2052
L. E. MURCHAND W. F'. GIAUQUE
Vol. 66
THE THERR.IODYSA?IIIC PROPERTIES OF SODIUM HYDROXIDE AND ITS MONOHYDR-4TE. HEAT CAPACITIES TO LOW TEMPERATURES. HEATS OF SOLUTION' BY L. E. NI-RCH AND W. F. GIAUQUE 1 1 0 ~T m p e r a t u r e Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, C d . Reeezved A p r d 27, 19BB
The heat capacities of sodium hydroxide ( I2-32O0K.), and sodium hydroxide monohydrate (16338.25'K.) have been measured and used to prepare smooth tables of thermodynamic properties. The melting point of the SaOH-PiaOH.HzO eutectic was found to be 335.78'K. (O'C. = 273.15"K.) and the eutectic heat of fusion is 3207 i 100 cal. mole-'. The heat of fusion of KaOH.HZO is 3776 rt 30 cal. mole-' a t its melting point, 338.25"K. These values of the heats of fusion are based on the eutectic composition of 73.1 wt. % of SaOH. The heats of solution of a series of solids with PiaOH.(O to 1) H20 gave a straight line relationship and thus no evidence was found for an intermediate hydrate such as NaOH.Z/aH20 or N F O H . ~ / ~ Has ~ Ohas been suggested by others on the basis of similar but less accurate measurements. Also, NaOH:H@ with a small water deficiency and NaOH with a small amount of water appear to give the same eutectic temperature, indicating no intermediate hydrate. The calorimetric data have been used with the third law of thermodynamics to calculate the,dissociation pressure of water over the system NaOH.HzO-NaOH and the results are in excellent agreement with the dissociation pressure observations of Baxter and Starkweather, who investigated SaOH.( "lowest hydrate")-XaOH, which shows that no intermediate hydrate appearedin their experiments. S a O H = NaOH(inf. dilute soln.)AH-lzs~.l;"K = - 10,653 =I= 10 cal. mole-'. NaOH.H20 = NaOH(inf. dilute soln.)AHpss16= -5134 i 10 cal. mole-l. NaOH, 5298.1~ = 15.400 gbs. inole+. XaOH.H*O, 520~.~s = 23.775 ghs. mole-'. S a O H . H 2 0 = NaOH H20(g), AH2g8,,6= 16,039 cal. mole-', A H 8 = 14,870 cal. mole-l, (P~,p)89~.15 = 0.14 mm.
+
Despite the importance of sodium hydroxide, there are few accurate thermodynamic data on this substance and its numerous solid hydrates. Douglas and Deverz have made accurate heat content measurements on solid and liquid NaOH over the range from 298 to 1000°K. and its low temperature heat capacity has been measured to GOOK. by Kelley and Snyder.3 There were no heat capacity data on NaOH below 60°K. and none of the solid hydrates appears to have been investigated. This paper presents heat capacity data on XaOH from 12 to 320'K. and on SaOH.H20from 14°K. through its melting point at 338.25OK. The only previous investigation of the heat of solution of the above solids in water appears to be that of de F ~ r c r a n d ,mho ~ dissolved a series of solids containing water over the range 0 to 1 HzOper mole of NaOH. A plot of the data from this pioneer experiment shows them to be quite inaccurate. However, de Forcrand interpreted t>heobservations as indicating the presence of a hydrate il'aOH.2/3H20 and the existence of an intermediate hydrate generally has been accepted by various authors for the past GO years. Recently, Mauret5 has suggested SaOH-0.5Hz0 as the composition of the assumed intermediate hydrate. Actually there are no data of sufficient accuracy ever to have justified the assumption of any intermediate hydrate within the range 0-1. We have repeated de Forerand's experiment with presently available accuracy and find that all heats of solution lie on an accurately straight line when plotted against moles H?O/mole S a O H ; thus no intermediate hydrate was indicated. It has ordinarily been assumed that Na0I-I and NaOH.H20 solidify from its concentrated aqueous (1) This work was supported in part by the National Science Foundation. ( 2 ) T. B. Douglas and J, L. Dever, J . Res. Natl. Bur. Std., 53, 81 (1954) (3) J. C. R. gelley and P. E, Snyder, J . Am. Chem. SOC., 5'3, 4114 (1961). (4) R. de Forcrand Compt rend.. 133, 233 (L9Ol). ( 5 ) P , Llaurat, .rbzdi, 240, 2131 (1955).
