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where K is a distribution coefficient such that KC#zO = C A =~ moles alcohol in micelles per liter of solution, C:Hpo, moles alcohol in water per liter of solution, and C'd is the CMC in moles detergent per liter of solution. I n the range where the CMC lowering is approximately linear with %A, C'd is 1 1 (AFO + AF~") - 5 linear with KC,"' as is observed experimentally. - ln,fnx,, - - In n - Infizl = When the aqueous phase is saturated with alcohol n n kT kT a CMC, the data of Schick and Fowkes13 can The results in Table VI1 were obtained with aggre- bet the used to estimate the CMC to be roughly 0.4 gat,ion number n = 80 ( 2 5 O ) , f1 = f n = 1, AFOjkT times the CMC of pure detergent. This gives rise = -12.21, and AFm/kT = -In (1 - ZA), where to a distribution coefficient of about 1.8at the CMC ZA is the molecule fraction of alcohol in a micelle, (as defined), taking the solubility of dodecanol in x1 the mole fraction of free detergent, and z ~ the , water as 0.9 X moIe/liter. If the logarithmic mole fraction of micellized detergent. The critical relation between x1 and X A is used directly the exconcentration is defined such that XI = 0.98xT perimentally observed linearity of CMC and alcowhere XT is the mole fraction of total detergent. The hol concentration is not predicted except by linear reduction in critical micelle concentration with in- approximation of (1 - XA)3.56. A similar result was creasing 2.4 is shown in Fig. 7. This relation is obtained by ShinodaZ2using the less exact treatment roughly linear to a CMC lowering of about 60%. of the electrical contribution to the micellar free The data are represented over a greater range by energy as indicated by Hobbs.2a log 21 = log XIo 3.55 log (1 - 2.4). This procedure for obtaining F,1 is admittedly approximate insofar as the model for decreasing TABLE VI1 the change density may be an oversimplification. ELECTRICAL A N D ENTROPY CONTRIBUTIONS TO THE FRFE ENERGY OF MIXEDMICELLES OF SODIUM DODECYL SULFATE However, the calculations clearly indicate that the mole fraction of alcohol in the micelle is considerA N D DODECANOL AT CONSTANT AGGREGATION ably smaller than that in the mixed monolayer, as CMC, mole fraction, x 0 x 104 is found experimentally. To a large extent, this *Frn = Mole fraction difference is duo to the fact that the additive reduces aloohol in -_ AFT* kT micelle, X A Fel/kT" kT A F ~= 0 In(1 - X A ) the free energy of micelle formation much more by 3.44 0 1.55 1.55 0 decreasing the electrical work than by increasing 3.43 0.0127 1.54 1.52 0.0125 the entropy of mixing in the micelle (see Table VII). micelle diameter and aggregation number; this process can be imagined to occur by simple replacement of a lauryl sulfate ion with a lauryl alcohol molecule; a further decrease in free energy of mixing AFmof the detergentz2is included. The equation of Overbeek and Stigter then becomes
+
I
.0625 .I25 .3125 .50 -75 a Corrected 21).
3.28 .0644 1.32 1.23 3 . Io .1334 1.10 0.96 2.48 .3742 0.58 .40 1.72 ,6914 .27 0.40 1.3848 .07 ,017 for smooth charge distribution (see reference
The relation between the mole fraction alcohol in the micelles and the alcohol concentration in the mater is given by
After this paper was submitted for publication, B pertinent article by A. Wilson, M. B. Epstein and J. Ross appeared in J. ColZoid Sci., 12, 345-355 (1957). Using solutions of sodium dodecyl sulfate containing 2.5% of dodecano1 a t 25-28", they measured x1 to be 0.49-0.57. We calculate yIo = 39.5 dynes/cm. and from reference ( I ) y' = 32.5 dynes/cm. in 1 second, 29.0 dynes/cm. in 5 minutes. Using equation (Z), we find xlql = 0.54 and 0.40, respectively.
Acknowledgment.-The authors wish to express their appreciation to Miss Helen L. Robbins, Miss June R. Hughes and Mr. S. J. Rehfeld for assistance %t,h measurements and calculations. (23) M. E. Hobbs, ibid., 65, 675 (1951).
