Question

at you 7.54 Consider a binary mixture of a and b at T 300K and P = 40 kPa. A graph of the fugacity of species a as a function of mole fraction is shown below. Use Henry's law as the reference state for species a and the Lewis/Randall rule for species b. Show all your work 40 38 36 T-300 K P: 40 kPa 34 32 30 28 26 24 22 20 18 16 14 12 10 4 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Xa 0.1 0.2 0 (a) What is the Henry's law constant, Hy, for species a? (b) What is the activity coefficient for species a at xa law reference state!). Show your work. (c) Is the activity coefficient for species b at x (d) Is the a-b interaction stronger than the pure species interactions? Explain. (e) Consider the vapor phase to be ideal. What is the vapor-phase mole fraction of a in equilib- rium with 40% liquid a? 0.8? (remember the Henry's 0.4? At x 0.4 greater than or less than 1? Explain. FH(KPa)

Answer 1

Law Cinstant, Ha, fa cpecies a t Ca Henry's the qrah observe Ne Can line the draw tangent initially a So liquid Species a ih a Augacity plot Nalue CA) fraction of mole the mixture Where o Ca-o Species a. Value fmole line the extend The thal Ca) After faction Species of a Henry's Laa Conctant is the that it Seen Now Vertical grid intercejt of the the to Value of xa=l the when Line f Species- Constant Henry's Law Then the is 19.5 kpa a bThe activity Cffiient 0.e? at of Specias a (7a). Coefficient activty Express Ja Here of Speies a m Tefevn ce stabe fugacity and State Yeference Law use can We above equationf Fa' the Tewrite A L Ra Ja

the given gure find Values bf at the From 12 kpa D.8 3 kpa and as and a = 0.4 n kpa for fa, 19.5 kPa for fm equatin ubstitute Calculate . 0.y for to and Ha 12 kpa Ra o.y C19.5 kpa) for 21 kpa from equatior «ubctitute a / 195 ka for Caleulate 0.8 for a Ha and 2t kpa 1.99 Coefficient of Species a ab activity 7here fore the is .sy and and a 0.8 qibbs-Duhem equation states the express Can We ad Cna) x4dC Ln 3b=0 XL and activity Speciec b is fraction this, mole Species b is of Coefficient qibhsDuhem euation ditferentiate the We Can (TL4P dza dza equation differentiakion Note negative dCinb) a left cide Sacond the becaus activity the based CoeffrcienE an a the Value f LewisRandal state reternce where Coetficient f peeies b mole fraction af activity natural tog the as o as InCa) i taken

also a Cxa) - Species a0.4, 7 isfaund activity cetficient for Specias b Value the Therefore, at negative, then the as C<1) "tess than i's d) than pure species a-binteractions stronger The of Species b is activity Coafficient because the than 4 CA) less Ce iuid, So each equilibrium Aith in A. The gat is fugacity phase Ja. = the Vapaur phase and caleulte above Case the Concider Species a Coetficient of of activity (Here: p= System pressure) - for p and /2 kpa for substitate Can kle Ra 2 kpa O.3 yokPa phate of activity Coefficient a Vapour There fove the fraction Jecies a of moke