solutions as pure compounds and we assumed this in beginning the present experiments. Thus, samples of KaOH with a small excess of water and ?jaOH.HzO with a small deficiency of water were used to infer the heat capacities of pure substances. Experimental Preparation and Analysis of the Samples.-The sodium hydroxide samples were prepared by passing moist nitrogen gas over sodium metal and drying the resulting liquid solution to the desired composition. The sodium used was Raker and Adamson Reagent Grade, which contains less than 0.01 mole % of impurities. The nitrogen gas was produced by boiling liquid nitrogen obtained from the laboratory fractionating unit, which includes very complete removal of COZfrom air at 270 atm. by adsorption in 4070 KOH solution. The distilled water for humidifying the nitrogen was boiled immediately before use t o remove any dissolved carbon dioxide, Sealed cans of sodium and a gold calorimeter were placed in a gas tight metal glove box with a Plexiglas window. This was flushed for several hours with dry nitrogen gas. A can of sodium then was opened and the exterior portions of the metal were removed with a stainless steel knife and discarded. Approximately 0.25 lb. of sodium was placed on a platinum wire mesh which was suspended above a flat platinum dish. The humidified nitrogen gas then was passed through the glove box and a liquid solution of sodium hydroxide dripped down into the platinum dish. The glove box also contained a heat lamp which was used to evaporate the solution to its final composition. To obtain sodium hydroxide with only a small amount of water, it was necessary to heat overnight a t about 350". Following the heating, the molten sample was poured into the previously weighed gold calorimeter. Both before and after pouring, samples were removed for carbonate analysis. The calorimeter then was capped, removed from the glove box, and weighed. Later the cap was soldered in place. The carbonate determinations were accomplished b37 dissolving small portions of the sample in water and transferring the liquid to 100-ml. centrifuge tubes with narrow tapered graduated bottoms. Barium carbonate was precipitated by an excess of barium chloride solution and the tubes were centrifuged. The precipitate was compared visually with various precipitates of known amount. The accuracy of this method was about 5 x 1 0 - 8 mole or about 0.005u& of the total moles of sodium hydroxide used in the analysis portion. Following the calorimetric measurements, the sodium hydroxide was removed by washing the calorimeter with water, weighing the washings, and titrating aliquot parts of
Oct., 1962
TIIERXODYXAJIIC PROPERTIVS OF
SODITJM
the total. The standard acid used in the titration was constant bniling sulfuric acid as described by Runzler.B The amount of water in the samples was obtained by difference. Sodium hydroxide monohydrate was made in the same manner except that, less heating was required t o produce a sample of approximately the desired composition. A representative sample of the material added to the calorimeter w a ~oh'tained by taking two portions before pouring and two after pouring. The sample of NaOH .0.04014H20 in the calorimeter wpighed 247.543 g. and contained adbout 0.01 mole yo of Xa2CO3. The sample of NaOH,0.97776Hz0 investigated weighed 219.456 g. m d contained about 0.013 mole of Na~C03. The weights were corrected for bu.oyancy. The density of KaOH was taken as 2.13 g. and that of NaOE. H ~ 0 7as 1.72 g. cm.-l. Mol. wt. S a O H = 40.005; mol. wt. NaOH. H20 = 58.021. Description of Gold Calorimeter VI.-The general features of the calorimetric apparatus were very similar to those described by Giauque and Egan8 and need not be mentioned. Hen-ever, the calorimeter, which will be used in subsequent work under the designation Gold Calorimeter VI, was considerably different and should be described briefly. It is shown in Fig. 1, which is largely self-explanatory. There were eight vanes 0.025 em. thick in the calorimeter. Gold wire, 0.0031 in. in diam. and containing about 0.1% silver, was used to wind a resistance thermometer-heater on the 1.0 mm. thick outer cylindrical wall of the calorimeter, but the procedure was different from that described by Giauque and Egan. Two layers of China silk, each 0.003 in. in thickness, were placed on the outer surface with the aid of three coats of Formvar varnish. (Nylon cloth was tried and proved unsatisfactory due to wrinkling.) The varnish was dried for 3 hr. a t 125". The gold wire and silk thread 0.004 in. in diam. were wound in parallel over the silk cloth. The tension during winding on a lathe is essentially all in the silk thread which was used to crowd the gold wire into a closely wound helix of 467 turns. The ends of the gold wire were soldered t o turns of 0.010-in. diam. double silk insulated copper wire; thus, the gold-copper junctions were kept very close .to the calorimeter t.emperatnre to avoid thermoelectric effect. The gold windings a w e covered with two layers of the same silk cloth, painted with three more coats of Formvar varnish and dried at) 125". The double silk insulated copper lead wires from the lower end of the calorimeter were placed between the two outer silk layers. The entire assembly was covered with heavy gold leaf to reduce radiation. A Leeds and Xorthrup strain-free platinum resistance thermometer, no. 1215333, calibrated by the National Bureau of Standards, was placed in an axially located vertical well that extended from t.he bottom to above the middle of the ca1orimei:er as shown in Fig. 1. Rose's alloy was used to establish good thermal contact between the standard thermometer and the calorimeter. The two thermometers were compared a l the beginning and end of each measurement. The gold thermometer gave a continuous record of the surface temperature. The introcluction of molten S a O H into the calorimeter a t about 350" posed an unusual problem, because such a temperature not only n-ould destroy the external thermometer, but also would cause flow of the low melting alloy and undesirable diffusion into t,hegold well holding t,he standard thermometer. This prohlem was solved by introducing the molten NaOH before t,he gold thermometer and anv low melting alloy were added. The later int,roduction of the low melting Z;aOH.H20caused no difficulty. One definesd calorie was taken as 4.1840 absolute joules and 0°C. as 273.150"K. (triple point of water = 273.16 exactly).
Results Heat Capactities of NaOH and NaOH.H20.As meiitioned previously, t'he low temperature calorimetric measurement,s were made on samples ( 6 ) J. E. Kunzlor. A n d . Chem., 26, 93 (1953). (7) J. A. Wunderlich, Acta Cryst., 10, 462 (1957). ( 8 ) W . F. Giauque and C. J. Egan, J . Clism. P h y s . , 5, 45 (1937),
HYDROXIDE ASD
ITS
-4,2
2053 ~IONOHYDRATE cm-
n
L,
VI
n
T P
4
n
1 7
/
THERMOMETER HEATER
3
WELL FOR PLATINUM RESISTAHCE THERMOMETER
Fig. 1.-Gold
calorimeter no. VI.
with the over-a11 composition NaOH.0.04014H20 and NaOH.0.97776H20. Although we infer later T.4BLE 1 MOLALHEATCAPACITY OF NaOH.0.04014Hz0
+
1 "mole" = 0.95986 mole of S a O H 0.04014 mole of NaOH.H20 0°C. = 273.15'X. Units are gbs. mole-' T,OK.
