Aug. 5 , 1957
HEATSOF FORMATION OF POTASSIUM CHROMATE
deep, closed a t top and bottom with Tdon-gasketed gel-F plates for visibility. The top window was removable. Connections to a reflux condenser of coiled polyethylene tubing, to drainage and to an inlet for liquid H F were provided through magnesium fittings in the walls. These were protected from atmospheric moisture with anhydrous CaSQ and could be closed by means of magnesium bodied stopcocks with Teflon plugs held in place by spring tension. The drainage outlet was used for obtaining samples of supernate. The H F (General Chemical Company, sulfur-free) was led through a copper coil condenser to a cooled calibrated magnesium reservoir with a Kel-F window from which measured quantities of H F could be delivered to the cell. The cell itself was provided with a cooling coil which maintained the temperature close t o -10". Thorough mixing of the solutions was ensured by use of a magnetic stirrer. The internal magnet was sealed in a polyethylene capsule for protection. The Nickel-Acetonitrile Complex.-A portion of pure nickel powder weighed with the magnet, and known volume of acetonitrile, measured by pipet, were placed in the dry cell through the top window, which was then closed tightly. One hundred ml. of H F was now delivered to the cell and stirring begun. In most cases the evolution of hydrogen, brisk a t first, was no longer observable after 30 minutes. Stirring was maintained for a longer period (Table 111) t o ensure attainment of equilibrium. When equilibrium was deemed to have been reached, the cell was drained and washed out with H F until the washes were colorless. The
4045
magnet with the unreacted nickel clinging to it was then removed quickly t o an anhydrous potassium fluoride desiccator and subsequently weighed. From the loss in weight of the nickel the concentration of nickel in solution was calculated. In two blank runs in the absence of acetonitrile and with different weights of nickel, it was found that complete transfer of the nickel could be accomplished by this method. Because of the formation of a fluoride coating on the metal, the weight increased each time exactly 3.62y0, agreeing within the accuracy of the analytical balance. All weights of nickel found during the course of the investigation were corrected by this amount before calculation of the concentration of nickel in solution. The data so obtained are those appearing in Fig. 1 and Table 111. Reagents.-The complexing agents used were of reagent grade in all cases except that of the diglycolic acid, which was of technical grade. The metal powders were of reagent grade. The metal fluorides were commercial materials obtained from Penn Salt. The IG(CO)a was' obtained from the International Nickel Company, and the Fe(C0)r from Chemical Commerce. Analytical.-All analyses were done by the analytical laboratories of the Central Research Department of Minnesota Mining and Manufacturing Company. In all cases where analyses were carried out on solutions, the solution of complexing agent was treated with an excess of the solid metallic fluoride. ST. PAUL, MIXN.
[CONTRIBUTION FROM COBB CHEMICAL LABORATORY, UNIVERSITY
OF
VIRGINIA]
Heats of Formation of Potassium Chromate, Potassium Dichromate, Chromate and Dichromate Aqueous Ions. Entropy of Dichromate Ion BY C. N. MULDROW, JR.,
AND
L. G. HEPLER
RECEIVED FEBRUARY 28, 1957 We have determined the heats of solution of KzCrOa(c),K2Cr2O7(c)and (NH~)zCr207(~) and the heats of reaction of K2CrZO7(c) and CrOt(c) with aqueous alkali and of K2Cr04(c) with aqueous acid. From the results of these determinations we have calculated the heats of formation of K2CrOa(c), K2Cr2O7(c),(NHa)2Cr207(c),CrOa'(aq) and Cr207-(aq) to be,. :espectively, -331.9, -4486.4, -425.0, -207.6 and -345.2 kcal./mole. From our heats of formation and reaction, equilibrium constants and entropy data from the literature, we have calculated the entropies of CrzO~'(aq) and HCr04-(aq) t o be 70.5 and 47.8 cal./deg. mole, respectively. The standard free energies of Cr04'(aq), CrzOl'(aq) and HCr04-(aq) have also been calculated t o be 170.1, -303.4 and - 179.0 kcal./mole, respectively.