(22) I(.Shinoda, THIXJ o w n ~ a 68, ~ , 1136 (1986).
A NEW HYDRATE OF SODIUM CHROMATE BY HANSJ. BORCHARDT Contiibz~tionfrom the General Engineering Laboratory, General Electric Company, Schenectady, New York Received July 16, 1967
The dehydration of NazCr04.4H~Owas studied with differential thermal analysis, thermogravimetry and X-ray analysis. Evidence for the existence of a thermodynamically stable intermediate hydrate having the composition Na2Cr0~.1.5Hz0is presented. Its position in the phase diagram of the Na2CrO4-hydrate system is discussed.
Introduction Inorganic hydrates were investigated intensely at the turn of the century. Studies of the Na2Cr04-hydrate system led t o the finding that hydrates with ten, six and four moles of water per mole of NazCr04 occur. A dihydrate was reported by Wyrouboff ,I but the existence of this compound
was disputed by Traube2 and R e t g e r ~ . ~At present, no text or reference work recognizes the existence of a NazCr04-hydrate with less than four moles of water. (1) E. N. Wyrooboff, Bull. 80c. franc. miner., 18, 50 (1879). (2) H. Traube, 2.Krist., 22, 138 (1894). (3) J. W. Retgers, Z . phyaik. Chem., 8 , 47 (1891),
'
Feb., 1958
A NEWHYDRATE OF SODIUM CHROMATE
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I n the present study, an extra peak is observed in the DTA pattern of NazCr04.4HzO. This suggests the existence of an intermediate hydrate. Confirmation is obtained with heating curves. Thermogravimetric measurements establish the composition as NazCr04.1.5H20 (sesquihydrate) and an X-ray powder pattern serves to characterize the compound. NazCr04.1.5Hz0 is not stable a t room temperature but has a limited stability range a t elevated temperatures and vapor pressures. Experimental DTA.-The DTA apparatus is a commercially available unit manufactured by the Robert L. Stone Company, Austin, Texas. The sample is prepared by grinding C.P. NazCrO4.4Hz0 to 100-200 mesh and mixing i t with an equal weight of calcined alumina. Alumina also serves as reference material. The samples are heated in an air atmosphere. Temperature is raised a t a rate of approximately 12"/min. Thermogravimetry.-A Chevenard recording thermobalance is used to measure the weight of NazCrO4.4HzO as it is being heated. Powdered NazCr04.4HzO contained in a small crucible is mounted on the quartz rod of the balance. Air saturated with water vapor a t approximately 25" is passed over the material. The temperature is raised a t a rate of 150"/hour. A weight loss curve is also obtained by raising the temperature to 75" and maintaining constant temperature thereafter. Heating Curve.-A slurry of NazCrOa.4Hz0 in contact with saturated solution is heated and its temperature measured as a function of time. The rate of temperature rise varies from 2"/min. initially to 0.5"/min. at elevated temperatures. The temperature is measured with a National Bureau of Standards calibrated thermometer, appropriate corrections being made for the emergent stem. X-Ray Analysis .-X-Ray experiments were performed at room temperature with samples quenched in liquid nitrogen from elevated temperatures. Samples of NazCrOa. 1.5Hz0 are prepared by mixing NazCr0~4HzOwith anhydrous NazCrO4 in the mole ratio of 0.6 to 1 to give an average composition of NazCrO4.l.5Hz0. This mixture is sealed in a vial and maintained at 70" for one hour after which the vial R i quenched to liquid nitrogen temperature. The sample is removed, mounted on a slide with Lubriseal grease and exposed to the X-ray beam on a General Electric model XRD-3D X-ray diffractometer. Copper X-radiation filtJeredwith nickel was used.