C,
T,OK.
Cp
T,OK.
CP
Series I 85.144 5.556 243.138 13.332 12.748 0.0463 92.324 6.161 251.057 13.519 14.363 ,0786 99.766 6.755 258.958 13.709 15.832 ,1086 107.193 7.323 267.063 13.896 17.549 ,1443 114.598 7.863 274.857 14.067 19.604 .1991 121.771 8.356 282.256 14.231 22.245 ,2825 128.834 8.791 290.534 14.381 24.849 ,3773 136.310 9.248 298.800 14.550 28.316 ,5403 143.615 9.657 307.266 14.678 30.865 ,6782 151.497 10.062 315.571 15.004b 32.618 ,7912 159.657 10.455 Series I1 35.345 ,9696 166.922 10.789 299.577 14.558 38.570 1.1918 174.234 11.097 307.097 14.736b 42.135 1.4982 181,839 11.408 314.655 14.927' 46.276 1.8531 189.477 11.657 Series 111 50.82 2.24" 197.459 11.970 285.744 14.239 55.682 2.693 205.038 12.226 293.601 14.397 60.983 3.211 212.952 12.480 301.237 14.574 66.496 3.750 220,978 12.718 308,931 14.794' 72.358 4.310 228.521 12.928 315.868 15.020' 78.532 4.904 235.742 13.123 a Lost insulating vacuum. Value given no weight. b Premelting of NaOX-NeOH.Ha0 eutectic, to be discussed below.
I,. E. MURCHASD W. F. GIAUQUE
2054
Vol. 66 TABLEI1
NaOH.0.97776I-IzO 0.97599 mole of NaOH.HpO 0°C. = 273.15"IC. Units are gbs. mole-' T,OK. C, T,OK. Cp T , OX. GP Series I 93.237 9.437 258.243 19.684 14.640 0.172 100.640 10.125 266.451 20.041 15.805 .226 108.459 10,838 274.178 20,354 17.270 ,304 116.411 11.521 281.991 20.718 19.265 .426 124.296 12.156 290.056 21.056 21.385 ,583 132.233 12.754 298.196 21,424 23.770 ,785 140.212 13.343 306.534 21.690 26.190 1.011 148.182 13.877 314.503 22.295" ~ 28.719 1,298 3 155.870 14,350 321.495 22.698" 31.728 1.663 163.733 14,839 338.25 Melted NaOH.H20 35.341 2.115 171.810 15.306 343.751 37.74 38.665 2,553 179.627 15.760 348.539 37.25 41 563 2.954 187.407 16.177 353.697 37.42 45.091 3.443 195.224 16.609 Series I1 49.493 4.083 202.756 16.999 301.862 21.610 54.442 4.728 210.416 17.383 310.080 22.002" 59.433 5.409 218.191 17.759 338.25 Melted NaOH.HZ0 64.481 6.087 226.063 18.168 343.751 38.19 69.989 6.779 233.965 18.542 349.527 37.77 76.196 7.522 241.893 18.915 355.027 38.63 82.888 8.322 249.963 19.305 a Premelting of NaOH-KaOH HzO eutectic, to be discussed below. R/IOLAL HE.4T CAPACITY OF
1 "mole"
3
3
7
1
& Y
______
~
____-_ 3
5
NaOH 0 97776 H20
335
0 Calories.
500
1000
Fig. 2.-(Lower scale) heat added less JC,dT per mple NaOH.0.97776Hz0. (Upper scale) Reciprocal of fraction melted (a) eutectic mixture, (b) NaOH.H20.
that sodium hydroxide may possibly form a dilute solid solution, NaOH .O.O1OHzO, the data were considered to be representative of mixtures of 0.95986 mole of NaOH 0.04014 mole of KaOH. HzO, and 0.02224 mole of NaOH 0.97776 mole of KaOH.H20. Even if the solid solution does exist, this should cause little error. The observed data are given in Tables I and 11. Smooth curves through the observations were used in computing the properties of NaOH and KaOH. H.0 a t even values of temperature. These values are given later. The heat capacities are given in gibbs mole-' (gbs. m0le-1).9 This unit also is used later for entropy, free energy/temperature, and heat content/ temperature. The Heats of Fusion and Melting Points of NaOH.H,O and its Eutectic with Na0H.-The measurement of the heat of fusion of NaOH.HzO was complicated by the fact it was off the monohydrate composition. Thus the total heat of fusion applies to the melting of some eutectic mixture as well as to the monohydrate. The procedure adopted was as follows: one run started well below the melting point of the eutectic and continued to a temperature above the melting point of the monohydrate. In order to allocate the proper portion of this total heat to the eutect,ic and the residual monohydrate, a second series of short runs was made to determine the melting temperature as a function of heat input. The f C,dT was subtracted from the heats added to give the net heat used for fusion. These results are shown in Fig. 2 as the curve with two sections convex upward. The uninterrupted run had the highest accuracy and was given 1 0 0 ~ oweight in evaluat,ing energy. The second series of many short runs gave
+
+
(9) 1 gbs. = 1 defined osl./defined OK. W. F. Giauque, E. W. Hornung, J. E. Kunzler, and T, B. Eubin, J , A*, C h m . Soc., 88, 6 2 11960).
