1954
R. A. ROBISSOX A N D R. H. STOKES
Vol. 65
directly measure the solubility of all silver species in solution. Jonto and Martin obtained data in aqueous solution a t 2.5’ for 2 and 3 reactions.
and Rideal and the variable values indicated by the work of Seward and the present authors. Xo direct comparison can be made between the results of the above treatment and those from the elegant work of Blander and co-workers,I who have recently Ag+ + C1AgCl K = K1 = proposed a quasi-lattice model treatment of similar -~ - 2.04 X lo3; AH = -2.7 kcal. molten reciprocal salt systems. It is hoped that [&+I icl-1 current work in this Laboratory based on the Ag+ + 2C1ilgClz- K = K2 = present approach in the same systems studied by [AgClz -1 [Ag+l[C,-12 = 1.76 X lo5; AH = -3.9 kcal. Blander will enable a direct comparison to be made, a t least for the value of K . Extrapolation of these data to 280” yields a K , of Acknowledgment.-One author (C.K.) would like 251 and a K z of 34 compared to K1 of 88 and K P to acknowledge support under a Sational Science of 7 . 3 determined in this work. Although certainly Foundation Research Participation Program for not identical, the order of magnitude of the con- High School Teachers. This work also mas supstants is such as to indicate that the complex for- ported, in part, under U. s. Atomic Energy Commation is not too greatly affected by differences in mission Contract AT (30-3)-241. the solvent media. (7) (a) hl. Blander, F. F. Blankenship and R. F. Newton, J . Phys. The above treatment offers an explanation for Chem., 6S, 1259 (1959); (b) M. Blander, zbad., 63, 1262 (19591; the apparent discrepancy between the constant (c) J. Braunstein and M. Blander, zbzd., 64, 10 (1960): (d) D. G . values of the ionic product obtained by Flengas €1111, J. Braunstein and AI. Blander, zbzd., 64, 1038 (1960).
ACTIVITY COEFFICIENTS I N AQUEOUS SOLUTIONS OF SUCROSE, MANNITOL AXD THEIR MIXTURES AT 25’ BY R. 4 . ROBIKSOX~ AND R. H. STOKES Department of Chemistry of the University of T e w England, Armidale, LV.S.W., Australia Recezied March 18, 1961
Isopiestic vapor pressure measurements are reported for sucrose and mannitol solutions and for sucrose-mannitol in mixed solutions. Some improvements in the technique of manipulating the isopiestic dishes are described, giving a reproducibility of 0.03%). A new method of calculating activity coefficients in the mixed solutions is developed, and equations for the activity coefficients at all compositions are derived. Each solute is “salted-out” by the other.
Introduction The isopiestic vapor pressure method has been widely applied to solutions of single electrolytes and has been used for a few pairs of mixed electrolytes.2 A recent paper from this Laboratory3 gave data for the sodium chloride-potassium chloridewater system, and other studies shortly to be reported deal with the systems sodium chloridemannitol-water and sodium chloride-sucrose-water, which are of interest in connection with diffusion studies in ternary systems. Here we deal with the simpler system sucrose-mannitol-water, which is as far as we know the first system of two non-electrolytes to be examined by this method. Notation.YR,
yc = molal activity coefficients of B and C, resp., in a
9 y ~ 0 c p ~ O
yco pco
soln. containing component B a t a molality mB and component C a t a molality nic = molal osmotic coefficient of this soln. = activity coefficient of B in a soln. containing B only a t a molality V Z B = molal osmotic coefficient of this soln. = activity coefficient of C in a soln. containing C only a t a molality mc = molal osmotic coefficient of this s o h .
(1) Present address: National Bureau of Standsrdfi, Washington 2 5 . D. c. (2) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Second Edition, Butterw-orths Scientific Publications, London, 1959. pp. 443-449. (3) R. A . Robinson, J . Phys. Chem., 65, 662 (1961).
