______PRESENTED FOR """"""'...,...THE ______DEGREE _
OF
/Vo. .:~ ~ CJ · • # # r ' • ' .. .,._ .,._ - "• THE SOLUBILITY OF CHLORIDE
IN A MIXED SOLVENT
( ------20%' METHANOL) FROM ------15°0 TO 45°0 INTRODUCTION .. •• 0 • • •
EXPJj)RIMENTAL METHOD •• • • • • 17.
Mat~rials • • • • •• 17.
Electrodes •• ... • • 19.
Cell • • •• ... • • 20.
Other Apparatus .... • 0 23.
TABLES AND GHAPHS •• 25.
CALCULATION OF RESULTS ." • 0 38 ..
DISCUSSION •• . . • • 44 ..
SUMMARY " . " .. " . 49 ..
HEFERENCES •• • • 51. 11HE OF CHfUSTCHURCH, N.;;>:,
With the development of theories of interionic attraction and of solvent interaction solubility data have been used for the estimation of ionic diameters and the degree of solvation of ions. The parallelism between the dielectric constant of a medium and its solvent power on ionic crystals has been recognised for a long time, and the quantitative ex- pression which links these properties may be derived from Bo~'s equation. This gives the free energy of an ion, carrying charge Z1 , where e is the charge of an electron, in a medium of dielectric constant Dr as
E 1 Dr where al"is the radius of the ion, which is assumed to be spherical. Then the work of transferring the ion from a medium of dielectric constant DJ. to a, medium of di,el,ectric constant.
(~-
This work of transfer can be equated to a free energy change, whose value is 2 ..
G - k T ln
per iont where f1 and f 2 are the activity coefficients of the ion in the two media ..
Imagine a fairly insoluble salt such as silver
chloride dissolved in a medium of dielectric con~tant D19 and
also in a medium of dielectric constant n2 • If G8 is the molal free energy of the solid silver chlorid.e, and -G~ and -GD the sum of the partial molal free energies of the ions in 2 saturated solutions of solvents of dielectric constant n1 and D2 respectively, then
-G~
By assuming that the satu~ting salt is a perfect
solute, this expression can be replaced by
- and - where N1 and N2 are the mol. fractions in the two solvents .. In a medium of particular dielectric corll!Jtant there must also be an additional term per mol. due to electrical forces, since the ions are assumed to be charged spheres. So that and ...
where N is the Avogadro number, and from these equations is
obtained -
To correct for the ions not being perfect solutes, an expression for the activity coefficients must be added to both sides so
RT ln f 1 ::: RT ln N2 + Nz!=-~-=- + RT ln f2 2al D2 where f is the activity coefficient on the molrll concentration scale. On changing to S, the solubility ln molse per li trtt 1 the oquatJ.on becomes
where y is the activity coefficient on the volume concentration scale. From this
... Nz 2 e2 '\ - 1 1 .... 1 ---- 1!J 2a1 RT -D2 -Dl/
2 as ln y = cl zl according to the Debye-Huckel theory, where (-Y is the ionar concentration, and A and B are comstants. This gives the relationship between the solubilities :tn two solvents tn terms of the Debye-Huckel for~ula for the solvents and of their dielectri< constants .. Actually the effect of the Debye-Htickel eorrections is rather small, as the two terms$ being about equal :tn magnitude1 nearly cancel each other. Because of this, plotting ln S against.! would be expected to give a straight line for any D one substan~e .. However the treatment by which the Bor6lequation is derived is essentially elementary, and the equat:ton should only be regarded as an approximation. In the simple derivation of the energy of interaction between ion and solvent BoMn assumed the dielectric medium to be homogeneous and structure- less. Actually water is molecularly complex, and the single molecules are highly polar .. Owing to the intense electric fteld in the immediate vicinity of the ions, the solvent molecules are completely oriented, and are powerfully com- pressed by the field. When the solvent is a mixture of water and methanol, then the system becomes still more complex.
The more polarizable molecules will be preferentially oriented around the charged ions, and by changing the composition of the bulk of the solvent, and also affecting the dielectric constant of the medium close to the ions, the adsorption of water has a tremendous effect on the solubility. Consequently only the rough agreement, as found by Bjerrum~ 2 5 is to be expected. 6 ..
METHODS OF MEASUREMENT ~...-----~------"
The methods of measuring solubility are numerous and make use of various types of phenomena, the choice depending on the degree of solubility and the accuracy required.
While analytical methods are quite satisfactory for salts which are appreciably soluble, they are of limited value when applied to salts which are only slightly soluble. Glowezynski 1 has determined the solubility of silver chloride in water by evapor- ation and separation of the silver electrolytically from cyanide solution .. The silver was dissolved in nitric acid 9 and titrated with ammonium thiocyanate. He obtained a value of 1·20 x 10-5 mols .. per litre at 25°0. Davis; Ricci with Sauter2 have measured by titration methods the solubilities of barium iodate, silver acetate and silver sulphate in dioxane - water mixtures. These solubilities must be of the lowest order that such methods can measure with any degree of accuracy. For accurate values the solubility of silver .chloride must be deter- mined by using other methods.
Popoff and Neuman3 developed an optical method, using the Tyndall effect, to obtain a value of 1•278 x lo-5 mols. per litre for the solubility of silver chloride in water
Neuman4 later increased the sensitivity of this 1 • method, when he measured the solubility of silver chloride in aqueous solutions of some sulphates and nitrates, by increasing the concentrations of the reacting silver and chloride ions till a trace of solid silver chloride was detected in a Tyndallometer.