= 0.02224 mole of NaOH
+
a total heat of fusion 0.22% lower due to the increased sources of error, hut the curve of temperature vs. heat added should provide an accurate shape factor. The increments of the interrupt,ed run were all increased by 0.22% t,o bring them into conformity with the more accurately known total heat although the effect of doing this was trivial in determining the heat used for t,he eutectic. The int,egral heats added, including the 0.22Oj, adjustment, vs. temperature during the detailed heat of fusion are given in Table 111. TABLEI11 HEATADDED& h v s f CpdT FOR 1 "MOLE" OF NaOH.0.97776H20, CAL. MOLE-' T,OK. E - SCpdT T , "K. E fCpdT 336.202 445.7 327.84 4.3 330,73 6.4 337.025 586.5 333.319 17.5 337.447 730,6 334.873 58.5 3317.869 1107.9 335.339 130.4 338,077 1881.4 335.517 210.3 338.255" 3416.0 292.5 XaOH.H20 melting 335.604 complet,e Eut. melt.ing complete (338.26) 3708.9 (335.64) ( 390) 338.25 True m.p. 335.78 True m.p. See discussion in text. a Temperature too high.
-
Figure 2 shows the break in the curve a t 390 cal. mole-l of NaOH present, as the heat required to melt the eutect8ic. Figure 2 a t (a) shows a plot of temperature us. the reciprocal of the fraction of the eutectic melted and this is extrapolated to the eutec-
~
THERMODYNAMIC PROPERTIES OF SODIUM HYDROXIDE AND ITS MONOHYDRATE 2055
Oct., 1962
tic melting point, 335.78"1 0. It may be noticed that the upper temperature limit of eutectic melting occurs 0.14" lower than the true melting point due to impurity. Impurity such as carbonate would be soluble and relatively concentrated in the small amount of liquid resulting from eutectic melting. This may be shown to correspond to a total impurity of 0.023 mole yoin the sample. A similar treatment of the sample of NaOH. 0.04014H:O gave 120 cal. for the amount of heat associated with 1 mole of NaQH. The melting temperature was found to be 336.1 OK., which agrees approximately with the more accurate value 335.78" E
K.
Three sets of measurements were made on the eutectic melting accompanying the heat capacity measurements of the XaOH.0.04014HzO. All of the series mere broken into paxtial runs but the third run was specifically designed to give detailed information concerning the shape of the temperature vs. fraction melted curve in the upper portions which are useful in the T us. l/f plot. The second run was designed to give the most accurate value of the total energy through the whole region. The first run terminated with a broken vacuum line before melting was complete but was useful in showing energy agreement over the region covered. The useful information is presented in brief form in Table IV which as in Table I11 shows the detailed run corrected to exact agreement with the more accurately measured total energy. The data on the eutectic melting during measurements on the NaOH-0.0401H20 are considerably less accurate than those on the monohydrate, partly because the heat of fusion per mole of KaOH present is only about 1/3 of the former and both values are the excess over f C,dT. Also, the vacuum was poor and variable during these measurements in the range above 300°K. The later work on NaOH. HzO had improved conditions. However, all of the three series of excess heat absorption agreed to within 5%. TABLE IV HEAT ADDED Mrnus f C,dT FOR 1 "MOLE" NaOH.0 04014 HzO, cal. mole"' T,OK.
E
Series 2 317 86 320.92 323.99 327 01 329.88 332.25 334.58 335.40 336.50
- .f CpdT
T," K .
0 0
332.865
3.2 4 9 6 5 8 9 22.2 37.3 82 5 120
334 97 335 188 335.343 335 457 335.569 336.131
E
OF
- SCpdT
Series 3 2 6 . 0 from Series 2 55.65 69.3 84.1 99 7 114 5 120
According to phase relationships, such as those indicated on the diagram given by Standiford and BadgerLo showing NaOH.0.5H20 as an existing phase, an over-all composition of NaOH-0.04014HzO should lead to a peritectic at about 370°K. (10) F. C. Rtzndiford and W. L. Badger,
(1934)
Ind. Eng. Chem., 46, 2400
between NaOH and NaOH*0.5H~O and no eutectic. The fact that heat absorption occurred below 336* K. could mean that a portion of a hydrate such as h'aOH.0.5H20 failed to crystallize in the present experiments on Na0H~0.04014€1~0, although we consider that there never have been experimental data good enough to provide a reasonable basis for assuming the existence of a solid with a composition a t or near NaOH.0.5Hz0. The sample was cycled through the region of heat absorption several times without changing the heat requirement appreciably. We concluded that no peritectic reaction such as that indicated by Standiford snd Badger occurred during the cycling, especially considering the opportunity for a reaction between the small amount of monohydrate surrounded by such a large excess of anhydrous NaOH. We hesitate to make an alternative assumption that the temperature 336.1"K. corresponds to the peritectic temperature of NaOH and a compound such as NaOH.0.5Hz0, for which there is no evidence, and it seems necessary to assume that the two heat absorptions apply to the melting of the same eutectic a t 335.78"K. If the compositions of the two primary eutectic phases were known, the two eutectic heats, together with the over-all compositions of the ?SaOH. 0.97776H20 and IfaOH~0.04014H~0, will give both the molal heat of fusion of the eutectic and its composition. When this calculation was made assuming pure NaOH and SaOH.HzO as the phases, the eutectic compositioii derived was 72.3 wt. yoNaOH. However, Rrodale and Giauque" found thc cutectic compositioii to be 73.1%. In order to obtain the correct value of the eutectic composition it would be necessary l,o increase the 120 cal. "eutectic melting heat" to 157 cal. mole-l of KaOH present. There are a t least two rather obvious ways of explaining this discrepancy. A. When the molten sample of NaOH.0.04014H20, a t 350°, was poured into the gold calorimeter, it was essentially quenched and the dissolved water may well have been dispersed in microscopic phase regions, possibly with a considerable size distribution, ranging to macroscopic. It is difficult to predict the effect of this on the eutectic heat of fusion, melting temperature range, and composition. Assuming KaOH as an essentially pure phase, solidification of the eutectic would mean adding NaOH to themacroscopic enclosing solid, leaving microscopic NaOH HeO. We would expect that both the microscopic melt and the microscopic NaOH. H20 would be subjected to large negative pressures as the bulk material cooled and that the solid monohydrate would have the much larger negative pressure. Thus the free energy of the NaOH-H20would be reduced much more than its partial molal free energy in the microscopic melt and the melting point would be raised. Also, some of the microscopic melt inclusions may have failed to crystallize, thus reducing the measured heat of fusion. The plot of T us. l/f, which yields T = 336.1"K. by extrapolation rather than 335.78"K., as obtained from the monohydrate, would lose much of
-
(11) G. E. Rrodale a,nd W. F. Giauque, J . Phys. Chem., 66, 2051 (1962).