In this work, B = sucrose, C = mannitol. It should be noted that y 2 and yc0 were used with a different meaning in an earlier paper.3 Experimental The sucrose was supplied by the Colonial Sugar Refining Company; it had been twice recrystallized from the “standard sucrose” used as their laboratory standard. A sample of sucrose obtained from the Kational Bureau of Standards, Washington, gave identical isopiestic results. The sucrose was dried i n vacuo over calcium chloride at room temperature. hlannitol was four times recrystallized from the Colonial Sugar Refining Company’s commercial product and dried in the same may. Solutions were made up in conductance water. The isopiestic apparatus used in this work and in that described in an earlier paper3 consisted of glass vacuum desiccators of the “old-fashioned” design, with a cylindrical body and a conical base, which is more readily mounted on the rocking stand than the modern nearly spherical pattern. Each contained a silver-plated copper block, 15 cm. in diameter and 2.5 cm. thick. 4 round the circumference of this block, eleven silver dishes could be placed, leaving a clear central space 8.5 cm. in diameter. The dishes were 3 cm. in diameter and 2 cm. deep. In the central space was placed a device made of tinned copper wire and sheet, shown in Fig. 1. At the start of the run, the hinged lids of the dishes were held open by the upper circle of wire. A t the end of the run, the ground joint in the desiccator lid, carrying the tap, was slowly rotated through 360’. The glass inlet-tube of the tap unit, engaged between the flat plates a t the top of the device, caused it to rotate on the copper block, and as it did so the gap in the wire circle allowed each dish lid in turn to fall into the closed position. The vacuum was t hcn hrokm, and thtl dishes were removrd, wiprd dry, and
ACTIVITYCOEFFICIENTS IN SOLUTIONS OF SUCROSE, ~IANNITOL AND MIXTURES
Nov., 1961
weighed. The lids fitted so closely that evaporation losses during weighing were not more than 0.1 mg. Another source of error in isopiestic measurements is the formation of air or vapor bubbles in the liquid in the dishes during the initial evacuation; in breaking, these somebimes cause droplets of solution to be lost. Evacuation on a water-pump often will cause this trouble if the room temperature is higher than that of the water supply. To eliminate it, we adopted the practice of cooling the copper block to about 0' in the refrigerator before setting the dishes in position. Small drops of the sodium chloride reference solution were placed on the block to ensure good thermal contact between the block and each dish. Equilibration periods in the 25' thermost'at were from two to five days; temperature cont'rol was & 0.005", and the desiccators were rocked through an angle of 15' once every five seconds. Scatchard, Hamer and Wood4 reported that they used no sucrose solution which had been made up for more than a Tveek. We agree that this precaution is essential and, indeed, because of the possibility of microbial action, the sucrose and mannitol solutions were made up freshly for each run. Attempts to run sucrose solutions for periods longer than four or five days often led to poor reproducibility, which was at,tributed to such microbial action. Similarly, t,he dilution or concentration of a set of solutions which already had been equilibrated seldom gave a good result. All weighings were made on a semi-micro balance, and corrected to vacuum.
Activity and Osmotic Coefficients of Sucrose and Mannitol as Single Solutes.-Table I gives molalit'ies of isopiestic pairs of sodium chloride and sucrose solutions. Each sodium chloride coiiceiit!ration is the mean of triplicate dishes and each of the noli-electrolytes the mean of duplicat,e or triplicate dishes. The extreme difference in Briplicates was not more than 0.05% in the molality and duplicates agreed wit'hin 0.03y0. Table I1 gives similar results for sodium chloride and maniiit,ol solut'iom
Fig. 1.-Device
1955
for closing lids ofiisopiestic dishes with desiccator under vacuum.