By extrapolation he calculated the solubility in pure water at
25°0 to be 1•273 x lo-5 mols. per litre. Dave and Krishnaswami 5 nephelometrically obtained 1•388 x 10-5 mols. per litre. Johnson and Low6 measured the solubility of silver chloride in nitric acid solutions at o°C by both a nephelometric and a potentiome tric method, obtaining good agreement between the results. Conductance methods, first extensively used by Kohlrausch7, are very suitable for measuring low solubilities.
International Critical Tables, by a short interpolation from his data at other temperatures, obtain a value of 1•304 x lo-5 mols. per litre for the solubility of silver chloride in water at 25°0@
More precise measurements of low solubilities can be made by means of electromotive force methods. Brown and Macinnes8 used a potentiometric titration method for measuring the solubility of silver chloride in potassium nitrate solution.
Concentration cells were used, the solution on one side of the liquid junction was kept constant~ serving as a half-referen~e cellp while potassium chloride solution was added to the other half. The liquid junction potential was then allowed for~ and a correction applied for the change in volume. In computing 8 ..
the solubility of silver chloride in pure water, some of Neuman's data was used, and a value of 1•314 x lo-5 · mols. per litre at
25°0, in good agreement with the figure from conductance measure- ments .. Electrometric titration was used by Dunning and Shutt9 in determining the solubility of silver chloride in aqueous solutions of glycine and urea .. The value for the solubility j_n pure water obtained was 1•68 x lo-5 mols. per litre~
A method using cells with liquid junctions, but whose liquid junction potentials are eliminated 11 has been developed recently by Owenlo .. Since essentially the same procedure is followed in this work 11 the method is described in detail .. The cell may be represented as follows -
KCl (x) m _ \LAgNOJ (x) m \ 1 KN03 (1-x) m KN03 m KNOJ (l-x) m ~ AgCl» Ag
The total ionic coricentration in each solution is 2m 11 but a fraction x of this is composed of chloride ion in the left-hand 2 compartmentt and silver ion in the right-hand compartment. The e .. m.f. of such a cell is given )y
E = RT ln a' Ag Ej ]'
where Ej is the sum of the unknown liquid junction potentials9 and a'Ag and a"Ag represent the activities of tha silver ions 9 .. in the right-hand and left-hand solutions respectively. If we write
k = 0•00019844T = RT log e 10 -F since the solubility product in the left-hand solution is
tt att K - a .lAg .. 01 then the expression becomes
E = k log a'Ag a" + EJ. -rCl - so that E~' - k log a r 11 -- - k log K -t- .,1'•'j .Ag a Cl .ldl
The introductions of the concentrations x m, and the individual ionic activity coefficients leads to
k log f' f 11 Ej E - 2 k log xm = - k log K Ag 01 since the molalities of the silver ion and chloride ion are both x m.. Variation of x while m is held con.stant must yield on extrapolation to x ::.o
[ E- 2k log.x m] : -k log K k log f' Ag f" 01 x_-)'o 0 as Ej becomes zero under these conditions, there being the same solution in each compartment. For convenience in graphing the 10 ..
experimental results, the term 2 k .A m 9 where A is the
Debye-Huckel limiting slope 9 given by
for a solvent of dielectric con,stant D at a temperature T 9 is added to both sides. Then
[E ... 2 k log xm '"'r2 k - k log K+ fk log f' f" 4-2 k Arm]::: L Ag 01 !Aj;J x~o x·~~jo
If this expression is plotted against m t the value obtained by extrapolation tom: o is equal to~ k log K ~· as the activities of the silver and chloride ions at m: o are unity, and the thi term on each side also vanishes. Using this method, Owen10 obtained the value of
1"334 x 10-5 mols .. per litre for the solubility of silver chloride in water at 25° .. The following table shows the amount of agreement obtained.
Observer.
G1owczynski Analytical titration 1·2 x lo-5 Popoff and Neuman Tyndall effect 1•278 x lo-5 Neuman tt II 1·273 x lo-5 Kohlrausch Conductance 1• 304 X 10""5 Brown and Macinnes Potentiometric titration 1· 314 x 1o-5 Owen E.M .. F. measurement. 1•334 X 10-5 lL.
The variation in the physical condition of the
precipitated silver chloride is undoubtedly responsible for most
of the discordance. Pinkus and Hanrez24 by a potentiometric method measured the solubilities of seventeen samples of silver
chloride in 0•1 molar potassium nitrate solution at 25°. They got the same value for all solutions except the fine colloidal
suspensions9 ~vhich gave rather higher resul ts 11 showing that the particle size of the silver chloride affects the solubility. 11 Davis measured the solubility of silver chloride
in 10% methanol solution, obtaining the value of •990 x lo-5 mols .. per litre at 25°0, and the present work continues the in- vestigation to the solubility of silver chloride in 20% methanol
solution. From a knowledge of the value of log K over a temperature range there can be derived thermodynamical data for +- ... the reaction Ag.Cl-7Ag. +Cl From the Van't Hoff isochore
0 can be obtained the change in the heat content$ H » since
so that
The change in the heat capacity at constant pressure, Cp 0 ~ can be obtained by differentiating the change 12.
in heat content with respect to temperature 9 in accordance with Kirchoff's equation
The change in entropy can then be calculated by using the formula
Latimer and Slansky21 have obtained the entropy of solution of HCl, NaCl, KCl and KBr in water-methanol solution from pure water to pure met~anol. The entropies were obtained from the formula
The heats of solution have been measured by Slansky, and the free energies of solutions were obtained from solubility and activity coefficient data. From the entropies of solution thus found~ and the entropies of the compounds given 22 by·Latimer9 the sum of the partial molal entropies of the ions forming each compound were calculated from
0 0 x- ::: As 13.,
-os -+-So so -+-so so+so so +so H-t- Cl""' Na+ Cl- 1\~ cl- K+ Br-.