2056
L. E. MURCIIAKD W. F. GTATTQV~
its meaning since its slope would be a function of the effect of particle size on melting temperatures over the size distribution. There is a t least some reason to suspect the slope of the T us. S / f curve of NaOH.0.04014H20 which appears to be about 40% greater than would be expected from the impurity as otherwise estimated. It is difficult to see how the production of microscopic phase deposition could have been avoided. It is somewhat analogous to the well known mechanism used in "precipitation hardening" of alloys. It, would explain the observed average melting temperature around 336.1"K. us. the 335.78"K. value from the waterrich sample. Xot only do we have confidence in the thermometry, but Brodale and Giauquell checked the lower value a t 335.76OK. The temperature discrepancy is far beyond the limit of error and leads us to prefer the above explanation rather than the one which follows. B. It is, however, also possible, as a limiting case, that the solid eutectic phases are a dilute equilibrium solid solution of KaOH.HZ0 in NaOH and pure NaOH.HaO. It is, of course, possible that a combination of (A) and (B) have complicated the measurements. The data have been analyzed on assumption (B) and this is important, because if a solid solution of KaOH.H20 in KaOH is present in the eutectic of the well behaved low melting NaOH.0.97776HzO,the effect should be considered. Fortunately, it is possible to show that the molal heats of fusion of the eutectic and XaOH.HzO, as derived from the results on KaOH .0.97776H20, are independent of the amount of water which may possibly be present in the KaOH phase as a solid solution. The analysis is as follows; the two phases are S a O H . H 2 0 and solid solution XaOH.AHzO. NaOH+0.04014Ha0will contain 0.95986/(1 - A ) moles KaOH.AH20 aiid (0.04014 - A ) / ( l - A ) moles NaOH.HzO and this phase controls the amount of related eutectic. NaOH .0.97776H20 will contain (0.97776 - &4)/(1- -4)moles XaOH. H,O and 0.02224/(1 - A ) moles NaOH.AH20 and this phase controls the amount of related eutectic. Considering the over-all eutectic composition, let the molal ratio H20/XaOII = B. The eutectic wt. % of KaOH = 73.1%.
B
=
0.817
The ratio moles NaOH .HzO/moles KaOH,AHzO = ( B - A)/(l - B ) in the eutectic. Combining the above equations it is found that XaOH.0.04014H20 has (0.04014 - il) moles eutectic (B - A ) and NaOH.0.97776H20 has 0.02221 ____ -(1 - B )
0.1216 moles eutcctic
It may be noted that the number of moles of eutectic in the water-rich sample is independent
Vol, 66
of A . The eutectic heat of fusion is 390/0.1216 = 3207 100 cal. mole-l aiid 120/3207 = (0.04014 A)/@ A ) from which A is found to be 0.010 and the solid solution SaOH.0 .O1OHzO, a t the eutectic melting point, 335.78OK. Using the above compositions it is found that the amount of monohydrate to be melted after the conclusion of the eutectic melting is 1- 0.1216 = 0.8784 mole. The melting heat added after the completion of eutectic fusion was 3317 cal. mole-' of SaOH present in the saniple, and the heat of fusion of NaOH.HaO = 3317/0.8784 = 3776 i 30 cal. mole-l, and this result is independent of A , since the analytical result B contains the information. The consequences of correcting the heat capacity measurements for NaOH. HzO in possible microscopic states or in solid solution in NaOH requires comment. In the case of the derived data for pure NaOH.HzO, based on a sample NaOH. 0.97776H20, the effect should be negligible. There is such a small proportion of the nearly pure S a O H phase present that a considerable error in its heat capacity would be necessary to produce an effect. There is of course no expectation of microscopic phases in the NaOH.0.97776H~Osample. The possibility of error in deriving the heat capacity of pure NaOH is greater but should be quite small, not only because the amount of NaOH.H,O in the XaOH is small, but because in general the heat capacity of microscopic phases is not greatly different from that of the macroscopic material. The principal interfacial surface tension effect is on the heat content and the increase a t the absolute zero is comparable with that a t ordinary temperatures, thus requiring only a minor heat capacity effect. It is believed that little crror will be made by assuming that all SaOH.HzO in the S a O H .0.04014H20 sample may be considered to have the same heat capacity as pure NaOH.HzO and this has been done. A curve of T us. l/fraction of NaOH.HrO melted is shown a t (b) in Fig. 2 . The fraction of monohydrate melted a t any point included the portion melted as part of the eutectic. This particular plot is not as appropriate as that for the eutectic melting temperature since the lowering in this case is essentially all due to SaOH, which may be regarded as