EDITHH. LANM.4N
390
AND
(b) Using the above values and that accepted by Spencer and Motes for the reaction
+
H g 0 = Hg ‘/zOz A.F?sn = 13,850 3Pb0 ‘/so2 = PbsOi = -6,910 PbaOi 0 1 = 3PbOz = --9,580
++
PbO
+ ‘ / z 0 ~ = PbOz
=
;;1
, ,
BEVERIDGE J. M.iIR Summary
1. The potentials of two electrodes ha1.e been measured and the potential of a third electrode calculated from these. The values are
+ +
(6)
-5,500
P ~ O ( S ) - P ~ ~ O ~ ( S ) - O H -0 2488 * 0 0005 volt PbaO4(s)-PbOi(s)-OH0 1293 * 0 01J1 volt f 0 280 * O.O(J1 volt PbO(s)-PbO,(s)-OH-
(c) Using the preceding values and that calculated by Spencer and MoteYfor the reaction
+ + 202
Pb 3Pb Pb
1/202
+
0 2
= PbO = PbaOi
AF298
_ -
= PbOs
( 8 ) Spencer and Mote,
THIS
= - 45,100 = -142,210
-
50,600
(7) (8)
JOURNAL, 54, 4618 ( 1 9 3 2 ) .
[CONTRIBUTION FROM
THE
Vol. 56
2 . The free energy changes have been calculated from the measured values of the cells. LINCOLN, SEBR.
RECEIVED KOVEMBER (i,1933
CHEMICAL LABORATORY OF BRYNMAWRCOLLEGE ]
The Compressibility of Aqueous Solutions B Y EDITHH. LANMANAND
Introduction The compressibility coefficients of many aqueous solutions of both electrolytes and nonelectrolytes have been determined during the past fifty years, and the data obtained in this field, prior to the year 1919, have been summarized bj7 Cohen and Schut in “Piezochemie.” Since that time, accurate determinations of the compressibility of aqueous solutions of various organic substances have been determined a t Harvard, but, a t the time this work was undertaken, no further work had been done on solutions of electrolytes. The existing data in this field had been obtained a t different temperatures over varying pressure ranges, and a t random concentrations. It therefore seemed .worth while to redetermine the compressibility coefficients of certain inorganic salts and their acids and bases, all a t the same temperature, over the same pressure range, and a t equivalent Concentrations. The substances chosen were the chlorides and hydroxides of lithium, sodium and potassium, hydrochloric and acetic acids, and potassium acetate. The compressibility of glacial acetic acid was also determined. Determinations were made a t three concentrations for each substance : i. e . , one mole of substance to twenty-five moles of water, one to fifty, and one to one hundred. All measurements were made a t 25’ and between IO0 and 300 megabars. Preparation of Materials and Analysis of Solutions.The salt solutions were made up from Baker analyzed chemicals It was not considered worth while to re-
BEVERIDCE
J.
MAIR
crystallize these substances, since a n impurity of several tenths of a per cent. could not cause a change in conipressibility which could be detected ( e . g., the difference in conlpressibility of NaC1.25Hz0 and KC1.25H20 is only 0.78 X The concentrations of the chloride solutions were determined by precipitation with silver nitrate, and the more dilute solutions were made up by adding the calculated amount of water to a weighed portion of the standard solution. The hydrochloric acid was prepared by distilling one to cne c. P. acid, and noting the pressure during distillation. The concentration was then computed from the pressure,’ and verified by precipitation with silver nitrate. This was then diluted by adding the calculated amount of water to give HC1.25H20 (and HC1.50HzO and 100H?O). The sodium hydroxide solution was prepared by dissolving the c. P. base in water in a gold dish to prevent contamination by silica. Only a small amount of water was used in order t h a t the less soluble carbonate might remain undissolved. The solution was then filtered, diluted to the approximate concentration desired, and stored in a Pyrex bottle. Carbonate was then tested for by adding definite amounts of barium chloride solution (of known concentration) to samples of the solution. The precipitates were allowed to settle, the supernatant liquids decanted and B a + + tested for by sulfuric acid. The amount of B a + + necessary to prccipitate the carlmiate was then calculated and added to the sodium hydroxide solution. After allowing the precipitate to settle, the solution was siphoned into a bottle containirig carbon dioxide-free air. The solution was at all times protected from contamination with carbon dioxidc by means of soda lime. Silutions of potassium hydroxide and lithium hydroxide were prepared in a similar manner. The concentrations were determined by titrating against thc hydrochloric acid, using phenolphthalein as an indicator. Weight burets were used. The more dilute solut i x x were made up accurately by addition of the calcu(1) Hirlett, THISJ O ~ J R X A L31, , 390 ( 1 9 0 0 ) .