Water 13•6 27•6 37•9 43•9
10% Methanol 14·1 27•7 37·6 43•5 20% Methanol 14·4 27•1 36•7 42·9
Partial Relative Ionic so H+ !!!_~!2•
so so so so Na-1- K+ Cl- Br-
Water 14·0 24•3 13· 6 19·6
10%' Methanol 13·6 23<>5 14<~1 20•0
20% Methanol 12 .. 7 22·3 14·4 20·6
The entropy of solvation of the pair of gas ions 9
M~ and x- 9 is given by the equation
,6so = s 0 ~t-s 0 Solvation t..r'- x.-
The entropies of the gas :tons are calculated by means of the Sackur-Tetrode equa til. on"
s - R ~]
where k = Boltzmann constant m !Ill mass of a single molecule v - volume of 1 gm.-mol .. in c. Co h - Planck's constant N = Avogadro number 14.,
When this expression is expanded it becomes ~ 1 2 2 s ::: R ln (mT) v + R ln l.g1fk} ;- 5 R h3 N 2
1 fl. ln M +- ,2 R ln T - R ln P - 7" 26 7 ;~ 4,. 96 7 .. = 2 2 as PV = k N T ~ and evaluating constants. a
This is expressed in calories per grn-mol., and for an ideal gas at 1 atmosphere
0 S ::: ~ R ln M 5 R ln T - 2 • 300 " 2 2
The entropy correction for volume change ',d.s R ln _g.!: 46 Sp.Vol., for any solution. 26 Latimer and Buffington suggested that the entropy change for the process
Ion(gas) -~~,?·Ion . (so.lvrated) is a function of the ion chargell and th(e radius o.r the ion cavity in the solution so that ,1\ S = f (a:) 27 Latimer and Kasper considered the theoretical evaluation of the funretion., They assumed that the total entropy of solva- tion was due to two effects: As1 t the entropy change due to the pOJ.arisability Of the inedium 9 and 82 p the Change due to the compression of the solvent» through the electrostatic attraction of the solvent molecules. 15 ..
After evaluating the expressions they derived for these quantities, they concluded from a comparison of the theoretical and experimental values that that the entropy of solvation was largely due to the compression of the solvent. So the orientation of dipoles gave only a small entropy cihange.~~ but the lowering of thermal energy of the compressed molecules ~as large. This was the opposite of th~ magnitude of these effects in the free energy of solvation.
Latimer and Slansky21 calculated the sum of the ionic entropies of solvation for certain salts, and found that -As increases from water to methanol
% methanol NaCl KCl KBr.
0
10
20 20· 5
50
100 58e 5 This may be due to the larger entropy of the methanol molecules 9 so that there is a greater decrease in entropy when they are bound by an .ion. Expressing this physically» this means that in water hydrogen bonding gives a tetra-coordinated structure 9 and so the entropy of the water molecules is less than if the liquid were normal, and the motion of the molecules were 16.
random. The entropies of solvation of pairs of gas ion~ in methanol~ although larger than in water, are less spread for the different salts9 and the effect of the ion size is less in methanol. Ma. terials.
~.2!~!!Si~_.Qh!.Qri2:~· Hopkin & Williams• !Analar salt was purified by two recrystallisations from distilled water .. The crystals were dried in an air oven at 120° for several hours., -----==-"""""Potassium ____ Nitrate. _ British Drug Houses' salt of A. R. purity was purified in a similar manner, by two recrystallisations and drying .. ------"""""--Silver Nitrate., Johnson Matthey and CO's. pure silver nitrate was twice recrystaJ.lised from distilled water. The salt was dried in an ai.r oven at 100° for several hours. The final pro- duct had a very faint brownish tinge.,
!All these salts were kept in a dessicator while not being used, to prevent the absorption of moi~ture ..
Meth~!:!.2!• Kahlbaum's 11 Purett methanol was purified by fractional distillation with an efficient still head 50 ems. high. The middle fraction of the distillate was refluxed for several hours over a water bath with 1% by weight of calcium turnings., Then this was filtered and redistilled .. The liquid distilled over at a constant temperature, the first and last portions being dis- carded .. This methanol had a B.. P. of 64·5°0. Weissberger and
The refractive index was determined by means of an Abbe refractometer» and for the Sodium D line at 20°0 was 1·3293. Weissberger and Proskauer give the refractive index as le3286~ and W.J. Childs13 gives a value of 1.3292 .. In making up the 20% methanol - 80% water solvent, this alcohol was assumed to be pure 9 and distilled water was used .. The liquids were weighed out on a balance accurate to ·01 gm.
The solvent was made up in approximately four litre lots, and was stored in a bottle,from which it was drawn off by means of a siphon. A calcium chloride tube~ the only access to the air, ensured that the proportions remained unaltered by preventing absorption of water .. As a check the density of the solvent was determined with a pyncknometer. Harned and Thomas14 give the value of ·9681 at the same tempera~ ture.