-
Investigation of the experimental data on which the thermodynamic properties of CrOe=(aq) and CrzOT=(aq) as given by the Bureau of Standards,' Bichowsky and RossiniZ and Latimer3 are based showed that these values were not reliably known. Especially, it became apparent that the heats of formation of these ions and of various chromates and dichromates (e.g., KzCr04, KzCr207,etc.) were based on questionable heats of reaction of CrOs and heats of solution of chromates and dichromates. Calculation of standard heats of formation a t 298°K. from the results of many of the pertinent earlier investigations is difficult because most of that work was carried out under such conditions that heats of dilution and heat changes in correcting observed heats of reaction to 298°K. are both large and uncertain. Therefore we have undertaken an investigation of the thermochemistry of KzCrz07(c),CrzO7-(aq), KzCr04(c) and Cr04=(aq) by means of solution calorimetry. This work (1) "Selected Values of Chemical Thermodynamic Properties," Circular 500, National Bureau of Standards, 1952. (2) F. R. Bichowsky and F. D. Rossini, "The Thermochemistry of Chemical Substances," Reinhold Publ. Corp., Kew York, N. Y., 1936. (3) W. M .Latimer, "Oxidation Potentials," Second Ed., PrenticeHall, Inc., New York, N. Y., 1952.
also has involved the study of CrOa(c) and Crz07(c). Experimental
("4)~-
Our high-precision solution calorimeter used in previous investigation^^.^ has been improved by several changes. The rate of stirring has been increased and more efficient stirrers have been used. This improved stirring has markedly lessened the time required to attain thermal and reaction equilibrium in the calorimeter, without significantly changing the calorimetric drifts, and has therefore reduced extrapolation uncertainties. A second improvement has been more accurate timing of the heating periods. The calibrated stopwatch has been replaced by a Standard electrical timer read to 0.01 second. The timer is wired through a triple pole-double throw switch that is used to switch the electrical power from the dummy heater to the calorimeter heater. We estimate that the total uncertainty in elapsed time for the heating periods due to variation in the frequency of the local 60 cycle a.c. current, etc., is no more than 0.05 second. All of the reactions investigated have been rapid. In every experiment the reaction was completed and steady after-period drifts were obtained less than five minutes after breaking the sample bulbs. The heating periods varied from 55-200 seconds. All of the heats have been determined a t 25.0 d= 0.3". (4) R.L. Graham and L. G.Hepler, THISJ O W R X A L , 78, 4816 (1956). ( 5 ) C. N. Muldrow, Jr., and L. G. Hepler, i b i d . , 78, 5989 (1956).
Materials.-The
potassium dichromate ( K2Cr2O7)used
was Mallinckrodt primary standard analytical reagent and
the potassium chromate (KzCrOr) was Mallinckrodt A.C.S. Reagent. The ammonium dichromate [( NHa)zCrz07]was Mallinckrodt analytical reagent. -421 of these reagents were thoroughly dried before use. Two brands of CrOI were used: Coleman and Bell C.P. and Baker and Adamson Reagent. Samples of both were analyzed by reaction of CrOa with standardized ferrous ammonium sulfate solution and titration of the excess ferrous ions with standardized potassium dichromate solution. The titrations were carried out in sulfuric acidphosphoric acid solution with sodium diphenylarninesuifonate indicator. The two samples of CrOa were found t o be 99.7 and 99.6% pure, respectively. By making use of a dry box, we were able t o load CrOa into a weighed calorimeter bulb, weigh the bulb plus CrOa and fasten the bulb to the calorimeter stirrer without exposing the CrOa t o the atmosphere. The perchloric acid and potassium hydroxide solutions used in the calorimetric runs were prepared by dilution of previously standardized stock acid and alkali solutions.
Results The difference in the heats of formation of Crz07=(aq) and Cr04=(aq) was determined in two different ways, each of which involved the calorimetric determination of two different heats of reaction. We have expressed the difference in these heats of formation in terms of the standard heat of reaction 1 a t infinite dilution. This has been done for two 2Cr04-(aq)
+ 2H+(aq) = Crl07-(aq) + H10 AHI'
+
KlCrO4(c) = 2K+(aq) CrOd=jaq) 311, (2) &CrOa(c) H+(aq) = 2K+(aq) '/LrzOi=(aq) 4'/zH$O AH3 ( 3 )
+
so dilute that no potassium perchlorate was precipitated. The results of these experiments are given in Table I. The starred heats for reaction 2 indicate solution in 7.5 x M potassium hydroxide and the others refer to solution in pure water. I I E A T 01' S O L U T I O N
TABLE I HEATOF REACTION (3) (2) Moles KZCrOP AH? X los/ (kcal.1 950 ml. mole) soln.
