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Activity and osmotic coefficients of aqueous nickel (II) nitrate solutions
M-1323 J. Chem. Thermodvnamics1982, 14, 531-545
Activity and osmotic coefficients of aqueous nickel (II) nitrate solutions M. SARBAR,
A. K. COVINGTON,
DepartmentoJ‘Physical Chemistry, University L$ Newcastle-uponTvne. NE1 7RU. U.K. R. L. NUTTALL,
and R. N. GOLDBERG
National Bureauof Standards,Washington.D.C. 20234.U.S.A (Received2 April 1981: in revisedform
13 November1981)
The osmotic coefficients of aqueous nickel (II) nitrate have been measured at 298.15 K by the isopiestic method at molalities ranging from 0.052 to 5.5 mol. kg-i. The solubility has also been determined by direct analysis of the saturated solution and is (5.386+0.010) mol. kg-‘. The measured osmotic coefficients were used to calculate activity coefficients using four different correlating equations. Error estimates and comparisons with previous literature values are given.
1. Introduction The literature data’” leading to osmotic coefficients for nickel (II) nitrate solutions show a large degree of scatter and in several instances are based on relatively imprecise vapour pressure or freezing-temperature depression measurements. We report a detailed isopiestic study leading to the osmotic coefficients, and thence to the activity coefficients, of aqueous nickel (II) nitrate solutions.
2. Experimental REAGENTS
The Ni(NO,), .6H,O, NaCl, and CaCl,. 2H,O used were “Analar” reagents.“’ Detailed analytical information on the Ni(N03)2. 6H,O received from the vendor is as follows: mass fractions of trace impurities were chloride, 10 x lO-‘j; sulphate. 50x 10m6; zinc, 1 x 10m6; sodium, 2x 10e6; potassium, 2x 10w6; and calcium, 1 x 10-6; assay as Ni(NOJ)* .6H,O was 99.5 mass per cent; and the pH of a 5 g sample in 0.10 dm3 of CO,-free water was 5.2. These analytical results were based on the observation of opalescence and turbidity for the chloride and sulphate. respectively ; the assay for the metals was done by atomic absorption spectrophotometry. The nickel assay was based on precipitation of the nickel ion as the salt of ethene diaminetetraacetic acid. 0021-~9614/82/060537+09
$02.00/0
( 1981 Academic Press Inc. (London) Limited
538
M. SARBAR
ET AL.
Attempts to dry the Ni(N0,)2 .6H,O at temperatures ranging from 393 to 573 K proved unsuccessful due to decomposition of the salt as evidenced by visible decomposition and the appearance of oxides of nitrogen in the oven. It was therefore necessary to prepare a stock solution of the nickel nitrate and to base the measurements on the analysis of this stock solution by precipitation of nickel ions as the dimethylglyoxime salt. A description of the experimental procedure follows and is similar to that described in reference 3. A solution was prepared containing dimethylglyoxime at a mass concentration of 10 g. dm 3 in a solvent composed of 95 volume per cent ethanol and 5 volume per cent water. Nickel nitrate stock solution containing about 0.60 g of nickel was diluted to a total volume of 200 cm3 ; 5 cm3 of 0.05 mol.dmP3 HCl was added to this solution which was then heated to about 350 K. The dimethylglyoxime solution, calculated to be in excess by about 10 per cent of the amount required to ensure complete precipitation, was added slowly to the nickel nitrate solution with stirring followed by the dropwise addition of aqueous NH, solution (z 7.4mol.dmm3) which was continued until the solution was basic as evidenced by the odour of ammonia from the solutions. The precipitate was allowed to settle for 1 h and a few additional drops of dimethylglyoxime solution was then added to confirm complete precipitation. The solution was filtered through grade 4 porosity sintered glass crucibles which had been dried to constant mass at 413 K, the precipitate rinsed very carefully with acetone to remove excess dimethylglyoxime, and then dried to constant mass at 413 K (drying for periods of longer than 18 h proved to be more than adequate). Six replicate analyses on the nickel nitrate stock solution yielded a molality of (4.833 f 0.015) mol. kg- ‘. Throughout this paper, numbers in parentheses denote the estimated standard deviations of the measurements and numbers following “i” denote estimates of random error obtained by multiplying the estimated standard deviations of the means by the appropriate factor in the t-distribution for 95 per cent confidence