.....,."""""Solutions ______• Weights calibrated against the laboratory standard by the usual methods were used for weighing out the salts. They were considered accurate to •0001 gm. As it was important that the ratio of salt in each solution {x 1 - x) should be very accurately known 9 weighing by difference could not be employed., Accordingly the calculated amounts of salt were exactly weighed and transferred to the stock-bottles 9 great care being taken to brush out any salt adhering to the walls of the weighing vessel.
The solvent was weighed out accurate to •01 gm., and the •05 m stock solutions thus made up were diluted successively to the 19 ..
other strengths. In this way the ratio of the salts in th.e
solutions was constant.
These silver chloride electrodes were of th~ electrolytic type. They consisted of •75 sq.cms squares of platinum gauze welded to platinum wire which made contact with mercury through glass tubes.. These were plated with silver by deposition from a cyanide solution (7 gms. AgNo 3 10 gms KCN in 200 c.c., distilled water) using a silver rod as anode, a current of 2 milliamps. per electrode being passed for 16 hours. The excess potassium cyanide present immediately removed any silver cyanide tending to form at the anode.. It had been found that when silver cyanide came into contact with.the electrodes,
J;Ha.tches subsequently appeared on chloridising., For this reason a solution of potassium silver cyanide (K Ag (CN)2) formed by crystallisation from a solution containing KCN and AgN0 3 had been found unsatisfactory, in addition the silver cyanide deposited round the silver anode caused a drop in current due to polaris ation, and so gave a thin silver deposit.,
After plating,~~ the electrodes were washed in running tap water for eight hours, and fi~ally rin~ed in distilled water. This was most sat~:factory, boiling diBtilled water could not be used as it frequently caused cracks in the sealo 20.
Electrodes were then chloridised anodically in •1 N H 01 solution for 30 minutes with a current density of 6 milliamps. per electrode, the treatment recommended by Allmand and Hunter.15 The electrodes were both plated and chloridised in series as recommended by Owen, 10 to ensure that the thermodynamic properties of the metallic silver cancelled in the operation of the cell. El,ectrodes prepared in this way agreed to ·1 m.v. except on a few occasions. All electrodes were left standing in the chloridising solution for four days as recommenMed by Smith and Taylor,16 and before use were washed in running tap water and then in distilled water.
After use, the electrode~ere cleaned as follows: silver chloride was removed by means of •880 ammonia solution, and the silver by standing in warm dilute nitric acid. Sometimes cold acid was used~ and was found to be effective. After cleaning, the electrodes were washed in running tap water and finally stood in distilled water. Electrodes were used only once to avoid any possible poisoning.
The cell used was similar to that used by Owen~lO and is shown in Figure I. It consisted of three separate com- partments, joined by two three-way taps F and G. The end compartments possessed two side-tubes each, and a barrel into 21 ..
which the silver chloride electrodes were fitted. After the electrodes had been fitted into rubber stoppers and rinsed in cell solutions 11 they were placed in the end arras 11 the joints being made air tight with collodion.. Rubber plugs with clips were placed over the outlets of the taps F and G. All air was then displaced from the cell by hydrogen, which was passed in through taps D and E. The solutions were made up in bottles fitted with calcium chloride tubes and siphons which could be attached to the
f:i.lling tubes A 11 B11 and c. by meam:; of ground glass joints., Be fore filling the cell, pure electrolytic hydrogen was presaturated with the solvent, and then passed through each siphon in turn 9 so that it bubbled through th'e solution and displaced all the air from above it. Potassium nitrate solution was first run into the centre compartment 9 and into the barrels of the taps F and G.. The side arms were next partly filled with their respective solu tions, and this was left standing for some minutes. Then the solutions were flushed out through the taps F and G, and the arms were refilled until the solution was about one inch below the stoppers~ The outlets of the taps F and G were closed, and th~ whole cell was placed in the thermostat. It stood there for fully twelve hours before measurements were made, an aged cell such as this came to equilibrium very quickly after a change in tempera ture to give a value which was reproducible within narrow limits. 22.
A ~ -
- r.~~··~j~·. ~ \ . '<. c- .
( ____ ·~·..) 23 ..
If cells were not put aside to age, they took a long time to reach equilibrium after each change of temperature~ and the va.lues obtained would be much greater than those obtained by letting the cell stand overnight,
A disadvantage of the cell used was the formation of the three-way taps F and G. Those used by Owen lO had the three arms lying in the same plane and spaced at 120° to each other. This enabled him to flush out the barrels after each reading and so obtain clean reproducible boundaries., In the present apparatus, however, the barrels could not be flushed out 9 and consequently mixing occurred» so that sometimes a white precipitate of silver chloride was thrown down in the centre com partment, and even appeared at times in the compartment containing the potassium chloride-potassium nitrate solution. This mixing would account for small discrepancies noticed at higher tempera tures, and also for variations in E.M.F. obtained on lowering the temperature at the end· of a run.,
Between runs the cell, the mixing bottles and the siphons were cleaned in a hot chromic acid solution, washed in tap w~ter and distilled water, and then dried in an air oven.
Measurements were made at seven temperatures:
15°c. 20°C, 25°0p 30°c; 35°Cp 40°C, 45°0. A gas heated thermostat was used, controlled by a mercury-toluene regulator@
This maintained a steady temperature 9 as recorded on a thermometer which had been calibrated against the laboratory standard. To keep the temperature of the thermostat at 150 C it was necessary to
use a lead cooling coil, through which tap water was run. ! The changes in temperature were made by running in hot water as cold
water ·was run out. The temperature change was then gradua.l 11 and was carried out in about five minutes.
