II
J. A. Campbell. Douglas Nelson, and John Rudesill
~ ~. Harvev M L J Colleae Clarernont, California 91711
O n e of the most common physical chemistry experiments, now even appearing in freshman courses, is the determination of the distrihution coefficient of an acid between an aqueous and nonaqueous phase. The senior author has used this experiment for thirty years with enthusiasm. But, this enthusiasm has been tempered with the experience that minor discrepancies in experimental results produce large deviations in, calculated distribution coefficients as shown in Table 1. These are the independent data of two careful students who agree to 1% on all titrations of the aqueous phase yet obtain average values (even eliminating the worst set of each student) of KD of 0.178 and 0.159 and of Km of 0.0383 and 0.0272. Errom propagate badly in this experiment. Furthermore, the literature data are far more discrepant than those in Table 1. Hence, we have redetermined some values of K and calculated the corresponding values of AHo and ASo. This experiment thus becomes part of our effort to introduce real thermodynamic measurements into
*
Table 1. Student Results Illustrating Error Propagation DeviaFunnel
C(aq)/C(na) E. Adams
C(a )/C(na) D.
0.164 (0.0640) 0.154 0 0269 0.160 0.0347 (0.174) 0.0347 0.149 (0.0126) 0.160 (0.0280) (0.176) (0.0~80) 0.165 0.0475 (0.189) 0.0475 Av. 0.0383L Av. 0.159= a 6
tion in C
chandler
A Distribution I i p t x i m n t
beginning chemistry course~measurementswhich will yield numerical values interpretable in terms of molecular properties and chemical intuition, not merely numbers to be laboriously calculated. We have used the following acids: acetic, propanoic, butanoic, pentanoic, benzoic, benzilic, formic, and the following solvents CCL, CHCla, CsHlo(p-xylene), CsHe, and the other xylenes, all coupled with water. The system is described in terms of the following symbolism: (aq) refers to aqueous solution, (na) to nouaqueous solution.
+
HA(aq) = H+(aq) A-(ad HA(aq) = HA(na) (HA)*(na) = 2HA(na) K. = C(aq)a2/(1 - a) Kn = m/C(aq)(l - a ) = distribution coeffiicent K M = 2m2/(C(na) - m) monomer-dimer constant
-
where C(aq) = total acid concentration in the aqueous phase, C(na) = total acid concentration in. the nonaqueous phase, m = concentration of acid monomer in the non-aqueous phase, and a = decimal fraction of acid dissociation in the aqueous phase. We can eliminate m between the last two equilibrium equations to get Kr
0/,
0.0310 0.0254 0.0276 ( 0 0334) 0.0222 0.0267 (0.0341) 0.0304 (0.0465) Av. 0.0272=
Probably in error. Omit all 2's. Omit all 5's.
-
= 2K~%'~(aq)(l - ~ ) ~ / [ C ( n a ) KoC(aq)(l
Table 2. Eauilibrium Constants. Entro~ies, . . and Enthalpies
Aoid
Aoetio Aoetio
Acetic Pmpanoie Propanolo Propanoic Butanoic I3utanolo Uuthnoio
454
Sugpted ~n~trst
C(na)(F) 2 2 2 0.5 0.5 0.5 0.3 0.3 0.3
Dime
Solvent (=a)
CHClr pCaHm CCh CHCII p-CaHa CCII CHCk pCaHta CCI.