a dissociation component of the compound. I n such a case the melting temperature curve must be flat at the compound composition and linear extrapolation of the T 2's. 1,'scurve betmeen 1.0 and 0 is not valid. For this reason the 1If us. T curve was given zero slope as it approached the T axis. The melting point was found to be 338.25 0.03OK. The melting of an off composition substance such as that considered here presents some difficulty in its final stages as follows: as the melting proceeds, the heavier residual solid will sink to the bottom and final melting will produce a liquid somewhat closer to the composition of pure SaOH. HzOnear the melting surface than that in the upper portion of the calorimeter. h close examination of the temperature data near the final meltirlg temperature indicated that the small amount 01
*
-
THERMODYNAMIC PROPERTIES O F SODIUM HYDROXIDE
Oct., 1962
residual solid had brought the calorimeter temperature to the true melting point. The Heats of Solution of NaOH and NaOH.H,O. -Since the idea that a solid phase of composition at or near NaOH.0.5H20 got its start from the early heat of solution work of de Forcrand,&it was decided to repeat his experiment. Five solid samples of various proportions of NaOH and H20 in the range of 0-1 H20/NaOH were investigated. The measurements were carried out in a calorimeter similar to that described by Kunzler and Giauque.12 The various compositions were prcpared in a manner similar to that used for the heat capacity determinakions. The samples were sealed in glass cylinders with thin glass cover plates cemented with Apiezon wax on the bottom end and paraffin on the top end. The cover plates were broken under water by lowering a glass plunger to start the solution process. The weights were corrected for buoyancy. The results are given in Table V. Corrections from the final concentration to infinite dilution were made by means of the data in Circular 500 of the Xational Bureau of Standards.13 TABLE V HEATSOF SOLLTIOS OF SOLID SAMPLES OF OYER-ALL COMPOSITIOS KaOH.XH,O IN THE RANGE 0-1H20 Xole ratio HzO/ NaOH final soln.
2057
BND ITS h!!ONOHYDRATE
- -i; e
$11
0 DE FORCRAND
v
0 THIS WORK
“ I
I
’d9
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 Moles HzO/moles NaOH.
0.8
0.9
1.0
Figure 3.
an experiment can give information 011 the composition of a solid phase. His X-ray data are inconclusive. Extrapolation of the straight line in Fig. 3 gives NaOH
=
XaOH(infinite diln.)AH298.1SoK = -10,653
f
10 ea]. mole-’
KaOH.H20 = NaOH(infinite diln.) AH298.160~ = -5134 -f 10 cal. mole-’
From the comments made previously concerning the possibility of a dilute solid solution of NaOH. AHzP, HzO in XaOH as an equilibrium solid phase, one NaOH wt. cal. must consider the possibility that the solids in sample sample mole-’ the heat of solution experiments contained phases 15 9634 181 -5147 -137 -5284 0 9i447 such as KaO€I:.H20 and a dilute solid solution 14 6635 79230 185 -6138 -137 -6275 such as Na011~0.010H20. This would not in14 4166 51715 171 -7552 -137 -7789 validate the conclusion with ressect to the absence 11 8207 26192 191 -9077 -137 -9214 of evidence for an iatermediateAcompoundsuch as 11 4267 11810 184 -137 -10,008 -9871 NaOH ,0.5Hz0. However, with respect to the extrapolated value The heat of solution data are plotted in Fig. 3, for the heat of solution of pure KaOH, the existwhere they are compared with the measurements of de F ~ r c r a n d . ~ The present results show that ence of a dilute solid solution would mean the asthe heat of solution is accurately linear when sumption of Raoult’s law over a range within 1 plotted vs. moles HzO/mole XaOH. This gives mole % of the pure substance, which should lead no support to the suggestion that there is an inter- to little error. The effect of possible microscopic phase regions mediate rompound between XaOH and NaOH . is more difficult to visualize. The most concenH20. and 0 this seems The data of de Forcrand are scattered about the trated sample was S a O H ~ 0 . 1 1 8 1 H ~ less likely to have produced microcrystals in a straight line through the present results and we 0.8819 consider that any inference that an intermediate mixture of 0.1181 mole NaOH.H20 hydrate was present during his experiments, such mole of KaOH. In any case, no deviation from as XaOH.2/3H20 nhich he suggested, is not justi- linearity in the heats of solution was observed a t this point. fied. Thermodynamic Properties of NaOH and NaOH. It also should be mentioned that Mauret,j who suggested KaOH.0.5H20, did so on the basis HzO.