Feh., 10:N
T H E COMPRESSIBILITY O F
AQUEOUSSO1,UTIONS
39 1
lated amount of water, and checked by titration against and the compressibility calculnted from the following hydrochloric acid. equation (70 - w , ) D The acetic acid solutions were made up by diluting c. P. P l U U - 3uu = -t 0' 13.560 ?Y200 glacial acetic acid, and were titrated a,gainst the lithium hydroxide using phenolphthalein. KAc.51H20 and where p = compressibility pet cc. per megabar KAc.101 H?O were prepared by adding equivalent amounts p' = compressibility of mercury = 4 X 10 - 6 of KOH and HAC. NaOH KOH LiOH NaCl KCI LiCl HCI H4c A set of calibrated wcights was used in 2 25 all analytical work, and vacuum corrections 2.00 were applied In the gravimetric analyses, the concentrations were computed from the 1.75 average of two analyses which checked t o within 5 parts in 10,000 (with the exception 1 60 of the hydrochloric acid. I n this case, the analyses checked only within 0.130j,, b u t 1.25 this concentration was further checked by E calculation from the pressure reading during 100 distillation). In the one instance in which the concentration of a diluted solution was 0 75 determined by analysis as well as computed from the amount of water added, the results 0 50 checked within 0.02%. The concentrations of solutions determined by titration were 0 25 calculated from two or more analyses which checked in general t o less t1ia.n 0.0370 (never 0 more than 0.1%). The density determina30 32 34 36 38 40 42 tions were accurate to less than one part in p x 106 10,000, the greatest difference in accepted Fig 2 -The compressibility plotted against m results being 0.02%. When plotted against concentration, smooth curves were obtained and points ?e, = weight of mercury added ccrresponding t o a from the d a t a of Baxter and Wallace2lay on these curves. change in pressure of 200 megabars The densities represent the weight in vaczm of one cc. of W I = weight of mercury ccrresponding t o 200 megasolution. bars ( =0.1473 grams) when piezometer i:; filled with Hg only Method and Apparatus D = density of solution The compressibility determinations were made by the ?Y= weight of solution method in use a t H a r ~ a r d . ~ 13.55 = weight of 1 cc. of mercury a t pressure of 300 The glass piezometer used is shown in megabars I Fig. 1. It was a modified form of the pieInstead of adopting the usual procedure of adding zometer used for fused salts,4and was found random amounts of mercury and plotting the weights simpler t o fill than t h a t generally used for A liq~ids.~ against the corresponding pressure in megabars, and then It was fitted at A with a stopcock having a solid barrel, instead of the stopper reading from the curve the weights corresponding to just 300 and 100 megabars, considerable time was saved by ordinarily used. An open cup at the top taking two points only, one close t o 300, and one close t o contained mercury into which the platinum 100, i. e . , mercury was added until the pressure on thc wire dipped. Although this stopcock somescale corresponded t o approximately 300 megabars. times .tuck, especially when in use with the After a period of fifteen minutes, the pressure was deteralkali solutions, it was always possible t o rcnicve i t easily by means of an Achesel mined accurately in the usual manner by adding weights until the circuit was just broken. Mercury was then stopcock rcziovcr. The piezometer was removed until the scale reading approximated 100 megabars, filled with solution by means of a funnel and, after fifteen minutes, the pressure was accurately c!rawn out t o a long capillary which was determined again. The first point was then eheckcd by inserted a t A . The stopcock, which was putting back the mercury which had been removed. As well-ground and provided with a minimum Fig. 1.-Pieamount of Ramsay grease, was then inserted these two points were close t o 300 and 100 megabars, zometer. and turned until i t "set," i. e . , it could be respectively, the weight of mercury corresponding t o a change of pressure of exactly 200 megabars was calcuturned no more. lated by direct proportion. In the two cases in which All determinations were made a t 25" (*0.01). The both methods were used, the results checked within ~ i i e pressure was measured fifteen minutes after application, part in 3500. (2) Baxter and Wallace, THISJOURNAL, 38,70 (1916). The weight of mercury equivalent t o a change of pres(3) Richards and Shipley, iOid, 38, 989 (1916), and previous sure of 200 megabars when the piezometer was filled with papers. mercury alone was first determined (=0.1473 g.). The (4) Richards m r l Jones, {bid.,31, 1.55 (1900). ~~
EDITHH.
