Lecture 26 Chapter 16 Ideal-dilute solutions and Colligative Properties

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1 Lectre 26 Chapter 16 Ideal-dilte soltions and Colligative Properties nnonce: HW de next Monday Remember Seminars Friday Hledin at 3:00, Bchwalter at 4:00 We ll go over exams on this afternoon Otline: Mixing of non-ideal soltions H mix 0 G mix cold be anything p Liqid/gas eqilibria µ () l = µ () l + RTln p Review Mixing of ideal soltions H mix = 0 S mix = n tot R ( X lnx + X B lnx B ) G mix = n tot RT ( X lnx + X B lnx B ) We also derived how liqid chemical potential depends on composition p µ () l = µ () l + RTln p if p < p, then µ (l) < µ (l) (mixing lowers the chemical potential) Therefore, the chemical potential for the liqid sbstance in a mixtre is dependent on the chemical potential for the pre sbstance pls a factor that is dependent on the ratio of the vapor pressres (of p in mixtre to p of pre sbstance). Raolt s Law Let s simplify this last relationship that connects chemical potential with ratio of vapor pressres. We can se the experimental reslt that (for similar liqids) the mole fraction of the sbstance in the mixtre is approximately p /p, or the ratio of the partial vapor pressres of each component in a mixtre to its vapor pressre as a pre liqid: 1

2 p = X p (Raolt s law) Vapor Pressre (torr) X benzene Pre benzene Pre tolene Binary mixtre obeying Raolt s Law (Fig 10.3 from MT) Total Benzene Tolene We can see (since the mole fraction is always less than 1) that the vapor pressre is always redced for a sbstance when additional sbstances are added to the mixtre. The reason for this can be nderstood simply by considering that only molecles near the srface of the liqid may easily escape. So, it makes sense that the mole fraction in the mixtre shold directly affect the vapor pressre. Raolt s law is valid for similar sbstances this is becase then interactions with other sbstance will closely mimic those with the pre sbstance. We can se Raolt s law to write the eqation for the chemical potential of the liqid : µ () l = µ () l + RTlnX 2

3 This eqation is valid only for ideal soltions (similar interactions, mix H = 0). Remember that mix H = 0 does not mean that there are no interactions, it means that the interactions in the mixtre are the same as those in either pre sbstance. Even for non-ideal soltions nder what conditions might Raolt s law be obeyed? When the mole fraction of a sbstance approaches one. In this case, the solvent obeys Raolt s law The moleclar explanation for this limiting behavior is that each of the molecles will have only molecles identical to itself in its next-neighbor sphere. and the solte obeys Henry s law p B = X B K B (Henry s law) Notice here that while the vapor pressre is proportional to the mole fraction (as is the case for Raolt s law), the constant of proportionality is not the vapor pressre of the pre sbstance. This constant (K B ) is chosen to be tangent to the experimentally determined crve at X B = 0. Show diagram for transition from Henry s law regime to Raolt s law regime. Positive Deviation from Raolt s Law Vapor Pressre Slope = K B ctal Raolt s Law X Ideal-dilte soltions: are those that behave as above non-ideal mixtres for which the solvent obeys Raolt s law and the solte obeys Henry s law. 3

4 Henry s law constants are inversely proportional to the solbility (vapor pressre is inversely proportional to solbility). Right? If something is very solble then we wold expect it to not escape into the vapor phase. Sample Henry s law constants for aqeos soltions (298 K) (from Tinoco) Solte K B (atm) He 131 x 10 3 N 2 86 x 10 3 CO 57 x 10 3 O 2 43 x 10 3 CH 4 41 x 10 3 r 40 x 10 3 CO 2 2 x 10 3 C 2 H 2 1 x 10 3 s we saw before for non-ideal gas behavior, more electrons lead to greater intermoleclar attraction, and in this case, greater solbility. Why? Larger dispersive interactions it is easy to indce dipoles. Example Origin of the bends in deep-sea diving. The bends are cased by bbbles of N 2 gas that form in the bloodstream as the diver rises too qickly from a dive. save for homework. Real Mixtres Show acetone-chloroform pressre vs. mole fraction diagram (from Levine) 4