limits. The molality of the CaCl, stock solution was measured by six replicate gravimetric chloride analysest4’ and was (5.7709 ~0.0015) mol. kg-‘. The NaCl was dried at 423 K for 2 d and stored in a desiccator over solid calcium chloride and “Drierite”. Both the CaCl, and the NaCl were highly purified reagents having indicated purities of 99.86 and 99.97 mass per cent, respectively. The major impurities in the CaCl, were arsenic, strontium, lead, and barium, while in the NaCl the major impurity was potassium. Freshly degassed doubly distilled water was used for the preparation of all solutions used in the isopiestic measurements. Molar masses used in calculations were Ni(N03)*. 182.72; CaCl,; 110.99; and NaCl, 58.4428 g.mol-‘. SOLUBILITY
MEASUREMENT
A gravimetric dimethylglyoxime analysis was also performed on a saturated solution of aqueous nickel nitrate which had been allowed to equilibrate over solid Ni(NO,), *6H,O for 14 d at 298.15 K. The results of six replicate analyses yielded a
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
solubility of (5.386 f 0.010) mol. kg-‘. Linke and Seidell(5) report a solubility on the measurements of Sieverts and Schreiner@j’ of 5.413 mol. kg- l. ISOPIESTIC
539 based
MEASUREMENTS
The isopiestic measurements were performed using a conventional apparatus.“’ The cups or dishes were of the “flip-lid” type which could be closed rapidly and were fabricated from silver, with approximately two-thirds of the available cups having been gold-plated. Nickel nitrate solutions were contained only in the gold-plated cups, while the NaCl and CaCl, solutions were placed into either the plated or unplated ones. The possibility of reaction of the Ni(NO& solutions with the cups was tested by the addition of a few drops of concentrated hydrochloric acid to some of the solutions which had been in contact with the cups for 14 d ; the tests showed no detectable AgCl precipitate. Solutions of Ni(NO,), and the reference electrolyte(s), having molalities estimated to be approximately isopiestic, were prepared freshly on the day the equilibrations were to begin. The empty cups were weighed and 2.0 cm’ of the Ni(N03)2 solutions and the reference solutions were placed into their respective cups which were then rapidly closed and weighed again. Three nearly identical cups of Ni(N03)2 and reference solution (six cups total) were placed on a brass plate (2.5 cm thick and 19.7 cm in diameter) mounted in each glass desiccator and held in place, and thermally insulated from the glass walls of the desiccator by rubber mounts. The cups containing Ni(NOJ)* solutions and the reference solutions were alternately placed on to the brass plate so as to reduce effects on the measurements due to temperature gradients on the brass plate. The desiccators were sealed with Apiezon type L grease and evacuated to a pressure of about 2300 Pa by means of a water aspirator followed by a mechanical pump. When doing this, care was taken to remove any bubbles formed in the solutions so as to eliminate essentially the possibility of spattering of solutions which might be caused by formation of bubbles during the equilibrations. The evacuated desiccators were then placed in a large water bath, the temperature of which was regulated by a Haake type E3 proportional thermoregulator to within kO.01 K. The room temperature was generally maintained in the range 293 to 297 K. The temperature of the bath was set at 298.15 K as determined by a mercury-in-glass thermometer which had been calibrated at the National Physical Laboratory. The desiccators were rocked laterally back and forth at a rate of 20 min-‘. Following the equilibrations, which lasted from 8 to 35 d, the desiccators were removed from the bath, opened, and the cups rapidly closed and weighed within 5 min. All weighings were performed on a Mettler type A30 automatic balance having an imprecision of 0.1 mg. The automatic balance permitted the weighings to be performed very rapidly, thus reducing any evaporative losses from the cups. The evaporative loss rate was measured and found to vary from 0.0005 to 0.0010 mg . s- 1 for an individual cup; thus this effect was considered to be negligible and was not corrected for. All weighings were done relative to a standard weight which served as a tare and the accuracy of the balance itself was checked by comparison with a set of calibrated weights from the National Physical laboratory.