Moles HClOd AH3 X 1031 (kcal./ 950 ml. mole soh. KnCrOa)
hloles KzCrOa/ 930 ml. soh.
Moles K9CrO.d (kcal.1 950 ml. mole) soln.
0.01084 ,01506 02064
4.32 0.02571 4.32 4.724 5.256 4.30 ,02714 4.36* 8.432 9.557 4.33* 10.427 14.34 11.463 14.34 14.481 19.11 15,604 19.11
AH2
+
K?Cr20i(c) = 2K"(aq) CrlOi-(aq) RZCr2O7(c) 20H-(aq) = 2KC(aq) 2Cr04'(aq) HIO
+
+
AIL
(4)
AHa (5)
The results of these experiments are given in Table 11. All of the heats of solution of potassium dichromate to give CrzO,=(aq), except one, were carried out in very dilute perchloric acid to lop4 Jf). The starred run indicates solution iri pure water. S o potassium perchlorate was precipitated in any of these runs.
(1)
purposes: (a) for the calculation of several heats of formation, (b) for the calculation of AS; from AH; and AF,". Because the entropy of every species in (1) except CrzOi=(aq) is known, a value for AS; makes possible the calculation of the partial molal entropy of Cr207=(ay). The first method for the experimental investigation of the heat of reaction 1 involved determinatiori of the heat of solution of potassium chromate to give potassium and chromate ions and determination of the heat of reaction of potassium chromate with aqueous perchloric acid to give potassium and dichromate ions. The calorimetric reactions are given by eq. 2 and 3, respectively. I n the case of reaction 3, the solutions were in every experiment
+
to infinite dilution in order to obtain AH," and AH,", which are, respectively, 4.2 and 4.6 kcal./ mole K2Cr04. We have also calculated AH," = 2 AH: - 2 AH: = t 0 . 8 kcal. The estimated uncertainty in the measured heats AH2 and AH3 is 0.05 kcal./mole and the uncertainties in the extrapolated values for AH," and AH: are 0.1 and 0.2 kcal., respectively. The second method for the experimental investigation of the heat of reaction 1 involved t h e heat of solution of potassium dichromate to give potassium and dichromate ions and determination of the heat of reaction of potassium dichromate with aqueous potassium hydroxide to give potassium and chromate ions. The calorimetric reactions are given by eq. 4 and 3, respectively.
4.37 4.03 3.97 3.89 3.76 3.77
1i.e have extrapolated the heats of (2) and (3)
I U I r: I1 HE4T HEATor SOLUTION (4) Moles KzCnOi/
x 1031
AH^
llules KnCrOi
x
103'
950 ml. soln.
(kcal.1 950 ml. mole) soln
1.139 2.006 2.610 3.445 3 199
19.87 19.77 19.86 19.18 18.80
OF
Rfoles KzCrzOI
~ i i ~ x 103/ 950 ml.
fkcal.,' mole)
suln.