A Leeds and Northrup Co .. potentiometer was used, having a range from 0-2·2 volts and reading to •1 m.v. The
Weston standard cell used to calibrate the instrument was checked against the laboratory standard, and corrections for temperature were applied whenever it was used. A Cambridge Instrument Co .. galvanometer of the
D'Arsonval type was used9 having a sensitivity of 1800 m.m. scale divisions per mi~ro-ampere at 1 metre. It was necessary to have this s~sitivity on account of the high resistance of the 25.,
In Table I are recorded the observed electromotive forces of the cell
AgNO' (x) m I Ag, AgCl KN03\l-x) m AgC11 Ag., at the seven temperatures 15°CJ 20°0 9 25°0 9 30°CJ 35°0 11 40°0 and 45°Co The values of the expression
[E - 2 k log x m + 2 kAJID] calculated from these e"m.f's are given in Table II .. These values are plotted against x in Graph I and extrapolated to x = o 9 the list of the intercepts being given in Table III"
These values of the intercepts are plotted against m in Graph II » and the intercepts at m = o are the values of - k log K given in Table IV .. 26.
TABLE I .. ----~ Observed Electromotive Force s ..
Temperature. 15°c. 20°c. 25°0. '30 oc. 35°0. 40°0. 45°0.
X .!!l--=-.2.:.<2.2·
0·6 "4236 •4186 e 4134 •4081 0 4031 •3985 <~~3936 0•4 •4033 •3976 •3920 •3873 •3820 • 3769 •3716 0•3 ·3886 0 38'30 •3774 •3718 •3661 •3610 •3549 0•2 ·3690 •3631 •3563 •3509 • 3448 •3396 •3334
!-::_Q~]·
0·6 ·4002 .. 3948 "3890 •3841 •3788 •3739 ·3685 0•4 ·3801 .. 3744 ·3684 •3626 •3568 •3517 •3465 0•3 .3656 •3597 ·3537 •3479 •3421 •3369 •3301 0"2 "3453 e 3390 •3325 •3264 •3203 •3139 • '3080
~-=-Q.:. 0 2 • 0"'6 @3819 "3760 •3700 .. 3643 •3586 •3535 "'3479 0°4 0 3616 • 54 ·3492 •3432 •3369 •3317 •3243 Qo3 '"3474 •3410 0 3340 o3289 •3217 <>3159 •3097 0•2 0 3270 ·3201 ·3130 •3066 •2999 •2937 ·2871
~-=-Q.:.Q1·
0•6 .. 3489 •3426 •3365 • 3301 e3238 0 3182 0 3119 Q .. 4 e3288 .. 3222 e3159 •3092 •3022 •2961 •2895 0•3 •3144 o3080 ·3012 ·2942 •2872 •2803 •2738 o•2 ·2946 e2875 •2801 •2727 •2656 •2584 •2518 27.
TABLE I (/J
0°!!~~E2~~i~S_!!1u~2f [E- 2 k log xm+ 2 k A/lu) Temperature. 15°0 20°0 25°0 30°0 35°0 40°0 45°0
X ~-= O•Ql o•6 ·6130 •6115 ·6097 •6081 •6067 •6055 •6041 0•4 ·6128 •6114 ·6093 ·6084 •6070 •6058 •6044 0•3 ·6126 ·6111 o6096 ·6083 •6070 "6056 •6039 o•2 •6129 •6114 o6092 o6083 •6069 •6057 "6042
~-=-Q!03
0•6 .6118 e~6102 •6084 •6074 •6062 '"6047 "6034 0•4 ·6119 "6103 ·6086 "6074 "6061 •6045 •6033 0"3 o6117 •6102 •6086 •6073 "6060 "6042 •6028 0°2 •6116 "6100 •6083 "6072 "'6057 "6041 •6029
m = • 2
0•6 o61ll <>6093 ~>6075 <>6059 •6043 •6033 •6019 0•4 <>6109 <>6092 •6074 •6060 "6042 •6032 •6016 o·3 <>6110 •6093 ·6071 •6057 •6043 •6032 "6017 0•2 •6107 •6089 ·6070 •6056 "6040 •6029 •6014
~-=-Q,:01 0•6 ·6099 •6082 •6066 •6049 •6033 •6022 •6009 0•4 ·6098 ·6082 ·6067 •6052 •6035 "6021 •6007 0<>3 ·6097 ·6084 ·6068 •6051 •6035 ·6017 "6006 o·2 <>6100 o608'3 ·6065 ·6048 "60'34 ·6018 •6008 28. GP~PH OF VALUES IN TABGE II. ( E - 2 k log xm + 2 k A \fiD ) ag~:dns t x. 0.?
Volts. . tttt1 .6130 .m .;
m = o. 03
m = 0.02
.6100 " u .;; IDt~~mllif~~r: ...- .•
Itt'" u
·HHI
..,.
' 0 . 6060
. 6070
. 6060
. 6050
.6040 (Continued ) GPJiPR UF' VAL UES IN TAB LE II. (Continued) 29.
= o.o 0.2 0.6 V lts. = 1 .6070 '"' m = o. OS Q. J • r-; o6-Q C) ~ = 0.03 .,
Tl:h = 0 o 0"2 . 6040
~~ o 6 3 0 I H+++-H HfttH .01
•.6 ' 60
• 6040
."030
~HH IHH . 602.0 D 0 ~I
.6030
• 6020 ~ .. ::: I: • · ~ .6010 .; ... .' . 6000 -.. GRAPH II. 30. - k log K against m.
m - n: p. gq 0.02 o.o~ o. 06 ffi.TT a
·t· 'r +rt: ,.;h' i+t ' ft]
:._!+;l"'FI± 1-+i:.n ;:;
ii
,....._
: '-++
K=J I :~ :;J.U H:!tt . 6030 '""+ •fT· ~- ·~ lt'~it ::i ,... 141! .6020 fl•IJEffi Pi' · +~ . 6010
It 34o
!ABLE III- ..