540
M. SARBAR
ET ,41
A test of the accuracy of the apparatus and of the procedures was performed by doing an intercomparison of KCI and NaCl solutions. The results yielded two sets of isopiestic molalities. In the first set. the molalities were KCl. 1.1139 (0.00072) and NaCl, 1.0678 (0.00097) mol. kg - ‘, while in the second set the molalities were KCl, 1.3162 (0.00084) and NaCl, 1.2544 (0.0010) mol. kg I. These yielded isopiestic ratios of (1.0432 f 0.0049) and (1.0493 I 0.0050). respectively. The evaluated measurements of Hamer and Wu@’ yield isopiestic ratios of 1.0437 and 1.0502, respectively, and so the results are in satisfactory agreement with the “best” literature values.
3. Results The results of the isopiestic measurements are given in table 1. In each case, the given molality is the mean value obtained from three cups contained in a given TABLE
(0.00038)” (0.00008) (0.00131) (0.ooo4) (O.ooO3)
mW(NW21 mol.kg-r 2.8106 3.1832 3.3889 3.8459
(0.0024) (0.0024) (0.0026) (0.0004)
molalities
m(NaC1) ___~ mol,kg-’
mWWGi mol.kg-r 0.05260 0.12630 0.2807 0.4477 0.8359
1. Isopiestic
0.07453 0.17858 0.4100 0.6739 1.3550
(0.00027) (0.00015) (0.0013) (0.0004) (0.0003)
t
m(Ni(N03),i
d
mol.kg-‘--
35 29 1: 20
-__
1.2560 1.7790 2.2394 2.7130 2.7188
I
m(CaC1,; ~.. mol.kg-’ 2.7384 3.0764 3.2619 3.6717
at 298.15 K with equilibration
mlNiW0d21 mol. kg-r
d
(0.0019) (0.0032) (0.0035) (0.0016)
14 14 19 19
(0.0013) (0.0006) (0.0028) (0.0029)b (0.0043)
4.3018 4.7937 5.1587 5.5105
” Numbers in ( ) are estimated standard deviations. b This point was given zero weight in our final correlation ’ Super-saturated solution.
(0.0021) (0.0007) (0.0039) (0.0061)’
times
t
m(NaC1)
t
mol. kg- r
il
2.1712 3.2612 4.2648 5.3452 5.3383
(0.0034) (0.0021) (0.0029) (0.0150) (0.0025)
m(CaCI,; mol,kg-’ 4.0824 4.5272 4.8701 5.2032
(0.0023) (0.0012) (0.0022) (0.0033)
11 10 9 12 11 I d 19 22 22 22
of results,
desiccator. The estimated standard deviations of the three measurements and the equilibration times are also given. In performing the calculations, we have adopted four different correlating equations for the osmotic coefficients : f$ = 1+A,B-3(I/me))‘[+l/{l
il +B(l/me)“2)
+21n(l+B(l/me)‘i2\
+B(Z/me)'~2)]+~C(m/me)+~D(m/me)2+~~(m/me)3+~~~,
(la)
4 = 1-~A~(Z/me)1’2-)~2(I/me)~~+1n(Z/me)~ +C~~,Bi((i+1)/(i+3))(m/me)‘i+1”2,
(2a)
OSMOTIC
COEFFICIENTS
OF AQUEOUS
(fJ= 1 -+A, (Z/RI”)“* +Cyz, Bi((i+
c$ = 1+/z+:-
l)/(i+
NICKEL
3))(m!me)“+
541
NITRATE
I)‘*.
Ua)
If~+(m/m”){2(v+v~)/v)~ +(nt/m”)~{2(v+ \‘L)” *jv~C~+(nl/me)3(2(v+v~)2/v~D~+~“~
where A, and A, are theoretically fixed constants, (9) which for electrolytes of charge type 2--l in water at 298.15 K are 2.3525 and 0.92238 respectively, m is the molality, I is the ionic strength on a molality basis assuming complete dissociation, and me = 1 mol. kg-‘. B, C, D, E, etc. in equation (la) and the Bi’S in equations (2a) and (3a) are adjustable parameters. Equation (4a) is that used by Pitzer and Mayorga,“” for which f4 = -A~(l/rne)“*/~l
+h(l/rne)“2~.
