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# Introductory Physical Chemistry CH 331

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This 5 page Class Notes was uploaded by Sienna Shields on Thursday October 15, 2015. The Class Notes belongs to CH 331 at North Carolina State University taught by Stefan Franzen in Fall. Since its upload, it has received 9 views. For similar materials see /class/223995/ch-331-north-carolina-state-university in Chemistry at North Carolina State University.

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Date Created: 10/15/15

Chermstry 331 Lecture 14 Pnase Dragrarns NC State Dennmon ofa pnase dragrarn Wm WM mme in mm 5m new We mm a m mquot bumme mm mm mmu meme pm mm mm m mm hues mam wenslenue cums Nmemere rs me new Degrees offreedom Illmm mm Mme me We mm m mnmm between mum and Evarandmem rs sm e mm D Free energy dependence a ong the coexrstence curve rquot aseemwrwamese v mum and was r WWW ememns a e 5 W mm mm emmwm WWHW mm weer n wage mmmr mm mm WWW mmsz mm ammmmmwm Wem n mm m mm Wm Be Be m quotMaw mmWWW mywnrmmmese armrmmrmmr potentrar of coewstmg pnases We mm m m mm mm new as W Wm mm mm swam rerva we mm m mgr mm M be mm m WWW WMmanransmmmmesmm mmquot lt n mm wwwmrmn w W an r n m mm mismmmmm we We mm mer mum an Memsmchemma vmemm m G bbsenewvhnhe pm ethbnum r5 Freq WM 5mm pm n WWW e m m mamquot u u mmmm r murmur me 5mm in n equrrmmmrcremrerpaeme mm m pm in m n new Samaneaus e manEDhasemmemherwmacwr mmxesd anmnsmmm erchemma pmnrm a pm we awer mm cansiem Wm nevnm m are spamaneau 5 mm n 5 We Solidliquid coexistence curve To derive expressions for the coexistence curves on the phase diagram we use the fact that the chemical potential is equivalent in the two phases We consider two phases a and b and write WTiP WT Now we take the total derivative of both sides am am am aim al4PtalwlaldPa The appearance ofthis equation is quite different from previous equations and yet you have seen this equation before The reason for the apparent difference is the symbol u Remember that m for a single substance is just the molar 39ee energy The Clapeyron equation vw sar de swr Solving for dPdT gives dF m m p55quotArs B7quot Wei K V 7 m m rs m 5 m This equation is known as the Clapeyron the twophase boundary curve in a phase Augl and AMV between them TheClapeyron equation can be used to determine the solidliquid curve by integration equation It gives diagram with ArsHm p e Arslm y 7 Starting with a known point along the curve eg thet iple point or the melting temperature t one bar t a we can calculate the rest ofthe curve referenced to his point The liquidvapor and solid vapor coexistence curves The Clapeyron equation cannot be applied to a phase transition to the gas phase since the molar volume ofa gas is a function ofthe pressure Making the assumption that V gtgt Vi we can use the ideal gas law to obtain a new expression for dPldT dF AWN FAWN 3739 39TVT R The integrated form ofthis equation a 3A H M yields the ClausiusClapeyron equation is ash811 Applying the Clausi us Clapeyron equation lfwe use AH of evaporation the CC equation can be used to describe the liquidvapor coexistence curve and ifwe use AH of sublimation this equation can be used to describe the solidvapor curve The pressure derived from the CC equation is the vapor pressure at the given temperature Applications also include determining the pressure in a hi h temperature vessel containing a liquid eg a pressure cooker lfyou are given an initial set of parameters such as the normal boiling point for example you may use these as T1 and Pi Then ifyou are given a new temperature T2 you can use the CC to calculate P2 Constructing the phase diagram for CO2 e can use the Clapeyi onand ClausiusrClapeyi on equations to calculate a phase dia rarn cah begll i with the 02 diagram showh above Thetnple point for CO i5 511 atm and 21615 K The critical point for for CO2 is 72 85 atm and 304 2 K We a so have the following data W Note that we can calculate the Anti Aist lquot Aiist lquot 15 9 pm i 53 9ch ahd pm 0 78 gcm respe The density p rnV V so the molarvolurn vm wh Mp where M is the molar mass in Lil iltS of Lrnole we vsm 44 gmoiemsso gL 0 0287 vim 44 grnole780 gL 50 Amy vi 7 a 0 05047 0 0287 0 0277 Lrnole enthalpy of Sublimation from kJrnol ctively e is I m lt a Constructing the phase diagram for 002 Starting wi h the triple point we use the ClausiusClapeyron equation to calculate the liquidvapor coexistenc P 511expAvaleRT 2161521615T P 511exp2032T 21615l21615T Notice that ifwe were to calculate the critical pressure using this formula we would obtain 77 3 atm which is about 5 atm larger than the experimental number There are several 390 i s 3 mm x 31 AvaleRT 30423042T P 728 exp2032T 30423042T W m W W Va 5m 2mm 5m 2mm gquot m g mm m W m m mun m mun m 22a 2 m In 5v W u W u 2 gm un 40 g a W W m m a gh g mm m W m W A A m In 57 m In Ev W In u w 23 u s un 40 gr un 40 gm 2H m a 2H m a quotw W on m E on m E 812mm ivam 31mm vmm p uexpmwwpm mm m p uexv u r n mm mm mm H mm mm it 5m 2 5 5539 w L EX V 812mm ivam 31mm vmm p uexpmwwpm mm m p uexv u r n mm m Sahdwavar A Ham m z u mu m m g m n a E 812mm ivam 31mm vmm p uexpmwwpm mm m ugv u r m p mm m Sahdwavar if Ham m 5 u m u m 2m m znn um um um mu 812mm ivam 31mm vmm p uexmeHRnrnn Hymn m p uexp u rzm mm mm mm A 7 Hum rm E 5m 55quot m 2m quot m mu a D725 wn g1 am mm mm n umm mavevan um we mm m mummym 5 u my Mum 5 samm Ham m 5 u m u umm mavevan um we mm m mummym 5 u m m 5 2 m n Sahd mum p m r K 5 u m 5 u m umm mavevan um we mm usnvme mm m mmmwm 5 2 my Mum 5 m um we mm m mummym 5 mozvmn mms mm mm mm Ham m 5m 5m mu an ax 22a e m2 m2 23a 2 me 240 g m 2m 39 m m m m uxn m

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