!~~~!~~~~!_f£2~_firs~-~~~!~E21~~i2~-~2-!-=-2·
Temperature., 15°0 20°0 25°0 . 30°0 35°0 40°0 45°0
m = 0•0 •6128 •6112 •6094 •6082 •6068 •6055 •6041
~-=-Q.!Q]
•6114 .. 6098 .. 6080 •6067 10 6052 •6036 •6024
m =
•6106 e6089 @6071 •6057 •6041 •6028 °6014
m =QeOl 35 ..
!!BL~_il,.
5 5 ... k log K.. -log K(obs) .. - log K{ calc .. ) m0 x 10 00xlO 15°0 •6091 10•65 10•65 •475 •460 20°0 o6074 10•44 10•44 •599 ~579 25°0 0 6057 10•24 10•25 •752 "725 30°0 •6041 10"04 10•04 •953 •917 3500 o6025 9·86 9·86 1"180 1•133 40°0 •6010 9·68 9•68 1•452 1•390 45°0 .. 5996 9·50 9•49 1•778 1•716
!AB~!L....Y• Eo Eo k D do AgCl Ag
15oo •o5717 72o84 •9681 •2141 •8232 20°0 •05816 71"02 •9663 •2116 •8190 2500 •05915 69•20 •9644 •2088 •8145 30°0 0 06015 67•48 o9622 "2057 •8098 35°0 •06114 65o75 •9598 •2025 •8050 40°0 •06213 64·13 <>9572 •1991 •8001 45°0 •o6312 62·60 •9544 <>1955 •7951
!!J?LE Yl· 1 1 5 5 - 8 S). X 10 82 X 10 -Dl D2 a x. 10
15°0 •615 ·460 0 01288 ·ol371 1*05 2500 o990 ·725 "01350 •01445 1•12 35°0 1° 539 1•133 •01416 .01521 1•22 45°0 2•315 1"716 @01486 •01600 1•'37 L\ Ho LlG L\s0 D.opo 15°0 16p390 14jl040 8•15 -16•8 20°0 161)310 14,000 7•88 -17•1 25°0 16g230 131)960 7•61 "-17•3
30°0 16;t130 13 9 920 7•31 -17•7 35°0 16,040 13,880 6·99 -18•0 40°0 15,950 13,850 6•71 -18•3 4500 15~860 1311820 6•41 -18·6
0 LlH L\so Cpo
15°0 16p022 9e19 -34•7 25°0 15.!1'653 7•90 -35o5 35°C 151)\ 313 6o77 -36·3
!hl?1~L g ..
16,180 -20•0' 15,980 -20•5 15t770 -21<>4 J7o
Water - Methanol Solutionso ----~-----~~--~~--~------
Weight of CH30H% JAgCl KCl NaCl HCl 0 .. 23 .. 1 -22•9 -31•7 -36•4
10 -23•3 -2 4 -32•1 -36•0 20 -23<>6 -24•3 -32"'4 -35•7 From the observed electromotive forces E, values of the expression [E - 2 k log xm +- 2 k A JiilJ were calculated, the quantities k and A being given by means of the formulae
k = RT log 10 - 0•00019844 T --F e - ______ii_T ______and !A - <>506 ~78•54 X 298•1)~
The values of D, the dielectric constant of 20% methanol . f ok .. f 17 solut~on, were taken rom the results of A erlo., the values at intermediate temperatures being obtained by interpolation. The values calculated for each temperature are given in Table v. By using the method of Owen}0 the intercepts from the
second extrapolation give - k log K~ and values of - log K calculated from these data are given in Table IV.. Then the
, following method was employed to find m0 the solubility in mols. and c in mols. per per kilogram of solvent, 0 !) the solubility li.tre .. The thermodynamic solubility produet
K - aAg~t~ acl- ::: mAg ·I" mel- JAgt rl- as a ::: mf· 39 ..
m 2 = log 0
and - log f = A~ from the Debye-Huckel theory of dilute solutions.
So log mo - 1 log K A ~
1 :::: 2 log K A
since Co - mo do
For a first approximation, assume that = =
Then log m0 :;:; 1 log Ko 2
So a value of m0 may be derived. Substituting this value in the right-hand side of the equation gives a new value of
» m0 which is again substituted, the process being continued until a constant value of m0 is obtained. In this case two approximation~ were found to be sufficient to give constancy to m0 • The results obtained are listed in Table IV~ together with the values of C0 obtained by multiplying by the density d 40 ..
The densities used for this purpose were taken from the dat~ of 14 Harned and Thomas · 9 and are listed in Table V. It was necessary to extrapolate to find the density at 45°0.