and B” = 13(0)+~~1’exp[-cc(Z/me)1’Zj. We have followed Pitzer and Mayorga”” and kept b = 1.2 and o! = 2.0. The remaining coefficients are as follows: A, is a Debye-Htickel constant equal to iA, ; PO’, /J(l), C’@‘,D”, etc. are adjustable parameters; v = (v+ + v- ); and z+ and z- are the charge number of the ions. The corresponding equations for the mean ionic activity coefficients y? on a molality basis are: lny,
= -A,(Z/me)“Z,/{l
+B(Z/mft)*“f
+C(m/m”)+D(m/me)2 +E(m/me)3+...,
In y* = -A, (Z,/me)li2 -A2(Z;ma)ln(Z/rn”)
(lb)
+CF= ,Bi(m/me)“+‘“*.
(2b)
In?+ = -A,(Z/ms)“2+~~~1Bi(m/me)‘if1’~~,
(3b)
and In ;‘? = Iz+z-l.f’+(m/me){2(
v, \l.~)/~iBY+(mjrn~)‘12(~,+
v~)~‘~/v)cY
+(m,/mB)3j2(v+
v-)‘/v)Di’+.
. . . (4b)
For equation 4(b): f’ = -.4,(Z/me)112/{l
+b(Z/me)1’21 +(2/b)ln{l
BY = 2/r0’+{2f11)/~*(Z/me)j[1
-expj
+ b(ZlmY)“*).
-a(Z/me)“*~
I1 +~(Z~me)‘~*-~a2(Z/m”)11,
and
Using the isopiestic molalities from table 1 we have calculated osmotic coefficients for Ni(NO,), solutions using evaluated@,9’ values of 4 for the NaCl and CaCl, solutions and the values of the parameters in equations (1) to (4) using previously
M. SARBAR
542 TABLE
2. Coefficients
of correlating
equations; deviation
Equations (1): B, 0.2061 x lo+‘. 0.72x -0.121307, 0.36x 10-l; F, 0.295746x 0.18796x 10-3, 0.93 x 10-4.
10-l; lo-‘,
ET AL.
name of parameter, of parameter C, 0.1238. 0.11 x 10-l;
0.55x G,
Equations (2): E,, 0.210621 x lo+‘, 0.48 x 10-l ; B,, 0.601108 B4, 0.455068, 0.41 x10-l; B,, -0.48212x lo-‘, 0.60x lo-‘. Equations (3): B1, 0.127879 x lo+‘, 0.50; B,, -0.2878143 -0.41667483 x lo+‘, 0.80x lo+‘; 0.63 x lo+’ ; B4, -0.91255456 x lo+‘, 0.25 x lo+’ ; B,, 0.18490905 x lo+‘,
x lo+‘.
10-l; D. 0.29450, -0.373651 x lo-‘. 0.11;
1) = 0.0028;
TABLE
3. Mean
y*
4
m mol.kg-’ 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 0.200 0.300 0.400 0.500 0.600
0.8908 0.8548 0.8300 0.8108 0.7950 0.7815 0.7698 0.7594 0.7501 0.7416 0.6836 0.6491 0.6250 0.6067 0.5922 0.5802 0.5702 0.5617 0.5543 0.5137 0.4993 0.4959 0.4989 0.5064
0.9635 0.9516 0.9434 0.9372 0.9321 0.9278 0.9241 0.9208 0.9179 0.9153 0.8986 0.8897 0.8843 0.8808 0.8785 0.8771 0.8761 0.8757 0.8756 0.8839 0.8997 0.9191 0.9409 0.9644
s(equations
ionic
activity
a, 0.999948 0.999897 0.999847 0.999797 0.999748 0.999699 0.999650 0.999602 0.999554 0.999505 0.999029 0.998558 0.998090 0.997623 0.997155 0.996687 0.996219 0.995750 0.995279 0.990492 0.985518 0.980326 0.974895 0.969210
2) = 0.0020;
and osmotic
lo+*. B,,
n Saturated
coefficients
G”’
m ~mol.kg-’
of aqueous
0.700 0.800 0.900 1.000 1.250 1.500 1.750 2.000 2.250 2.500 2.750 3.000 3.250 3.500 3.750 4.000 4.250 4.500 4.750 5.000 5.250 5.386“ 5.500 5.510
m
m 44)
mol.kg-’ 0.001 0.010 0.100 l.CNIO
3) = 0.0032;
0.0002 0.0010 0.0019 0.0018 solution
s(ln
Yf )
0.0004 0.0023 0.0068 0.0068
4Yc)
0.0003 0.0017 0.0038 0.0038
mol.kg-’ 2.ooo 5.000 5.510
-0.196022
E, H.