Up to 2 M the osmotic coefficient of sucrose can be represented with a maximum deviation of 0.0009 and a mean deviation of 0.0004 in c p ~ Oby p
~
= 0 1
+ 0 . 0 7 4 0 ~+~0.0100mB2 ~
(3)
with the corresponding equation log
YBO
+
= 0 . 0 6 4 3 n ~ ~ 0 . 0 0 6 5 ~ ~ ~ ~(4)
But to describe the results over the entire concentration range, a more extended equation is necessary =
1
+ 0 . 0 7 0 2 8 ~+~0~. 0 1 8 4 7 ~ ~-~0' . 0 0 4 0 4 5 ~ ~+~ 3 0.000228VZ~~( 5 )
This represents the experimental data within 0.001 in BO. The corresponding equation for the activity coefficient is log
=
+
-
+
0 . 0 6 1 0 5 ~ ~0~ . 0 1 2 0 3 ~ ~0~. 0~0 2 3 4 3 ~ ~ ~ 3 0 . 0 0 0 1 2 4 ~ 1 ~( 6~)
The osmotic coefficients of sucrose given previously5 were collated from three source^^^^ and our present results give somewhat lower osmotic coeffimsaci mg nNac mn ?m3ci mn cients in the more dilute solutions. The new co0.2100 0.:3770 1.0694 1.7330 2.1469 3.2504 efficients are lower by 0.004 a t 1 M , 0.006 a t 1.5 M ,2855 ,3065 1.1088 1.7887 2.2481 3.3928 and 0.003 at 2.5 M ; at higher concentrations there ,4193 ,7293 1.1697 1.8618 2.7365 4.0731 is no significant diff erence. .4246 ,7372 1.1808 1.8914 2.8807 4.2796 The System Sucrose-Mannitol-Water.-In mak,4984 ,8572 1.1951 1.9123 2.9604 4.3947 ing these measurements, three of the dishes con,5277 .9045 1.5042 2.3547 3.1524 4.6631 tained the reference sodium chloride solution and .5761 ,9824 1.8018 2.7706 3.3733 4.9876 usually there were eight dishes containing four 2051 1.1852 1.8637 2.8576 3.455G 5.1056 pairs of mixed sucrose-mannitol solutions (or one ,9001 1.4819 1.9349 2.9588 3.9149 5.7951 pair coiitaiiiing sucrose solutions and three pairs ,9558 1.5657 containing mixed sucrose-mannitol solutions). B = Sucrose. Table I11 gives the mean molalities of the triplicate TABLE I1 reference solutioiis arid of the mixed solutions. ISOPIESTIC SOLVTIOSS UF Son~uai CHLORIDE AND MASNITOL~Also included are the quantity A defined by equamsnci mc mwa mc mNsa mc tion 15 and values of A/(mBmc). pref., the osmo0.1165 0.2164 0.3732 0.6846 0.5608 1.0264 tic coefficient of the reference solution, was inter,1623 ,3002 ,4146 ,7598 ,5761 1.0545 polated from tables7; the osmotic coefficient c p ~ O ,2100 ,3875 ,4246 ,7788 ,6048 1.1063 of a solution of sucrose alone at the same molality as ,2808 ,5163 ,4812 ,8799 ,6768 1.2376 that of sucrose in the mixed solution was calculated ,2855 ,5248 ,4984 ,9120 ,7000 1.2807 by equations 3 or 5; pen, the corresponding quana C: = Mannitol. tity for the mannitol component, by equation 1. Discussion of the Sucrose-Water and MannitolThe osmotic coefficients of mannitol calculated Water Systems.-Scatchard8 has drawn attention from these data are well represented ( i e . , with a maximum deviat,ion of 0.0013 and a mean deviation to the fact that much of the behavior of a sucrose solution in water can be explained by ascribing a of 0.0005 in qcn)hy hydration number between 4 and 5 to the solute. TABLE I
ISOPIESTIC & l I ~ C T I O S S O F S O D J C X C H L O R I D E A S D SUCROSEa
'pco = 1
+ 0.0034,iac + 0 . 0 0 4 2 ~ ~ ~ ~(1)
whence the :ictivity coefficient is given by
+
log yco = 0 . 0 0 2 9 5 ~ ~0.002'i4mc2 ~
(2)
(4) G. Scatchard, W. J. Hamer and S. E. Wood, J . An. Chem. Soc., 6 0 , 3061 (1938).
