. Exlan vaour ressure n you own words to a 10 th class student. 4. Henry s law constant for ethane n water at 20 o C s gven as 1460 atm cc/mol. Convert t to the unts of atm/mole fracton (Hnt: Ethane s sarngly soluble n water wth ts mole fracton close to zero). 5. What s bubble ont temerature of 40.0 mole% benzene and 60.0 mole% toluene mxture at a ressure of 1 atm. Get ntone constants for benzene and toluene from endx of the text book. 6. Calculate the dew ont temerature of a vaour contanng 40.0 mole% benzene and 60.0 mole% toluene at 1 atm. Get ntone constants for benzene and toluene from endx of the text book. 7. What do you conclude about the bubble ont and dew ont temeratures estmated n questons 4 and 5. 8. lot bubble ont temerature Vs. mole fracton of benzene (varyng from 0 to 1.0) and exlan the lot. lso, lot dew ont temerature Vs. mole fracton of benzene. 9. What s dstrbuton coeffcent? enzene and hexane are beng consdered to extract acetc acd from aqueous mxture. K for benzene s 0.098 and that for hexane s 0.017. For the same extent of extracton of acetc acd, would you need more of benzene or hexane? Exlan. 10. Can artal ressure of a solvent n a gas at a gven temerature be greater than ts vaour ressure at that temerature? 11. Exlan how Langmur adsorton sotherms are generated n your own words. 12. If a gas mxture contanng 10.0 mole% water n ar s brought n contact wth slca gel, the gel adsorbs water. If you wsh to determne the amount of adsorbent to reduce the water content to 1.0 mole%, you would obtan a value of X corresondng to 10.0 mole% or 1.0 mole%? Why?