x lo+*, 0.27 x lo+’ ; B,, 0.43593998‘x B,, 0.25006526~ lo+‘. 0.58 x lo+‘; 0.57; Es, -0.1594902, 0.54 x 10”.
J.kg-’ -1 -2 -3 -4 -6 -8 -10 -12 -14 -16 -41 -72 -105 - 142 -180 -219 -260 - 303 - 346 -818 -1326 - 1846 - 2366 - 2878
0.63x 10-l; 0.16x lo-‘:
0.10;
s(equations
&,
standard
x lo+‘.
Equations (4): t@“‘. 0.45006,0.54 x lo- * ; $$“, 0.2628 x lO+ ‘, 0.73 x 10-l 0.27 x lo-*; (8/3)D+, 0.2045 x lo-*, 0.33 x 10-3. s(equations
of parameter,
vdhe
; (2”*/3)C+, s(equations
Ni(NO,),
‘ii
9
0.5173 0.5311 0.5476 0.5664 0.6231 -0.6932 0.7773 0.8765 0.9929 1.1291 1.2885 1.4752 1.6941 1.9509 2.2520 2.6046 3.0165 3.4965 4.0547 4.7035 5.4593 5.9234 6.3458 6.3864
0.9894 1.0156 1.0426 1.0705 1.1425 1.2166 1.2921 1.3683 1.4451 1.5228 1.6013 1.6809 1.7616 1.8433 1.9258 2.0089 2.0920 2.1750 2.2573 2.3392 2.4209 2.4656 2.5034 2.5069
4#J) 0.0017 0.0021 0.0028
-0.25481
x 10-l.
4) = 0.0046.
at 298.15
a,
K G’” ___. J.kg-’
0.963260 0.957041 0.950549 0.943787 0.925722 0.906076 0.884968 0.862518 0.838840 0.814036 0.788203 0.761443 0.733869 0.705617 0.676843 0.647725 0.618453 0.589214 0.560176 0.531462 0.503130 0.487869 0.475145 0.473975
- 3376 - 3857 -4316 -4752 - 5722 - 6504 - 7080 - 7438 -7568 - 7462 -7114 - 6517 - 5666 -4555 -3180 - 1535 381 2570 5035 7776 10793 12551 14088 14233
sOnY+)
SC?*)
0.0074 0.0071 0.0075
o.cQ65 0.0335 0.0481
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
543
documented least-squares procedures. (g*l ‘) These values are given in table 2 together with their standard deviations s and, at the bottom of the table, standard deviations for observations of unit weight for the four different correlating equations. Table 3 contains a table of activity and osmotic coefficients, activities (a,, of H,O and excess Gibbs energies G’” calculated at selected molalities using equations (1) and the coefficients given in table 2. Standard deviations of calculated values of 4, In Ye, and y+ at selected molalities are given at the bottom of table 3. -Since the calculation of y* involves some uncertainty concerning the extrapolation from zero to the lowest measured molality, the values of y-+ calculated from the four different correlating equations will differ. At m = 5.5105 mol. kg- ‘, y* is calculated to be 6.386,6.488,6.349, and 6.292 using equations (l), (2), (3), and (4) respectively. 4. Estimates
of error and comparison
with previous results
The random error associated with a measured osmotic coefficient is proportional to the quantity {(sSm"/m,)2+(s,me/mr)2)1'2, where s, and s, are, respectively, the standard deviations for the salt under investigation and the reference salt at the molalities, m, and m,, at which the salts are in isopiestic equilibrium. This quantity, as calculated using the estimated standard deviations given in table 1, is greatest at the lowest molalities (it is 0.008 at m{Ni(NO,),) = 0.0526 mol. kg-‘) and then steadily decreases to an approximate average value of 0.0012 for molalities greater than 1 mol. kg- ‘. A comparison of estimates of random error, as obtained from the above quantity, with the individual deviations of the measured osmotic coefficients from the fit shows that the scatter of the points about the fit is completely accounted for in terms of the random errors associated with the individual measurements. Estimates of systematic errors and their propagation to the osmotic coefficients are given in table 4. We make a final estimate of error, random plus systematic, of 0.009 for the osmotic coefficients over the entire molality range. The relation of earlier work to our measurements is shown in the deviation plot of figure 1. The work of Ryabov ef al. (12) had earlier”’ been taken to be the most TABLE 4. Estimates of systematic error
Quantity
Estimate of possible systematic Effect of estimate of systematic error on 4 error in quantity low molalities high molalities
molahty of Ni(NO,), stock solution molality. . of CaCI, stock solution impurities m Nt(NO,), impurities in CaCl, impurities in NaCl isopiestic technique : temperature gradients, non-equilibrium between solutions, vaporization effects, etc.