( 5 ) Ref. 2 , Appendix 8.6, p. 478. (6) fa) It. A. Robinson and D. A. Sinclair, J . -4m. Chem. Soc., 66, 1830 (1934); (b) R. A. Robinson, P. K. Smith and E. R. B. Smith, Tyans. Faraday Soc., SB, 63 (1942). (7) Ref. 2, Appendix 8.3, p. 476. (8) G. Scatchard. J . Am. Chem. Soc., 43, 2406 (1921).
R. A. ROBLNSON AND R. 13. STOKES
1956 TABLE111
THESYSTEM: mref.
0.4475
0.5490
0.8495
0.9987 1.0694 1.1808
1.1951
1,8637
2.4220
3.7180
a
mn 0,6227 .4597 ,3139 .1555 .7561 ,5594 .3828 .1900 1.1776 0.9443 .7117 .5015 1.2411 1.1848 1.0509 1.6151 1.3081 1.0148 1,5970 1.4767 1.1259 2.5321 2.2820 1.9707 3.4904 3.3738 3.2571 3.0949 5.2913 5.1174 4.9530
SUCROSE-MANNITOL-WATER‘
-.!
mc
A
0.1604 0.0096 ,3332 .0139 ,4880 ,0131 .6559 .0081 ,1947 .0145 .4067 .0219 ,5953 .0207 .SO14 .0138 ,2528 .0311 .5105 .0501 ,7692 ,0557 1,0008 ,0510 0,4342 .0598 .G191 .0793 .7692 .OS83 .3172 .0574 .6043 ,0999 1.0012 .1150 0,3594 .0665 .4971 .OS39 .8979 .1130 .3874 ,1092 .6829 .1795 1,0494 .2485 0.1760 .0593 .3224 ,1040 .4637 .1507 .6557 .2169 ,2669 ,1093 .4SS9 ,1980 ,7081 .2710
-Equation
mBmc
A
0.0961 0.0094 .0908 ,0143 .OS55 ,0139 .0088 ,0794 .0985 .0146 ,0220 .0967 ,0908 .0216 .0906 ,0137 .lo45 ,0318 ,1039 ,0511 .lo19 ,0570 .lo16 .0509 .I110 .0591 .lo81 .OS13 ,1092 ,0895 ,1120 .0570 .1148 ,0981 ,1132 .1144 .1159 ,0640 ,1143 ,0824 .1118 .1142 ,1113 .lo75 .1152 ,1784 ,1202 ,2469 ,0905 .0588 ,0956 .lo77 .0998 .1543 ,1069 .2161 ,0774 ,1005 ,0791 ,1887 ,0776 ,2783
23% -0.03 .05 .10
+ + + + -)+
.09
.01 .01 .09 - .01 f .04
+ + + -
+ + -
-
-
+ -
.OG .OS .01 .04 .10 .06 .02 .09 .03 .ll .07 .04 .05 .03
.07 .07
- .02 - .ll
-
+
.ll .09
The reference soluti: was sodium chloride.
We propose to examine to what extent, this postulate can be used t80explain not only the properties of mannitol and sucrose solutions but also those of the mixed solut’ions. If hydrat’ionis the only cause for departure from ideality of a~naqueous non-electrolyt,e solution, the water activity of the solution is given by 1 - 0.018hm __ a‘v = 1 - 018(h - l ) m
(7)
By expanding ln aw in a series and converting to the osmotic coefficient, we obtain -55.51 In aw = m
+ 0.018(h - i)
4-
(
cps”
=a
1
+ 0.018(h - 9 V L +
112
-h
+ -3
m 3
-
0.0W(h2
has I;een pointed out by Guggenheim,s while McKay’O has worked out in considerable detail the consequences for a solution containing two electrolytes. We now develop on alternative treatment which offers some advantages in convenience for non-electrolytes. The method gives the crossdifferentials very directly. We assume that a t all values of mg and mc the cross-differential can be represented by
where f’(mB) is a function of mB only, and F‘(mc) of mc only. These functions are expressed as derivatives, their integrals with respect to mB and mc, respectively, being f ( m ~ )and F(mc). The form (10) is fairly adaptable to special cases, no other restrictions except continuity being placed on the functions. However, we expressly exclude functions such as products of powers of mg and mc, for which the method is unsuitable. The case of two electrolytrs, involving terms in ( m ~ mc)’” is likewise excluded. Integrating (10) a t constant mg between mc = 0 and mc = mc yields
+
In
YB
=
In
YBO
- h + i) m2
(8)
neglecting terms with higher powers of m. Putting 0.018(h~-l/~)= 0.0740 for sucrose gives h~ =4.61 whence the last term of equation 8 should have a coefficient of 0.0055. Clearly there is a contribuO cannot be accounted tion of 0 . 0 0 4 5 m ~to~ r p ~ which for by hydration. Xeverthelesp, the hydration hypothesis can be used to calculate, for example, C ~ B O = 1.1700 at 2 AI against 1.1880 calculated by equation 3. Thus the major deviation of the solution from ideality can be ascribed, up to 2 AI at least, to hydration. Equation 3 represents the data for sucrose only up to 2 M . To fit the results up to higher concentrations, the extended equation 5 must be used.
