Chapter 6 What is Henry s law pi p iL Xil pi Xil p iL for non ideal solutions low solubility pi i Xil p i dividing by V l or the molar volume of the mixture sometimes called Vmix X Vl Concentration Ci pi V l i Ci p i pi Ci i p i V l const KiHl If air water K iH Is the product of i p i Vmix a constant Is it different for different compounds Does it vary with temperature Does it change with concentration Does it change with salt or ionic content How do we measure it Chatper 6 Henry s Law 1 p K iH i Ciw traditionally K iH atmi atm liters mole 1 1 molesliters w C K iaw ia dimensionless Ciw K iaw C K Cia ia iH p pi i K iH Henry s law const Cia K iH K iH n V RT RT 2 If we go to the Appendix p 1200 new book and look at for Henry s law values for air water we see log Kiaw p iL and Ciwsat are referenced to their states how are these log Kiaw values computed Ideally since KiH pi Ciwsat If we go to a unit less form Kiaw where Kiaw KiH RT So log Kiaw log pi RT log Ciwsat For anthracene the Appendix has the following data log pi 3 01 Pa log Ciwsat 6 60 log Kiaw 2 8 1atm 101 308 pascals so 1st we need to get log pi in atm 10 3 01 Pa 101335 Pa atm 9 646 x10 9 atm to change pi in atm into Cair pi V nRT Cair pi RT R 0 082 L atm mole T 298 K this gives Cair 3 94x10 10 moles literair log pi RT 9 40 logKiaw log pi RT log Ciwsat logKiaw 9 40 6 60 2 80 and this is the book value 3 The old book is a lot cleaner It gives log poL and log pos directly in atmospheres and log Cwsat log Cssat are in moles liter and log KH in liters atm mol So to get log KH in the appendix p 621 of the old book for anthracene in old book p 621 logKH log pLo log Cwsat or logKH log pso log Cssat for a liquid anthracene log KH 6 11 4 48 1 63 for a sold anthracene log KH 8 1 6 46 1 64 KH RT Kiaw in new book and log Kiaw 3 03 4 going back to Henry s law p K iH i Ciw As Henry s law values increase there is a tendency for higher gas phase concentrations over water i e partitioning is toward air for high vapor pressure compounds the fugacity in the gas phase is high fi i Xifi pure liquid fi pure liquid p i pure liquid High activity i coefs favor partitioning to the gas phase i e Lower KiH and lower s favor the liquid phase Polar compounds 5 Figure 6 2 page 111 old book 6 Wash out ratios or W and how fast does the atmosphere clean up during a rain Usually defined as the conc in rain conc In air W Ciw Cia 1 Kiaw W x Cia conc in the rain Ciw with units of moles cc water or Ciw in units of moles i cc moles i g H20 The rain has an intensity I with units of grams of rain sec 1 cm 2 so now I x Ciw g rain sec 1 cm 2 x moles i g H20 Since W Ciw Cia 1 Kiaw I x 1 Kiaw x Cia moles of i from the atmosphere hitting the surface of the earth in the rain per sec 1 cm 2 And this is a flux 7 We will learn in the old book Chapter 10 Flux conc x depth 1st order rate constant in C Co e kt So if you know the rain intensity Kiaw and the height of the atmosphere you can estimate how fast the atmosphere will clean up with a given rain intensity Flux I x 1 Kiaw x Cia moles of i from the atmosphere hitting the surface of the earth per sec 1 cm 2 If the mixing height of the atmosphere is 300 m and we have a rain that gives an 1 of water in 2 hours I 2 5g cm 2 2x60x60 sec 3 47x10 4 g cm 2 sec 1 Kiaw phenol 2x10 5 krate constat I x 1 Kiaw x Cia Cia x30 000 cm in units of 1 sec 8 Concentration effects on KiH Ciw Xi Vw Vw molar vol H2O p p K iH i iw iw l iw pl Vw C iw iw Vw Under dilute conditions KiH is directly proportional to the activity coef saturated vapor pressure molar volume of water 9 What is the effect of concentration on KiH P iW water organic at saturation the vapor pressure pi p iw pi i Xi p i pure liquid sat X iw 1 pisat 1 sat sat iw pi iw p sat i K sat sat pl Vw sat iH w C iw The question becomes how does KiHsat differ from KiH If the activity coef changes with increases in concentration of Ciw then KHsat will change Why 10 The old book suggests from benzene partitioning data that little difference may exist between KiHsat and KiH for benzene K iaw Cair Ciw a difference of 4 was observed between saturated and dilute water solutions This means that KiH can sometimes be approx from K and estimated from sat iH sat p sat i K iH sat C iw Example If the Ciwsat for chlorobenzene 4 3x10 3 mol L at 25oC and p iL 1 6x10 2 atm what is the KiH sat p sat iL K iH K iH sat C iw K iaw 1 6 x10 2 atm 3 6atm L mol 4 3 x10 3 mol L K iH 3 6atm L mol 1 0 15 RT 0 082atm L mol 1K 1 x 298K A simple way of changing iw into iwsat this does not always work log i log isat 1 xisat 2 11 sat K iH p sat iw sat sat piL Vw w Ciw for infinitely dilute solutions p p K iH i iw iw iL iw piL Vw Ciw iw Vw 12 Comparison of iw and iwsat iw logCiwsat Ciw sat Tab 5 2 p618 mol L iwsat 1 CsatVmix old book benzene toluene chlorobenz hexCl benz octanol 2400 12000 19000 9 8E 8 37000 1 64 2 25 2 35 5 56 2 35 0 0229 0 0056 0 00447 2 75E 6 0 00447 2425 9879 12437 2 0E 7 18656 Why are iw values sometimes greater than iwsat 13 Effect of Temperature ln p i L vapHi 1 const R T by analogy sat ln x iw H Eiw 1 const R T x sat sat Ciw iw Vmix ln Cwsat so substituting E excess heat of solution H iw 1 const Vmix R …