--T’alues of C, a t eveii values of the temperaof loss in weight during the evaporation of solu- ture were read from smooth curves through the tions over the range 100 to 160’ until a change in data for NaOH.0.04014H20 and NaOH .0.97776slope in the amount PS. time curve appeared. Wc H,O. The values for the pure phases were then prefer to interpret his experimental observation of obtained by calculation. Tables of the heat capacity C,O, the entropy a graduallg changing rate as corresponding to the So, - (8’0 - H $ ) / T , and (HO - HoO)/Twereprepared appearance of solid XaOH. At these temperatures the saturated liquid has approximately the coin- by the usual methods. F and H refer to free energy position KaOH.0.5Hz0. We do not see how such and heat content, respectively. The values are given in Tables VI and VII. The (12) J . E. Kunalei and W. r Giauque, .I. A m . Chem. Soc., 74, table for XaOH was extended to 1000’K. by com3472 (1952). bination with the data of Douglas and Dever.’ (13) “Selected Values of CheinicaI Thoimodynamio Pioperties,” The low temperature heat capacity data were Series I, Natl. Bur. Std. (U.Sa),Ciio, 500, Table 92-3, Fob. 1, 1952. 31ole ratio IIzO/
Corr. to infinite diln., cal. mole-’
AHzsO t o infinite diln., oal. mole-’
+
2058
L. E. MURCH AND W. F. GIAUQUE
joined smoothly with the values derived from the heat content differences of Douglas and Dever a t higher temperatures. A recalculation of the heat content differences in terms of the data in Table VI gives values 0.3% high a t 100’ and 0.1% low a t 200°, and these amounts are well within the limit of accuracy at these temperatures. TABLE VI THERMODYNAMIC PROPERTIES OF NaOH Units are gbs. mole-1
- Hoe)/
-(Fa
T,OK. 15 20 25
30 35 40 45 50 55 GO 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 323.15 330 335.78 338.25 340 350 375 400 4 25 450 475 500 525 550 566.0( a)
CPO
0.088 .198 .364 .597 .895 1.263 I.671 2.098 2.545 3.016 3.967 4.877 5.832 6.631 7.384 8.185 8.717 9.292 9.810 10.294 10.737 11.140 11.510 11.850 12.172 12.468 12.737 12.996 13.238 13.472 13.694 13.759 13.900 14.086 14.228 14.260 14.413 14.561 14.606 14.700 14.776 14.807 14.830 14.945 15.220 15.520 15.936 16.481 17.178 17.963 18.806 19.711 20.303
SO
0.020 .059 .I19 .205 .319 ,462 .634 ,832 1,052 1.294 1.830 2.422 3.056 3.712 4,380 5.053 5.726 6.393 7,052 7.701 8.339 8.964 9.577 10.176 10.762 11.335 11.895 12.443 12.979 13,503 14,016 14.174 14.517 15.008 15.400 15.489 15.959 16,419 16,562 16.869 17.125 17,233 17.310 17.741 18.782 19.773 20.726 21.652 22.561 23.462 24.358 25.254 25.827
T 0.007 .015 .029 .051
.os1 ,119 .166 .223 ,288 .362 .532 .731
.954 1.197 1.456 1.727 2.009 2.298 2.594 2.893 3.194 3.497 3,801 4 1.05 4.408 4.710 5.010 5.309 5. 605 5.899 6.190 6.281 6.478 6.764 6 995 7.047 7.327 7 . 604 7.691 7.878 8.035 8.102 8.149 8.417 9.073 9.711 10.332 10.935 11.523 12.097 12.660 13.212 13.560 I
(Ha
- HoO)/
T 0,013 .044 ,090 .154 .238 .343 .467 .609 .764 .932 1.298 1.691 2.102 2.515 2.924 3.325 3.716 4.094 4.459 4.809 5.145 5.467 5.775 6.071 6,354 6.625 6.885 7.134 7.374 7 . GO4 7.826 7.893 8.039 8.244 8.405 8.442 8.632 8.815 8.871 8.992 9.090 9 131 9.161 9.324 9.709 10.062 10.394 10.717 11.038 11.365 11.698 12 042 12.267
566 ~ ( p ) (20.56) 5iti.O (20.56) 592,3(p) (20.56) 20.58 592.3(1) 20.57 600 20.50 650 700 20.43 750 20.36 800 20.29 850 20.22 900 20.15 950 20.08 1000 20.01
Vol. 66 28.51 28.84 29.45 32.01 32.28 33.92 35.44 36.84 38.16 39.38 40.54 41.62 42.65
13.56 13.80 14.25 14.25 14.48 15.91 17.25 18.51 19. i o 20 82 21.89 22.89 23.85 I
14.951 15.038 15,200 17.765 17.801 18.012 18.186 18.333 18.458 18.564 18.654 18.731 18.796
TABLE VI1 THERMODYNAMIC PROPERTIES OF NaOH.H20 Units are gbs. mole-’ -(P
T,OK. 15 20 25 30 35 40 45 50 55 60
70 80 90
1.00 110 120 130 140 150 I60 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 323.15 330 335.78 338.25(S)
QPO
SO
0.190 .484 .go9 1.468 2.098 2.771 3.470 4.166 4.856 5.543 6.846 8.060 9.170 10.157 11.054 11.898 12.677 13.403 14.078 14.708 15.306 15.884 16.438 16.968 17.47’3 17.982 18.477 18.958 19.440 19 898 20.341 20.480 20.783 21.210 21.544 21.620 22.018 22.402 22.521 22.775 22.986 23.074
0.057 .I49 .301 .514 ,787 1.112 1.479 1.881 2.310 2.762 3.717 4.711 5.726 6.744 7.754 8.753 9.737 10.703 11.651 12,580 13.490 14.381 15.255 16.111 16.952 17.777 18.587 19.383 20,167 20.939 21.698 21.934 22,446 23 183 23,775 23.909 24.624 25.329 25.548 26.024 26.421 26.590
I
- HOO)/
T 0 014 035 072 .127 ,201 294 ,405 .532 .674 829 1 173 1 553 1 060 2 387 2 820 3 282 3 740 4 203 4 668 5 134 5 599 6 OF2 (i 523 6 981 7 436 7 887 8 335 8 779 9 218 9 655 10 087 10 222 10 515 10 939 11 281 I1 359 11 775 12 188 12 317 12 597 72 832 12 931
-
(Ho HoQ)/T
0.043 ,114 ,229
.387 .586 ,818 1,074 1.349 1.636 1.933 2,544 3.158 3.766 4.357 4.925 5.471 5.997 6,500 6 ,983 7.446 7,891 8.319 8,732 !3,130 I).516 9,890 10.252 10.604 10,949 11.284 11.611 11.712 11,931 12.244 12.493 12.550 12.849 13.141 13.231 13.427 13.589 13,659
The Dissociation Pressure of Water over the System NaOH.H20-NaOH from the Third Law of Thermodynamics.-The above data, combined with available data on water, enable the calculation