+ mcf’(m~)+ F ( m c ) - F ( 0 )
(11)
Using the cross-differentiation relation
we obtain in a similar way In yc = In yco
TJZ~
0.01s*
Pu’evertheless, equation 8 predicts cpgo = 1.5075 a t 5 M . Equation 5 gives (PBO = 1.4501 so that even at 5 M hydration can still account for a major part of the deviation from ideality. Similarly, the mannitol data are satisfied by hc = 0.69 with a negligibly small term in mc2: equation 1 shows that there is a contribution of 0.0042mc2 to yc” which cannot be accounted for by hydration. Thermodynamic Theory for 3-Component Nonelectrolyte Systems.-The value in ternary systems of the cross-differentiation relations
.04
- .01
+ +
Vol. 65
+ WZBF’(VZC) + f ( m ~ ) - f(0)
(12)
In practice , f ( m g ) and P(mc) usually will he power series Lsith leading terms in mn and mc, so that F ( 0 ) = f(0) = 0 The Gibbs-Duhem equation is -55.51 d In n~ = Rind In ( ~ B Y B )f mc d In (mc-,~) (13)
which by equatioiis 11 and 12 gives
+
+
+
-55.51 d In uw = dmB T ~ B d In YB” dmc mc d 113 yeo -k lngi2cf”(Wlg) d V l ~f nL~F’(mc)dmc n l n f ‘ ( R l g ) d ? i w f m g t t l c F”(mc) dmc mc ~ ’ ( V L B )dma -lF ’ ( m c ) cllnr, = d(1nnv$) d(mc$9c0) ~ ~ V L (f’(mn) B ~ C +F’(mc))l (14) We now define a quantity A by A = -5.5.51 11) ow - ~ t ~ B p na ~ ~ c ‘ p c (15) ~
+
+
+
+
Let the composition of the refcrcrice sodium chlo(‘?) F, A. Quggenheirn, “Thermodynamlri an Advanced Trentinent for Chemists snd Phybicist?,” Noi th-Holland Publishing C o , Amsterdam. 1919, p 207 (IO) H A C McKay, Trans. Faraday SOC..61,902 (1955);H A C McKay and J Ii. Perring, tbad., 49, 163 (1953).