0.3 per cent 0.05 per cent 0.1 per cent 0.1 per cent 0.1 per cent 0.1 per cent at the highest molalities to 1.0 per cent at the lowest molalities
0.002 0.0004 O.CUO6 O.WO4 0.002 0.009
0.007 0.0006 o.ooo2 O.oool 0.002 0.002
total in quadrature
0.010
0.008
M. SARBAR ET Al..
544
0
AA 0
-0.02 - ‘,
o +
a -0.04 I 0
0 0
:
0 0
. .
0
0 :-:-L-~&--4 1
2
I 0
0 iJ-----d 3
! 4
5
6
m/(tnol~kg-‘)
FIGURE 1. Plot of {#(ohs.)-4(calc.)) for the various sets from our final fit, using equations (I), asa function of the molality. v’, Dieterici,“s) vapour-pressure measurements; + , Frolov et aI.,‘r3) isopiestic measurements (reference salt was not specified by the authors); A, Jones et 01.. t14) freezing-temperature depressions; A. Jones and Pearce,“” freezing-temperature depressions; +, King et al., (r6’ freezing-temperature depressions; 0, Ryabov et al.,(’ *) .rsopiestic measurements (reference salt was not specified by the authors); 0. Yakimov and Guzhavina,“” vapour-pressure measurements; x , this work, isopiestic measurements, reference salt is NaCl ; 0, this work, isopiestic measurements, reference salt is CaCI,.
reliable, but it is seen to differ by as much as 0.03 in 4 from our measurements. These workers(‘2) give few details about their experimental procedures and we are thus unable to explain the observed differences. M.S. thanks the University of Tabriz, Iran, for the award of a scholarship. R.L.N. and R.N.G. acknowledge support by the U.S. Department of Energy and the Office of Standard Reference Data of the National Bureau of Standards. These measurements were performed while R.N.G. was on secondment at the Department of Physical Chemistry, University of Newcastle-upon-Tyne, during 1980.
REFERENCES 1. Goldberg, R. N.; Staples, B. R.; Nuttall, R. L. J. P&x C/rem. Rej Data 1979, 8, 923. 2. Analar Standards for Loboratory Chemicals. Analar Standards: Poole, Dorset, England. 1977. 3. Charlot. G.; Bezier, D. Quanfitafive Inorganic Anulysb. Methuen: London. 1957. 4. Analytical Chemistry, Vol. II. Strouts, C. R. N.; GilfiJIan, J. H.; Wilson. H. N.: editors. Oxford University Press: London. 1955.