Results and Discussion Evidence for NazCrO4.1.5H20.-The DTA pnttern of NazCr04.4Hz0 is shown in Fig. 1. If no intermediate hydrate existed, one would expect two peaks on the DTA pattern, one for the dissociation of NazCr04.4Hz0 to anhydrous salt and saturated solution4 and the second due to water boiling from saturated solution. Instead, three peaks are observed, suggesting that the dissociation of tetrahydrate occurs in two stages; ie., the first two peaks result from the successive dissociation to intermediate hydrate and anhydrous salt and the third is due to water boiling from the saturated solution that is formed accompanying the dissociation. I n order to determine if an intermediate hydrate exists which is stable at room temperature, partially dehydrated N a ~ C r 0 ~ . 4 H was ~ 0subject to Xray analysis. No evidence for a substance other than tetrahydrate and anhydrous salt was found. This indicates that if the intermediate hydrate is a thermodynamically stable phase, vapor pressure(4) NanCrOr4HnO heated in a test-tube is observed t o dissolve partially in its own water of hydration when heated above the dissociation temperatlire. The appearance of extra peaks in the DTA patterns of hydrates due to the formation of saturated solution is discuflsed in detail by H. J. Borchardt and F. Daniels, THISJOURNAL, 61, 917 (1967).
I
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e3
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TEMPERATURE -"C.
Fig. 1.-Differential
thermal analysis pattern of NazCrOd. 4Hz0.
200
150
a
g
m
E 100
50
0
30 40 50 60 70 80 90 Temperature, "C. Fig. 2.-Vapor pressure-temperature relations of the NazCO4-hydrate system. The numbers 4,1.5 and 0 indicate, respectively, the stability regions of tetrahydrate, sesquihydrate and anhydrous salt. 0
10
20
temperature relations such as shown in Fig. 2 should exist. Here, the vapor pressure curve, Na&r04.4HzO(s) -t Na2CrOd(s) 4H20(g) is seen to end a t a quadruple point A (which must be above room temperature) where the four phases NazCrO4-4Hz0,intermediate hydrate (1.5), anhydrous Na2Cr04 and water vapor are in equilibrium. Along the curve A-B, the tetrahydrate is in equilibrium with (dissociates into) the intermediate hydrate and water vapor. This vapor pressure curve intersects the vapor pressure curve of saturated solution a t another quadruple point B. The vapor pressure curve of the intermediate hy-
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30
40 45 50 55 60 65 70 Time, minutes. curve of Na2CrOI.4H20 in contact with saturated solution.
35
Fig. 3.-Heating
m
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300 150 200 250 100 50 Temperature, "C. Fig. 4.-Thermogram of Na2Cr04.4H20.
drate -t anhydrous salt intersects the vapor pressure curve of saturated solution at point D. If the relationships indicated in Fig. 2 were correct, one would expect a heating curve of NazCrO4. 4H20 in contact with saturated solution to exhibit two breaks, one a t point B and another at point D. Figure 3 shows such a heating curve where breaks are observed at 64.0 and 75.4", presumably corresponding to the process
+ sat. s o h . + intermediate hydrate + sat. soln. Intermediate hydrate + sat. soln. + anhydrous NazCrOn + sat. soln.
Na~Cr04.4H20
(1) (2)
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I n order to determine the composition of the intermediate hydrate, NazCrO4.4HZ0was heated in an air stream saturated with water vapor at 25". The weight was measured as a function of temperature on a thermobalance. The resulting curve is shown in Fig. 4. The indicated temperature is that of the furnace. The sample temperature is lower. An arrest in the weight loss curve is observed when 2.48 moles of water are lost per mole of Na2Cr04; viz., final weight loss corresponds to loss of four moles of HzO, hence an arrest a t of total weight loss corresponds to loss of 2.5 mole HzO. This establishes the composition of the intermediate hydrate as Na2Cr04.1.5H20 within experimental error. Since the saturation pressure of water at 25" is 23.7 mm., point A is probably located below this pressure. A weight loss curve showing a break after 2.5 moles of water are lost is also obtained by raising the sample temperature to 75' and maintaining constant temperature thereafter. The thermobalance experiments do not show good reproducibility. This is a consequence of the very rapid dissociation of the hydrate which results in variable, usually high local partial pressures of water in the immediate vicinity of the sample (see footnote 4). Thus, the vapor pressure of water in the gas stream may bear little relationship to the vapor pressure a t the sample. This difficulty may be minimized by using small samples (