By combining the values of - k log K with the standard 0 potential of the silver chloride electrode E AgCl 9 the standard electrode potential of metallic silver can be c.alculated by the use of the relationship
0 0 E Ag = k log K + E AgCl
Data for E0 AgCl in 20% methanol solution were taken 14 from the results of Harned and Thomas 9 and are listed in Table v. Again it was necessary to extrapolate for the value at 45°0. The
0 values of E which were derived from the equation are also given Ag in Table v. The variation of - k log K with temperature can be ex- pressed in an equation found by applying the method of least squares. This equation was foun~ to be
- k log K = •6041 - 317 (t- 30) lo-6 cl 127 (t- 30) 2 10-8
Reducing this to the absolute scale• this becomes
log K = 5•466 "006373 T --- {1)
The values of log K at each temperature calculated by meansi of this 41.
equation are listed in Table IV.
Differentiating the above equation with respect to
temperature:t __d -'!""_,_ log __ K. = __4112•9 ....,.. __ - •006 373 dT T2
0 But §:_12eL!f .=; f!H ----(2) dT 2:353-Firr2
so that =
By substituting appropriate values of T in this expression, the
change in heat capacity is found for each temperature.
so derived are listed in Table VII. From the change in heat capacity, the standard entropy
0 change,~S , can be calculated. The equation connecting the .two is
But T L\S ::: .6H ~G where L1 G is the change of free energy and ~G - RT ln K ::: 2•303 RT log K.
Values of~S 0 andLla are li~ted in Table VII.
Differe~tiating equation (2)
is obtained., Differentiating equatjlon (1) there is obtained 42 ..
:::
Equating the two 9 since
dLl H0 ::: ---"""""'-dT
then _1!QE~------2 - 2· 303 RT
Rearranging this gives
The list of values of~Cp 0 calculated by means of this expression is given in Table VII@
For calculating the entropy of solvation9 the partial molal entrppy of the pair of ions, Ag -t- and 01- » was found first"
,,JJ_neec•· -so , + + -so Ag 01- -
0 it was only necessary to find the value of S AgCl g i ven b y Latlmer.. Then
L1so Solvation
The last two terms were found from the Sack~r-Tetrode equatlon
::: 3 R ln M + ~ 2 2 43o
The values of~S 0 Solvation at 25°0 of silver chloride in various methanol solutions are given in Table X, use being ·made of the figures of Owen and Brinkley,19 and of Davis.11 For
comparison the entropies of other salts in the same solutions are given, the values being those or Latimer and Slansky. 21 44 ..
The method may be summarised as a study of series of cells containing solutions of varying concentrations of the dissimilar ions giving rise to the junction potentials 9 but main- tained at constant ionic strength by the presence of an additional electrolyte, which takes no part in the .electrode reactions.
Extrapolation to zero concentrations of the dissimilar ions eliminates the junction potentials, and subsequent extrapolation to zero ionic strength eliminates the effect of the inert elec- trolyte. Justification for the extra-thermodynamic hypothesis involved in the extrapolation must be on empirical grounds 9 and the simplicity of linear extrapolations renders its verification 10 possible. Owen, who first us,ed this method I) found his extra- polations were linear within estimated uncertainties. FUrther work on buffered cells by Owen and Brinkley19 supported the valid- 11 ity of the hypothesis, and the results of Davis were in excellent agreement. The results of the present investigation are equally in agreement with the linear extrapolation, for although a few points do not lie on the lines, as can be seen in Graph I, the variation may be attributed to experimental error, which must be greater than in the experiments of Owen and of Owen and Brinkley ..
The radii of the circles in Graph I are plotted as •2 M.V. 9 and the intercepts obtained by extrapolation to x = o are plotted in Graph II with circles of radius •1 m.v. It can be seen that individual errors in Graph I are modified in plotting, and have not a great effect on the values of the intercepts. For this reason their influence on the final extrapolation in Graph II to m = o is very small, and they do not interfere with the excellent linearity obtained.
No measurements of the solubility of silver chloride in 20% methanol solution are given in the literature9 so no direct comparison of the results of this work is possible, but the solubility found may be compared with those found by Owen and 23 Davis. Koch givesthe solubility of silver chloride in absolute methyl alcohol as 3·9 x lo-7 mols. per litre at 25oc, so that the salt is practically insoluble in pure methanol. Davis found a decrease in solubility in passing from pure water to 10% methanol solution~ as was to be expected, and this trend is continued in the present work» as shown by the following results.
5 mo X 105 X 5 (Owen) mo 10 (Davis) m0 x 10 (Present work) .. 15°0 «>841 •604 •475 25°0 1•338 •970 •752
35°0 2mQ48 1•502 1•180 45°0 3•026 2o250 lm778
The values for the standard el.ectrode potelfiltial of silver in the three solutions show a similar trend.. They were obtained by combining the data for E0A of Harned and 01 18 1 g Ehlers and Harned and Thomas 4 with the values of k log K de- rived from the experiments., Eo Eo Eo Ag (Owen and Brinkley) (Davis) (Present Ag Ag work).
15°0 •8o9o "8179 •8232
25°0 "7992 "8087 •8145
35°C •7892 •7989 •8050
45°0 •7791 "'7886 •7951
By combinlng th'e solubill ty data .for silver chloridl3 i11 10%' and 20% methanol solutionsv a value for a» the raean ionic radius, can be derived ..
Th0 fm:-rau:ta used for calculating this quantity is
ln S1 - ~l~l~L- • 1 cl·o ~ !)1,·- and was derived in the introduct:i.on. As the activity coefficients tend to unity at infinite dilution in both media.\! the l>ebye ... n1ickel corrections cancel 9 and the expression becomes 47.