392
LANMAW A N D
compressibility of water a t 25" was then determined, giving the value 42.44 X Then, after two or more runs on each of twenty-seven solutions, the water value was redetermined: result 42.62 X 1 0 P . The average KC1 LiCI
BEVBRIDGR J. I k I R
Vol. 56
value, 42.63 X l O P , which was used in calculations, differs from the estremcs by less than 0.3Oj,. No results on the solutions were accepted which did not check ttj 0.3%; in general, they were in better agreement than this.
LiOH KOH NaOH
NaCl
Data and Results All data are recorded in Table I. Concentrations are expressed both in moles of water per mole of solute (column I ) ; and in mole,; of solute per 1000 g. of water (112, column 2 ) . T 7 and are, respectiwly, the volume of solution containin: one mole of solute, and the volunie of water in which the mole of substance is dissolved. B is the compressibility coefficient of the solution, and that of water. The apparent molal compressibility (pJ' of each substance has been calculated and recorded in column i . The compressibility coefficients arc plotted against the concentrations (expressed in moles of solute per 1000 g. sf water) in Fig. 2. At equivalent
- ( P V - p1v1) x 103. Fig. 3.---The apparent molal compressibility plotted against ;v '
TABLE I Solute
LiCl
NaC1
KC1
KAc LiOtI
h-aOH
KOH
H C1
HAC
HAC
HzO
Moles Ha0 per mole of solute
26.74 49.99 98.46 25.02 50.04 100.08 24.99 49.93 100.04 51.29 101.17 25,04 50.08 100.12 25.01 50.09 100.15 25.05 50. 03 100. 1fi 24.99 50.09 100.16 25.24 50. l f i 100.20 Glacial
m
Density
I'
2.0757 1.1103 0.5638 2.2182 1,1094 0.5546 2.2216 1.I l l 7 0.5549 1 ,0823 0.5457 2.2168 1.1083 0.5544 2.2192 1.1081 0.5542 2.2160 1.1095 0.5542 2.2218 1.1082 0.5532 2.1992 1.1065 0.5540
1 0440,5 1 02334 1 01094
502 07 921 53 1796 5% 471 30 922 42 1825 82 481 17 930 x?, 1835 43 977 77 1878 05 451 29 902 42 1805 54 451 46 902 84 lX0C 12 461 85 911 44 1815 88 470 79 923 87 1825 09 508 OG 958 211 1861 99
1 1 1 1 1 1
08013 040hl 01932 09043 04642 0223
1 04534 1 02274 1 05265 1 02640 1 01230 1 086i0 1 04391 1 02114 1 09853 1 0503') 1 024iil 1 03370 1 01623 1 00704 1 01315 1 00575 1 00173 1 04484 0 99704
1.1
483.20 903.31 1779.04 452 . lii 904.10 1808.35 451.45 902.17 1807.62 926. 72 1828.04 452.45 Sl04.97 1809.14 45 1 . 91 905. 15 1809.ti5 4.52.59 903.94 1809.81 451.53 905. OS 1809.85 &if,sik. Chem., 111, 419 (1929).
(3) Landolt-Bornstein-Roth, “Tahellen,” Fourth edition, 1012, p 400 ( 4 ) Curtius and Schultz, J p r u k l . Chem , [2] 42, 521 11890)
NiH4.2HX S N*H,.HX
+ HX