Xov., 1961
ACTIVITYCOEFFICIEZTS 13SOLI-TIONS OF SUCROSE-~TASNITOL ASI) ~ I T X T U R E S 1957
ride solution in equilibrium with the mixcd sucrosemannitol solution be mref and its osmotic coeffivient pref. Then A is simply A = 2?nrefPref
- mB'+QBo - "LC'PCo
1.2 \
(16)
Equation 14 then map he integrated from infinite dilution of both compoiients up to the composition mB, nac il = mBmC[f'
(mB)
f F'(mC)l
(17)
The remarkable feature of equation 18 is that (assuming that the vapor pressures of the single solute systems are known) a single measurement of the vapor pressure of the mixed solution yields directly the value of the cross-differential for that solution. The result is obtained only on condition that the 0 1 2 3 4 5 6 assumed form (10) is adequate to describe the crossmsaoroap. differential at all compositions from infinite dilution relation8 in the sucrose-mannitol-water of both components up to the actual composition of Fig. 2.-Solubility and sucrose-lsctose-~~stersystems. the solution measured. It is thus likely to apply with good accuracy in the case of mixed aqueous 0.0045 (mB m d 3 to equation 20. This is equivnon-electrolytes. alent to adding a term 0.0135 (mB mc) to equaThe following physical interpretations can be tion 21. Substituting hg = 4.61, hc = 0.69, we get given to the quantity A. (a) From equation (15) A = 55.51 In ( p ~ ~ p c O ) / ( p p ~ ) T'alues of A calculated by this equation agree well with those found as recorded in the first 22 entries where BO is the vapor pressure of water over a solution of sucrose alone a t molality mR; pco is that in the fourth column of Table 111; the differences over a solution of mannitol alone a t molality mc; p correspond to a mean error of 0.05% in the molality is that over the mixed solution containing sucrose of the reference solutions. This comparison cannot be valid above a total a t molality m5 and mannitol a t molality me; and concentration of 2 M . However, equation 22 does pw is the vapor pressure of pure water. suggest the form of a more extended equation: the (b) -RTA is the free energy change of the water in the following process: a solutionof mB first term on the right is the sum of the coefficients moles of sucrose in 1 kg. of water is mixed isother- of the first terms on the right in equations 1 and 3. mally with a solution of mc moles of mannitol in 1 By analogy, equations 1 and 5 might give 0.0737 for kg. of water; then 1 kg. of liquid water is isother- the first term in an equation applicable to more concentrated solutions. As the mannitol concentration mally separated via an osmotic membrane. Discussion of the Sucrose-Mannitol-Water Sys- cannot be much greater than 1 AI, it might be hoped that a term in the first power of mc would tem.-The analog of equation 7 for a mixture is suffice, but the appearance of mg4terms in equation 5 suggests terms up to mg3 in our new equation. We therefore try
+
+
,
(hBmB
+ hcmc)(ma + mc) +
1 s(mB
+ mc)*l(mB + mc) (20)
and
A = 0.018[h~+ hc
- 11 +
mBmc 0 . 0 1 8 2 [ m ~ ( h ~ 22hBhC - 2hB - hc mc(hc2 2 h ~ h o- 2hc - h u
+ +
+ 1) +
+ 111
(21)
But we have already found t,hat while hydration accounts for most of the departures from ideality of both sucrose and mannitol solutions, there is an additional small term in m3 in the expression for -55.51 In aw or in m2 for 9. Moreover, the coefficients of this term are almost the same: 0.0045 for sucrose and 0.0042 for mannitol. We therefore investigate the effect of adding a term
and find that we can well represent the experimental data by putting A = 0.0737 B = 0.04096
D = 0.001194 E = 0.0107
C = -0.01425 The sixth column of Table I11 gives values of A TABLE IV" SOLUBILITY OF MANNITOL IN SUCROSE SOLUTIONS me 0 1 2 3 4 5 5.902 mC(ant.) 1.186 1.075 0.960 0.860 0.779 0.718 0.672 SOLUBILITY OF SUCROSE IN MANNITOL SOLUTIONS mc 0 0 3 0 6 0,672 mR(aat) 6.053 5.988 5.919 5.902 0 The last column refers to solutions saturated with respect to both components.
F. J. KELLY,R. -4.ROBIKSOX A N D R. H. STOKES
1958
T'ol. 65
TABLE 17 MOLALACTIVITYCOEFFICIESTS OF SUCROSE (B) ANI) M.~NSITOT, (C) IN MIXEDSOLUTION AT 25"" -
M C
I\. c
.1In
1
0
1
2
I ,000 1,177 1.$2-1 1.731 1,000 1.094 1.216 1.351 B 1.023 1,214 1.471 1.785 0.3 C 1.003 1.100 1.22i 1,368 0.7 B 1.056 1.267 1.540 1.862 C 1,008 1.110 1.244 1.393 1.0 B 1,082 1.310 (1.595) (1.925) C 1.013 1,120 (1.259) (1,414) V:tlues in parentheses refer to solutions supersaturated to mannitol.
