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Vapor Pressure - Chapter 4 Vapor Pressure p = Pressure of a...

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Chapter 4 Vapor Pressure pº = Pressure of a substance in equilibrium with its pure condensed (liquid or solid) phase Why do we care? -spills -pesticide application -will lead us to Henry’s law constant
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Air Water Octanol A gas is a gas is a gas T, P Fresh, salt, ground, pore T, salinity, cosolvents NOM, biological lipids, other solvents T, chemical composition Pure Phase (l) or (s) Ideal behavior P o L C sat w C sat o K H = P o L /C sat w K oa K H K ow = C sat o /C sat w K ow K oa = C sat o /P o L
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Ranges of p º (atm) PCBs – 10 -5 to 10 -9 n-alkanes – 10 0.2 to 10 -16 n-C 10 H 22 ~ 10 -2.5 n-C 20 H 42 ~ 10 -9 Benzene ~ 10 -0.9 toluene ~10 -1.42 Ethylbenzene ~ 10 -1.90 propyl benzene ~ 10 -2.35 carbon tetrachloride ~ 10 -0.85 methane 10 2.44 Even though VP is “low”, gas phase may still be important.
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Phase diagram picture of three-phase diagram
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Ideal Gas Law nRT pV = p = pressure V = volume n = moles of gas R = gas constant T = temperature (Kelvin)
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Thermodynamic considerations (deriving the van’t Hoff equation) 2 1 μ μ d d = consider a gas: if T or P is changed and equilibrium is re-established: the change in chemical potential in the two systems is equal dp V dT S d dp V dT S d 2 2 2 1 1 1 + - = + - = μ μ where S = molar entropy and V = molar volume 12 12 2 1 2 1 ) ( ) ( V S V V S S dT dp = - - =
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at equilibrium S T H G G - = = - = 0 2 1 12 μ μ substituting: 12 12 V T H dT dp = for a liquid vaporizing, the volume change can be assumed to be equal to the volume of gas produced, since the volume of the solid or liquid is negligible 0 12 p RT V V gas = = Q. where did the n go? A. this is molar volume
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2 12 0 0 ) ( RT H p dT dp = 2 12 0 ln RT H dT p d = dx du u dx u d 1 ln = recall (calculus!) where H 12 = H vap (gas) or H sub (solid) = energy required to convert one mole of liquid (or solid) to gas without an increase in T. H vap is a function of T. As T approaches the boiling point, H vap increases rapidly At T < boiling point, H vap increases slowly from 0-40ºC, H vap can be assumed to be constant The van’t Hoff equation
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2 12 0 ln RT H dT p d = integrate assuming H vap is constant: a RT H p + = 12 0 ln B T A p + - = 0 ln Antoine equation if H vap is not constant: a c T b p + + - = 0 ln another Antoine equation
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Using H vap to predict VP at other temperatures -
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