In Table VI the necessary data is collected, s1 being Davis' figures for the solubility of silver chloride in 10%' methanol solution» and 82 are the values obtained in this work J'or 20% methanol solution a !. and ! are the reciprocals ~1 D2 of the dielectric constants of the two solvents, the values being taken from the paper of .Rkerlof or interpolate'd from them for intermediate temperatures .. The other va.lues for insertion in the equation are universal constants
2 N = 6oQ6 X 10 3 1 e = 4<~>774 x 1o- 0
z = 1 1 as the valency of silver and chlorine is unity.
'rhe values of a obta.ined by means of this expression are given in Table VI. 'rhe theoretical mean ionic radius may be calculated using the relation 2 -1 where r 1 and r 2 are the individual radii of the two ions. Uslng 20 da.ta due to Pauling the ionic radii of th(~ sil·
9 Dunning and Shutt0 whose calculation also led to a low value~ Plotting logS against! for the solubility of D silver chloride in water9 10%' methanol and 20% methanol gives three points 9 which certainly lie on a straight line» but there is not enough data for an adequate test of the BoMftequation9 and inclusion of the figure for absolute methanol of Koch23 shows that the plot is not a straight line 11 but deviates rather rapidly<> A greater range of methanol-water solutions will need to be in- vestigated before a more extens:i.ve test of the theory can be made~
The values for the entropy of solvation of' silver chloride are interesting» as they can be compared wtth other salts in the same solvents .. The values for all the salts increase with increasing concentration of methanol, as do those for hydrogen chloride, after reaching a minimum at about a 20% concentration of methanol .. Silver chloride follows the same trend, moreover the values for silver chloride are about the same magnitude as those of potassium chloride. Pauling gives the radii of the potassium ion and the silver ion as 1•33 i and 1•26 i respectively, so that the close agreement in the entropy of solvation is to be ex-
pected1 particularly as Latimer and Slansky postulate only a small effect for the difference in size of the positive ion.
The change in t'\Op0 between the work of Owen and
Brinkley and that of Davis 9 with only a small consequent lowering in the present work is notable, but no explanation seems to be availa.bleo 49.
1. Measurements of the electromotive force of cells with
liquid junctions of the type KCl (x)m IAgNO( (x) m Ag, AgCl KN0 (1-x)m AgCl, JAg. 3 lKN0 3 (m) ~KN0 3 1-x)m 0 0 0 0 0 have been made at 15 0 9 20 c, 25 C9 30 c. 35 c~ 40°0, and
45°0 11 using 20% methanol-water solution as solvent.,
2. From these results the solubility product and solubility of
silver chloride have been evaluated at each temperature by means of an extrapolation method for eliminating the liquid
junction potentials.
3. The standard electrode potential of silver in this solvent has been calculated for each temperature, and these values,
together with solubility data 11 have been compared with the corresponding values in water and 10% meths,nol solution.
4. The solubility data in 10% and 20% methanol solutions have
been used in Bo~1s equation as a test, by the calculation of
a, the mean ionic radius.
5. Derived thermodynamical quantities have been calculated for the reaction AgCl Ag+"' + Cl- , and compared with corresponding values in water and 10% methanol solution.
CllRISTCHlJHCH, N.L:. 5o.
6a The entropy of solvation of silver chloride in waterg
10% and 20% methanol solutions has been calculated, and com ...
pared with the entropies of other salts in the same solutions. 51.
1. GloVH}Zynski Kolloid. Beihefte (1914) 6 9 147. 2. Davis)) Ricci with Sauter J.A.c.s. (1939) 61,3274. 3. Popoff and Neuman J. Phy. Cham. (1930) 34»1853. 4. Neuman J.A.c.s. (1932) 54,2195. 5. Dave and Krishnaswami. J. Ind.Inst.dhem. (1933) Pt.14,153.
6. Johnson and Low J .. A.c.s. (1933) 55,2262. 7. Koh1rausch z. Physik. Ohem., (1908) 64!1129 8. Brown amil Macinnes J.A.c.s. (1935) 57,459.
9. Dunning and Shutt Trans. Farad.Soc .. (1938) 34 9 1192 .. 10. owen J.A .. c.s .. (1938) 60,2229.
11. Davis Thesis~ University of New Zealand~>
12. ssberger and Proskauer "Organic So1ventsn (19'35) .. 13.. Childs "Physical Constants" (1939).
14 <> Harned and Thomas J .A.c .. s. (1935) 57,1666o 15.. A1lmand and Hunter Trans. Farad. Soc. (1928) 24ll 300 ..
16. Smith and Taylor· u.s. Bureau of Standards. Journal of Research (1938) 20,837 0 . 17. .~:\kerlof J .. A.o.s. (1932) 54,4125. 18. Harned and Ehlers J.A.o.s. (1933) 55,2179.
19o Owen and Brinkley J .. A.o .. s .. (1938) 60' 2233.
20. Pauling J.A.c.s. (1927) 49g765o
21. Latimer and Slansky J .. A.c.s .. (1940) 62g2019. 22 .. Latimer "Oxidation Potentials" (1938} .. . 23 .. Koch J.Chem.Soc. (1930) 1339 1551.
Pinkus and Hanrez Bull.Soc.,Chem'.Belg.(l938) 47 11 532 .. 25. Bjerrum 9hemistry at 1931 meeting of Brit-
ish Association for the Advance- ment of Science .. 26 .. Latimer and Buffington J.A.c .. s .. (1926) 48,2297 .. 1"')7 e.,' @ Latimer and Kasper J .A.c.s. (1929) 51 9 2293 ..
THE LIBRARY UNiVERSII'Y OF CHRISTCH!JR.CH, N.:Z.