B
0
C
5
calculated by equation 23 and the last column gives the percentage error in the molality of the reference solution necessary to account for the difference between the observed and calculated A values. Activity Coefficients in the Sucrose-MannitolWater System.-Integration of equation 23 gives In
YB
+ 1 mc -4 + R ~ +B Cmsz + Dmn3 + ~ E v w ] (24) 1
=
In
YBO
for the activity coefficient of sucrose in the mixed solution, and In yc = In trig
[
yco
A
+
+2R 7ng + 3c -
- Vln2
+ D4 vzn3 + ~ T i i c ]
(25)
for the activity coefficient of mannitol in the mixture. Solubility Relations.-The solubility of mannitol in sucrose solutions is determined by the condition (TnC5CO)sat
= (mc-Yc)sat
where the quantities on the left refer to a saturated solution in water and those on the right to saturated solutions containing sucrose. The saturated solution in mater is knomn'l to be 1.186 &I; a t this (11) J. RI
Braham J . Am. Chem. Soc., 41, 1707 (1919).
2,082 1.485 2.138 1.507 2.217 1.541 (2.282) (1.569)
1
2.458 1 .606 2.513 1,636 2,592 1.681 (2,656) (1.717)
5.9
2.806 1.707 2.862 1,i 4 5 (2.943 j (1.799) (3,009) (1.843)
molality, yc0 = 1.017 and the solubility product is 1.207 mole kg.-'. m, now can be calculated for any given sucrose molality! yc being obtained by equation 23 : a few successive approximations are needed. The solubility of sucrose in mannitol solutions likewise can be calculated, the saturated solution in water4 being 6.053 111. Tab!e IV gives some solubilities calculated in this way. S o direct measurements of these solubilities are available but Fig. 2 compares the behavior of this system a t 25" with that of the sucrose-lactoscwater ~ y s t e m a' ~t 0". The molal solubility of lactose in water at 25" is less than that of maiinitol, and this difference is further enhanced by the lower temperature (0') to which the data in Fig. 2 refer. It is clear that the relative magnitudes of the solubility lowering in the presence of sucrose are very similar. Finally, Table T' contains values of the activity coefficients of both mannitol and sucrose a t round concentrations in mixed solutions. It will be noted that each component is (lsalted'' out by the other. We wish to thank the Colonial Sugar Refining Company for the supply of purified sucrose and for the gift of a semi-micro balance. (12) P. N. Peter, J . Phys. Chem., 32, 1856 (1928).
THE THERMODYNAMICS OF THE TERNARY SYSTEM MAKNITOLSODIUAMCHLORIDE-WATER A T 95' FROM SOLUBILITY AND VAPOR PRESSURE MEASUREMENTS BY F. J. KELLY,R. A . ROBINSOX'AND R. H. STOKES Department of Chemastry, University of S e w England, .4nnzdale, S . S . W., Australia Recezzed March I S , 1861
Isopiestic measurements 0'1 the ternary ST stem mannitol-sodium chloride-water a t 25' are used to derive equations for the activity coefficients of each solute. Solubilities of mannitol in sodium chloride solutions and of sodium chloride in mannitol solutions are measured and found to be in fair agreement with those computrd by extrapolation of the activity data to the saturated solutions. Each solute is "salted-in" by the other.
Introduction The activity coefficients of mannitol and sodium chloride in mixed solutions are required in conneetion with our current studies of diffusion in tllreecomponent systems. ~h~ data can he obtained from isopiestic measurements of the vapor pres(1) Notional Bureau of Standards, Washington 25, D. C.
sures of mixed solutions, and such measurements are reported in Table 11. This method has the advantage of being in Principle applicable at any ComPosition of the mixture, but in practice experimental limitations confine its usefulness to cases where the total concentration of the two solutes is fairly large. The study of the solubility of one solute in the presence of varying concentrations of the other
