110c-lecture14 - Composition of vapor phase vs. solution...

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Unformatted text preview: Composition of vapor phase vs. solution phase: ( ) ( ) ( ) ln ln ln 2 1 2 2 s n s n s n x + = ( ) ( ) ( ) 2 * 2 2 * 1 1 * 2 2 2 1 2 2 1 2 2 x P x P x P x P P P vap n vap n vap n y + = + = + = (unless * 1 P = * 2 P .) If * 1 P = * 2 P , 2 2 x y = If * 1 P << * 2 P , then y 2 1 If * 2 P << * 1 P , then y 2 0. Note that * 1 * 2 1 2 * 1 1 * 2 2 1 2 P P x x P x P x y y = = and so 1 2 1 2 x x y y > when * 2 P > * 1 P . Vapor phase is more enriched with the more volatile component ( 1 2 1 2 x x y y > ) if * 2 P > * 1 P . omposition of Vapor Phase is Different from Solution Phase P i = n i RT/V * 1 P * 2 P gas liquid solution y j x j y 2 > x 2 y 2 < x 2 A(l) + B(l) A/B(sln) 1 2 * 2 2 * 1 1 P x P x P tot + = Boiling Temperature Depends on Composition 25% A 75% B 50% A 50% B 80% A 20% B A(l) + B(l) A/B(sln) Boiling temp (bp) is T at which P atm = P tot P atm = 1 atm or 760 torr * * B B A A tot P x P x P + = * * * B A B atm A P P P P x = atm A A B B A A A A vap A P P x P x P x P x y * * * * = + = * * * A B A atm B P P P P x = atm B B vap B P P x y * = Consider the boiling point of a solution at P tot =1 atm=760 torr: ( ) ( ) * 1 * 2 2 * 1 * 2 2 * 1 2 * 2 2 * 1 1 2 1 1 760 P P x P P x P x P x P x P P torr P tot + = + = + = + = = ( ) * 1 * 2 2 * 1 760 P P x P torr + = * 1 * 2 * 1 2 760 P P P torr x = Boiling Temperature vs Solution Composition (Atmospheric pressure=760torr) x 2 = mol fraction of component 2 in solution at bp. If we know ( ) T P * 1 and ( ) T P * 2 at a given temperature, we can find x 2 at the bp: A solution of 1-propanol and 2-propanol at T=90 C, P 1 *=575 torr and P 2 *=1027 torr, 55 . 760 ) 1027 )( 41 . ( 760 41 . 575 1027 575 760 760 * 2 2 2 * 1 * 2 * 1 2 = = = = = = torr P x y P P P torr x 45 . 760 ) 575 )( 59 . ( 760 59 . 575 1027 760 1027 760 * 1 1 1 * 1 * 2 * 2 1 = = = = = = torr P x y P P torr P x Bp (97 C) of pure 1-propanol Bp (90 C) of 59% 1-propanol and 41% 2-propanol Bp (84 C) of 20% 1-propanol and 80% 2-propanol Bp (82.4 C) of pure 2-propanol P atm = P 1 + P 2 Fractional Distillation of Beer 43 . ) 14 . ( 92 . ) 28 . ( 08 . ) 28 . ( 08 . * 2 2 * * = + = + = O H O H et et et et vap ethanol P x P x P x y * * ln ln ) ( j j j s j P P RT liq + = Properties of an Ideal Solution , = = n T id mix id mix P G V ( ) 2 2 1 1 ln ln x n x n RT G id mix + = ( ) 2 2 1 1 2 , 1 , ln ln x n x n R T G S n n P id mix id mix + = = = + = id mix id mix id mix S T G H * 1 1 1 P x P = for 0 < x 1 < 1 1 * 1 ln 1 ln ) ( x RT liq s + = 2 * 2 ln 2 ln ) ( x RT liq s + = * 2 2 2 P x P = for 0 < x 2 < 1 = + = id mix id mix id mix V P H U benzene(l) + toluene (l) benzene/toluene (sln) B---B T---T B---T 1.0 0.8 0.6 0.4 0.2 x toluene = x 2 = x 1 * 1 P * 2 P * 1 1 1 P x P = * 2 2 2 P x P = * 2 2 * 1 1 P x P x P tot + =...
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110c-lecture14 - Composition of vapor phase vs. solution...

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