5.331, 5.342 5.806 5.829
'7.231 18.72 18.80 7.234 1S.60* 8 . 7 4 7 18.76 10.100 6.870 lS.ri9 16.320 19.999
REACrION (6)
Moles KOH AHs x 1031 (kcai.1 930 ml. mole soin. KzCrlO;)
17.04 17.04 34.34 48.72 48.72 48.7%
-7.29 -7.29
-7.39 -7.36 -7.43 -7.40
1J-e have extrapolated the heats of reactions 4 and 5 to infinite dilution in order to obtain AH: and AH:, which are, respectively, 20.0 and -7.3 kcal./mole K1CrzOi. We estimate the uncertainties in the measured heats A X 4 and A H j to be 0.1 and 0.05 kcal./mole. The estimated uncertainties and AH: are in the extrapolated values for A:I. 0.2 and 0.1 kcal. In order to calculate AH; from our values for AH: and AH: we need to know the standard heat of reaction 6 and have therefore Il"(aq)
+ OH-(aq)
=
HzO(1)
AH,"
(6)
calculated AH: = -13.36 kcal. from Bureau of Standards1 heats of formation. From the relation AH; = AH: 2 AH; - AH: we have calculated AH; = 0.6 kcal. This heat is in satisfactory accord with the value obtained by our first method and we take as a best value AH," = +0.7 kcal. I t is difficult to estimate the uncertainty in this heat because so much of the uncertainty arises from the various extrapolations to infinite dilution rather than from calorimetric or reaction difficulties. However, we believe that the uncertainty in the average AH; given above is less than 0.3 kcal. X large number of workers have investigated the various equilibria between CrOd(aq), Cr207=(aq) a n d intermediate species. In particular,
+
HEAT s OF FORMATION OF POTASSILX CHROIIATE
=lug. 5 , 1937
4047
who have discussed the earlier work on Crz03. On the basis of the results of these investigations we have chosen -270.0 kcal./mole as the standard heat of formation of Crz03(c). Cr?O,-(aq) H20 = 2HCrO(-(aq) K , (7) This is identical with the heat of formation chosen satisfactory agreement. On the basis of these in- earlier by BrewerlZ and close to that adopted by vestigations we take K7 = 0.029 and AF; = the Bureau of Standards1 (-269.7). We calculate 1-2.10 kcal. Neuss and Rieman6 also have in- from this heat of formation and Roth and Becker's vestigated the acid dissociation of hydrogen chro- heat of oxidation that the heat of formation of mate ion (HCr04-) as in eq. 8. They report K 8 CrO3(c) is - 138.0 kcal./mole. HCrOl-(aq) = CrO(-(aq) H+(aq) K, (8) We have used the above values of A€.: and the = 3.2 X and we calculate AFs0 = +8.86 heat of formation of Cr03 with the Bureau of Standards' heats of formation of H20 and OH-(aq) kcal. We have used these equilibrium constants and to calculate the standard heat of formation of free energies to calculate K1 = 3.37 X 1014 and CrOd(aq) to be -207.6 kcal./mole. By combining this heat of formation with heats of formation AF,D = -19.82 kcal. W-e further calculate AS: of K+(aq), HzO and OH-(aq) as given by the = ( A H ; - A F p ) / T = 68.8 cal./deg.mole. We take entropies of HzO, H + and CrO4= from the Bu- Bureau of Standards' and our AH;, AH;, AH:, reau of Standards and calculate from ASP that the AH$ and AH: we have calculated the heats of forpartial molal entropy of Crz07-(aq) is 70.5 cal./deg. mation of Crz07=(aq),K2Cr04(c)and K2Cr207(c) to be, respectively, -346.2, - 331.9 and -486.4 kcal./ mole. The heats of solution and reaction reported mole. We have also determined the heat of solution of above are sufficient to determine the heat of hydrolysis of Crz07=(aq) to CrOa=(aq) and thence the (NH4)2Crz0, in very dilute perchloric acid $1). The calorimetric reaction is given entropy of Crz07=(aq). However, in order to ob- to tain heats of formation of CrOl=(aq), Crz07=(aq) by eq. 10 and the results are given in Table IV. and the potassium salts, it is necessary to carry ( S H 4 ) 2 C r 2 0 7 (=~ )2SH4+(aq) + CrlO;-(aq) AH10 (10) out a t least one additional calorimetric investigation. Accordingly, we have measured the heat of We have extrapolated the observed heats to infinite 0.2 kcal./mole. reaction of Cr03 with aqueous potassium hydroxide dilution to obtain AH& = 15.3 to give chromate ions. This heat of reaction, This heat was used with our heat of formation of with the heat of formation of CrOs and the Bureau CrP07=(aq)and the Bureau of Standards1 value for of Standards heats of formation of the other sub- NH4+(aq) to calculate the heat of formation of stances involved, suffices to give us the heat of for- (NH4)zCrzOi(c)to be -425.0 kcal./mole. Kapusmation of Cr04=(aq). The calorimetric reaction tinskii and Shidlovskii13 investigated the heat of is given by eq. 9 and the results are given in Table combustion of (NH4)2Cr20ito give N P , HzO and Crz03 and reported the heat of formation of ("4)sCrOB(c) + 20H-(aq) = CrO,-(aq) HzO AH# (9) CrzO7 to be -430 + 6 kcal./mole. This is seen to 111. We have extrapolated these heats to infinite be in satisfactory agreement with our heat of fordilution and take AH," = -28.0 kcal.,/mole Cr03. mation. In so far as our work is concerned, the The estimated uncertainty in AH due to extrapo- only likely large source of error is the appreciable lation to infinite dilution and the small amount uncertainty in the heat of formation of CrOs. The of impurity in the Cr03is 0.2 kcal. combustion work avoids this difficulty and therefore it would be desirable to have a better heat of comTABLE I11 bustion of (NH4)zCrP07. REACTION O F CrOa(c) WITH OH-(aq)
Neuss and Rieman,6 Tong and King,7 and Davies and Prue* have investigated the equilibrium constant for reaction 7 and have obtained values in
+
+
*
+
Moles CrOa(c) X loa/ 950 ml. s o h .