5 We can see that at very low mole fractions, both acetone and chloroform obey Henry s law and that at high mole fractions they obey Raolt s law. What kind of behavior is this? Ideal-dilte However, at intermediate mole fractions the mixtre deviates from ideality the vapor pressre for each sbstance is less than that predicted by Raolt s law (negative deviation). Why negative? This is becase acetone and chloroform have more attraction for each other than they do themselves. Show acetone-carbon dislfide diagram 5

6 Here is a case of even stronger non-ideality, althogh here we can see that the deviation is positive. Why positive? acetone and carbon dislfide have less attraction for each other relative to their attraction for themselves. Note that they don t necessarily repel each other jst attract less. Let s back p a second. Remember or focs here is intermoleclar interactions How do we qantify the intermoleclar interactions in: ideal gaseos mixtres? no interactions ideal liqid mixtres? similar in mixtre compared to pre components Ths, or reference state for a liqid mixtre is the intermoleclar interactions in the pre soltions. In yet another dplication of notation, se for intermoleclar interactions. What shold be for an ideal soltion? + B B B = 2 lternatively, we can define w as the non-ideality w = 2 B B B w = 0 for ideal w < 0 for stronger attraction w > 0 for weaker attraction/replsion Note that Dill defines the closely related exchange parameter the energy to transfer one into otherwise pre B and one B into otherwise pre. 6

7 z + BB χ B = B (Dill Eq 15.11) kt 2 In the case of benzene-tolene we saw this mixtre was ideal, so w = 0 In the case of acetone-chloroform we saw that the -B interactions were stronger (more attractive) and the case of the observed non-ideality. + B B B < (more negative, w < 0) 2 On the other hand, for acetone-carbon dislfide we saw that the -B interactions were weaker (more replsive) and cased non-ideal behavior of opposite sign to that the acetone-chloroform case. + B B B > (less negative, w > 0) 2 It is possible for real soltions that mix G > 0 (either becase of enthalpy increases or entropy decreases pon mixing) sch that the components of the mixtre separate. Example: oil and water ctivities For an ideal soltion, Raolt s law is obeyed and we can write the chemical potential: µ () l = µ () l + RTlnX When the soltion does not obey Raolt s law, the form of the above expression can be retained by sbstitting the activity for the mole fraction: µ () l = µ () l + RTlna The activity is an effective mole fraction for non-ideal soltions jst as fgacity is an effective pressre for non-ideal gases. (We didn t do fgacity in lectre, bt Chapt 8 talks abot it.) By comparison to or general eqation for the chemical potential of a mixtre, we can see that a =? p / p. Therefore, the activity can simply measred as the ratio of the vapor pressre of component in in a mixtre and its vapor pressre as a pre sbstance. 7

8 Solvent activity Since all sbstances obey Raolt s law as the X 1, we can say: as X 1, then p p and therefore a X We can define a new term called the activity coefficient for sbstance (γ ): a = γ X (γ is not constant!!!) It follows then that? X 1, γ 1 and therefore a X as it shold The chemical potential for a solvent in a non-ideal soltion is therefore: µ = µ + RTln X + RTln γ Notice that the second two terms are zero for X = 1, so: as X 1, µ µ Can we qantify non-ideality Remember that G mix = n tot RT ( X lnx + X B lnx B ) for ideal soltions Keeping in mind that µ = µ + RTln X + RTln γ then what might G mix be for or non-ideal case? G mix = n tot RT ( X lnx + X B lnx B + X lnγ + X B lnγ B ) ideal mixing excess Gibbs energy of mixing G mix = G ideal + G excess This is great stff allows s to qantify the intermoleclar interactions! 8