OCt., 1962
EXPERIXENTAL I S V E S T I G A T I O ~ SOF
LIGHTSCATTERISG OF
of the dissociation pressure of sodium hydroxide monohydrate as a function of temperature.14 H20(g), 8298.15OK
=
45.106 gbs. mole-’ =
7.941 gbs. mole-’
29C.15OK
XaOH.H20 = NaOH
+ H20(1) Aff’2g8.16
H20(1) = ElzO(g)
==
5519 cal. mole-’
AHo2g8.15 = 10,520 cal. mole-’
COLLOIDAL SPHERES
2059
VI11 together with values calculated by means of the present data and the third law of thermodynamics. TABLEVIII CALIX-LATED ASD OBSERVED VALUESOF THE DISSOCIATION PRESSURE OF WATEROVER NaOH.H?O-NaOH, MM. T,Ox. Pcslod Pobsd B. 4- S.(ctctual o b d 273 15 0 012 0 04 (0 05, 0 03, 0.03) 208 15 0 14 0 15 (0 16, 0 15, 0 15) 323 15 1 14 1 15 (1.13, 1.15, 1.16) 335 78
1.93
Eutectic
+
Pl’aOH.H20 = NaOII H20(g) AN0298.16 = 16,039 cal. nzole-’
The excellent agreement, particularly a t 323.15’K., where observational accuracy is greatest, indicates that NaOH and NaOH.H20 approach Using data from Tables V and VI zero entropy a t limiting low temperatures. The lack at 273.15’K. is not surprising in AHOo= 14,890 cal. mole-‘ viewofof agreement the low pressure and presumably the slower AXo298.~5 = 36.731 gbs. mole--I equilibrium rate. We regard fortuitous cancellation of equal amounts of zero point entropy as highly improbable in such a case. AF293.16oK == 5088 cal. mole-l == The agreement also indicates that the “lowest” -RT 111 P H 2 0 (atm.) hydrate in the experiment of Baxter and StarkP H ~=O1.86 X 10-4atm. = 0.14mm.at298.15’1~. weather was KaOH.HzO. They passed moist air over pea-sized pieces of NaOH in a tube 70 Baxter and Starkweatherlfi made careful de- cm. long and 1.5 cm. in diam. and the extensive terminations of the vapor pressure of water over surface should have provided considerable opsodium hydroxide and its “lowest hydrate” a t portunity for the formation of any stable inter0, 25, and (50’. Their results are given in Table mediate hydrate such as NaO€I.0.5Ha0. (14) “Selected Values of Chemical Thermodynamic Properties,” Acknowledgment.-We thank G. V. Calder for Series 111; Natl. Bur. Std., March 31, 1947; June 30, 1948. assistance with the experimental measurements (15) P. Baxter and €1.W. Starkueatiiei, ,J. Am. Chem. Soc., 38,2030 and G. E. Brodale for assisting with the calculations. (19 16).
EXPERIMENThL INVESTIGATIONS ON THE LIGHT SCATTERING OF COLLOIDAL SPHERES. IV. SCATTERING RATIO’ BY TVr~sizrsuHELLEX, AUD ~XICHARD TABIBIAX~ Gheniistry Department, W a y n e Slate University, Detroit, Michigccn Received August 88. 1961
Light scattering of 18 monodisperse polystyrene and polyvinyltoluene latices was investigated a t an angle of 90’ with respect to an incident linearly polarized beam whose electric vector was, in succession, parallel and perpendicular to the plane of observation. The ratio of the two quantities obtained, designated as “scattering ratio,” u-which is closely related t o depolarization and polarization ratio-was found to be a very useful quantity for absolute particle size determinations exce t for particle diameters < I / * U, (on use of vioible light), a particular advantage being the relative insensitivity to changes in t i e solid angle of the scattered beam. Partial investigation of the spectra of u eliminated the problem of multivaluedness of results inherent, in any measurement of lateral light scattering. The concefitration de endence of u was investigated in detail. The particle diameters obtained from u, evaluated on the basis of theoretical dPta derived from the Mie theory, agreed very satisfactorily with electron microscopic results (range covered, 135 to 824 inp).
I. Introduction Size determinations on colloidal spheres from the total scattering a t 90” with respect to the direction of the primary beam give results which are in satisfactory agreement with electron microscopic d a h 3 ( 1 ) This work was supported by the Office of Naval Research. A preliminary account of this work was given a t the 134th NationalMeeting of the American Chemical Society, Chicago, Illinois, September, 1958. (2) E. 1. du Pont de Nemours &- Co., Elastomer Chemicals Department, Wilmington, Delaware. (3) R. Tabibian and 11’. Heller, J . Colloid Sci., 13,6 (1958).
if the &lie theory is used. This method requires an instrument constant in order t o translate the experimental data into absolute light scattering data. The principal objective of the present investigation is to outline a new modification of 90” measurements, related to depolarization measurements, which yields an absolute method of particle size determination. It consists of measuring the ratio of the total intensities of light scattered a t 90” from an incident monochromatic linearly polarized beam whose electric vector vibrates first