4.881 5.692 7.447
Moles O H - X l O s / 950 ml. s o h .
12.11 14.60 17.04
A H 9 kcal./
-28.01 -28.09 -28.10
The largest error involved in this procedure comes from the uncertainty in the heat of formation of Cr03. This heat of formation depends upon the heat of oxidation of CrsO: to CrOs as determined by Roth and Beckerg and on the heat of formation of Crz03. The heat of formation of Crz03 has been investigated recently by Mah10 (combustion calorimetry) and by Ramsey and co-workers" (temperature coefficient of dissociation pressure), (ti)
J. D. Neuss and W.Rieman,
T H x s JOURNAL,
TABLE IV
mole CrOa
66, 2288 (1934).
(7) J. Y.T o n g and E. L. King, i b i d . , 7 6 , 6180 (1953). (8) W. G. Daviee and J. E. Prue, T r a n s . Faraday Soc., 51, 1U45 (1955).
(9) W. A . R o t h and G. Becker. 2 . p h y s i k . C h e m . , 8 1 4 6 , 404 (1929). (10) A. D. Mah, THISJ O U R N A L , 76, 3363 (1954). (11) J. N. Ramsey, D. Caplan and A . A. Burr, J . Elecfrochein. Soc.. 103, 135 (1956).
HEATOF SOLUTION OF (SHa12CrYOi(c) Moles (NHdzCrzO7(c) X loa/ 950 ml. s o h .
4,256 4,976 8.426 9.610
A I i , o (kcal./mole i
.Y HdsCrzOI)
15,21 15.02 14.59 14.kii. C. A , . 5 0 , 98-19~ (1950).
free energy of formation of Cr+f+(aq) which can then be combined with our free energy of formation of Cr207=(aq) to give AF" and E o for the Cr+++/ Crz07=couple. Or the heat of reduction of Cr207" (as) to Cr+++(aq) can be combined with an estimated entropy of Cr+++(aq), and our entropy of Cr207=(aq) t o give AFO and E o for the Cr+++/ Crz07= couple. Data from the literature for the pertinent heats3.l4are so unreliable as to make these calculations virtually meaningless. From the results of the investigation by Davies and PrueYof the temperature dependence of the equilibrium constant for reaction 7 we calculate AS," = 8.5 cal./deg. mole Cr207= and AH," = 4.64 kcal./mole Crz07=. These data have been combined with our heat of formation and entropy of Crz07=(aq) and the National Bureau of Standards values for water to give the heat of formation of HCrOl-(aq) as -205.0 kcal./mole and the entropy as 47.8 cal. deg./mole. We also have calculated the standard free energy of formation of HCr04- to be - 179.0 kcal./mole.
comparison with hlnO4- (45.4),s ReO4- (4S.3),I5 and Clod- (43.2).3 We also see that the entropy of ionization of HCr04- (-38.6) as calculated from our entropy is in accord with the entropies of ionization of HS04- (-36.3), I-TS03- (--%), I-IJ'OI- (-29.9), HC03- (-35.1) as takeii from Latimer. 3 Our heat of solution of KzCr04(c) (lZI:) is i i i good agreement with the results obtained h y earlier workers.' Our heat of solution of I