-
-Distribution Monomer (na)
K M ( * Z ? I & ~ ~ ~AH"(*lO%) 296'K (kcal/mola) 0.02404 0.00561 0.000552 0.0168 0.00327 0.00011 0.0104 0.00'337 0.00074
/ Journal of Chemical Education
0.035 0.0105 0.0028 0.0348 0.00875 0.0027 0.0282 0.00847 0.0020
4.1 17.6 7.89 10.6 14.5 10.8 10.0 10.8
- a)]
Simultaneous use of C data from two different equilibrations allows calculation of K D and KM. Values of C(aq) and C(na) can he obtained independently by titratiou of both equilibrium phases or they can be obtained by titrating one phase and calculating 'C for the other by difference (from the total acid added originally to the system). We have determined C(aq) and C(na) by double titration as well as by a single titration and taking differences. I n careful work either approach is equally good, but, if only one C is to be measured directly, it. should be the smaller one. Otherwise, one may have to subtract two similar numbers with resulting great uncertainties in the result. (It is, incidentally, of some merit to have the students carry out both aqueous and non-aqueous titrations. We do both on a stir plate using the same standardized aqueous NaOH
AS"(oal/mole OK)
isssK . 6.3 12.2 45.3 21.7 27.7 38.8 33.6 28.4 29.7
313OK
6.4 12.7 44.5 18.5 24.6 34.5 27.4 22.4 22.0
(aqueous
Kd*2%) 296°K 313OK 0.0286 0.00191 0.00181 0.130 0.0258 0.0126 0.409 0.111 0.530
0.0337 0.00808 0.0042 0.170 0.0405 0.0240 0.639 0.170 0.094
-
non-aqueoua)-
AHo (*lo%) (keal/ mole) 1.8 3.7 8.5 2.9 4.9 7.0 4.8 4.6 6.2
AS'(cal/mols 'K) w
29G°K
313'K
-1.0 2.1 16.4 5.8 9.2 14.9 14.5 11.2 15.1
-1.4 2.0 13.9 1.7 5.1 9.2 7.2 4.3 6.6
solution and a stoppered flask to minimize COzproblems from the atmosphere.) We used the IBM 1620 to calculate values of K D and Knr from literature values of K . and titration values of C(aq) and C(na). Determinations of K D and K Mwere carried out at two temperatures and values of AHo", A H M o ,ASD", and ASa" also calculated. Table 2 lists the values for the systems which prove readily usable. The values of AH" and AS0 are reproducible to about * l O ~ o , the values of K to about *2%. The other systems gave problems involving large distribution coefficients, volatility, purity of commercial samples, etc. It is interesting to look at the values of AH0 and ASo and observe their systematic variation with molecular structure and polarity. The following trends are apparent. Increasing the polarity of the non-aqueous solvent: (1) generally increases AHo for the dimerization by providing stronger solvent-solute interaction, (2) decreases AHo for the distribution process by minimizing the difference in the solvent-solute interactions between the two phases, ( 3 ) decreases ASa of the dimer to monomer transition as interactions with the solvent increase, (4) increases the ASo of distribution, ( 5 ) also, increasing size of the organic acid tends to minimize the changes due to solvent-polarity effects, and (6) ASo decreases as T increases. All these effects can be
readily rationalized in terms of structural changes and their interactions with solvent effects, always remembering that the thermodynamic quantities measure changes between two states both of which must be considered in interpreting the effect. Experimental Directions We suggest that the students initially make up a non-aqueous solution of appropriate concentration (See Table 2) hy weighing acid into 8. 250-ml volumetric flask and then filline" to the mark with the non-aqueous solvent. The student then places 50.00 ml of non-aqueous solvent in numbers 2, 3, and 4 of five separatory funnels (or bottles) numbered 1 through 5. He then pipets 50.00 ml of this stock acid solution into containers 1 and 2, shakes container 2 and pipets 50.00 ml of its contents into container 3, shakes container 3 and pipets 50.00 ml of its contents into container 4, shakes container 4 and pipets 50.00 ml of its contents into container 5. He ends up with five containers eeeh containing 50.00 ml of a. non-aqueous solution of the acid of concentrations varying from C(na) to C(na)/8, with containers 4 and 5 both having concentrations of C(ns)/X, thus allowing a check on the precision of the titratians. Fifty milliliters of water shnkrn arc then p~petlrdinto cnrh r w t a i w r and he ron~ainer.~ until cquililmum is rrachrd I I ur 2 win ui v i ~ u n m --hakine I,? hand briw. the -\.,tcm t u ewdtl,ril~n~ . Thr I.a\wr :wr. nllc~retl to settle out, thedseparated and titrated (with 0:5, 0.1,or 0.01M NaOH as required) to determine the equilibrium values of C(aq) and/or C(ns) so that the calculations may be carried out. We are most appreciative of a. grant from the National Science Foundation Science Course Improvement Program which supported this work in the development of laboratory experiments.
Volume 46, Number 7, July 1969
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