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
545
5. Linke, W. F.; Seidell, A. Solubilities: Inorganic and Metal Organic Compound--A Compilation oj Soluhility Data from the Periodical Literature. Vol. I : A-h, Vol. II: K-Z. Vol. I : Van Nostrand: Princeton, New Jersey. 1958; Vol. II: American Chemical Society: Washington, D.C. 1965. 6. Sieverts, A.; Schreiner. L. Z. Anorg. Chem. 1934, 219, 105. I. Platford, R. F. Activity Coeficients in Electrol.vte Solutions, Vol. I. Pytkowicz, R. M.: editor, CRC Press: Boca Raton, Florida. 1979. 8. Hamer. W. J.; Wu, Y. C. J. Phys. Chem. Ref. Data 1972, 1, 1047. 9. Staples, B. R.; Nuttall, R. L. J. Phys. Chem. Ref. Dara 1977, 6, 385. 10. Pitzer. K. S.; Mayorga, G. J. Phys. Chem. 1973,ll. 2300. 11. Staples, B. R.; Nuttall, R. L. Nafl. Bur. Stand. (U.S.) Tech. Note 928. 1976. 12. Ryabov. V. P.; Ageev. A. A.; Nikolaev, V. P.; Frolov, Yu. G. Tr. Mask. Khim.-Tekhnol. Inst. 1972. 71, 307. 13. Frolov, Yu. G.; Nikolaev, V. P.; Ryabov. V. P.; Ageev, A. A. Termodin. Str. Rastvorov. 1974, 2, 55. 14. Jones, H. C.; Getman, F. H.; Bassett, H. P.: McMaster. L.; Uhler. H. S. Carnegie Inst. Washington, Publ. No. 60. 1907. 15. Yakimov, M. A.; Guzhavina, E. I. Russ. J. Inorg. Chem. (Engl. Transl.) 1971, 16, 934.; Zh. ,h’mrR. Khim. 1971. 16, 1758. 16. King, H. J. S., Cruse, A. W.; Angell. F. C. J. Chem. Sot. 1932, 2928, 17. Jones, H. C.; Pearce, J. N. Am. Chem. J. 1907, 38, 683. 18. Dieterici. C. Ann. Phys. (Leipzig) 1923, 375. 617.
Activity and osmotic coefficients of aqueous nickel (II) nitrate solutions M. SARBAR,
A. K. COVINGTON,
DepartmentoJ‘Physical Chemistry, University L$ Newcastle-uponTvne. NE1 7RU. U.K. R. L. NUTTALL,
and R. N. GOLDBERG
National Bureauof Standards,Washington.D.C. 20234.U.S.A (Received2 April 1981: in revisedform
13 November1981)
The osmotic coefficients of aqueous nickel (II) nitrate have been measured at 298.15 K by the isopiestic method at molalities ranging from 0.052 to 5.5 mol. kg-i. The solubility has also been determined by direct analysis of the saturated solution and is (5.386+0.010) mol. kg-‘. The measured osmotic coefficients were used to calculate activity coefficients using four different correlating equations. Error estimates and comparisons with previous literature values are given.
1. Introduction The literature data’” leading to osmotic coefficients for nickel (II) nitrate solutions show a large degree of scatter and in several instances are based on relatively imprecise vapour pressure or freezing-temperature depression measurements. We report a detailed isopiestic study leading to the osmotic coefficients, and thence to the activity coefficients, of aqueous nickel (II) nitrate solutions.
2. Experimental REAGENTS
The Ni(NO,), .6H,O, NaCl, and CaCl,. 2H,O used were “Analar” reagents.“’ Detailed analytical information on the Ni(N03)2. 6H,O received from the vendor is as follows: mass fractions of trace impurities were chloride, 10 x lO-‘j; sulphate. 50x 10m6; zinc, 1 x 10m6; sodium, 2x 10e6; potassium, 2x 10w6; and calcium, 1 x 10-6; assay as Ni(NOJ)* .6H,O was 99.5 mass per cent; and the pH of a 5 g sample in 0.10 dm3 of CO,-free water was 5.2. These analytical results were based on the observation of opalescence and turbidity for the chloride and sulphate. respectively ; the assay for the metals was done by atomic absorption spectrophotometry. The nickel assay was based on precipitation of the nickel ion as the salt of ethene diaminetetraacetic acid. 0021-~9614/82/060537+09
$02.00/0
( 1981 Academic Press Inc. (London) Limited
538
M. SARBAR
ET AL.
Attempts to dry the Ni(N0,)2 .6H,O at temperatures ranging from 393 to 573 K proved unsuccessful due to decomposition of the salt as evidenced by visible decomposition and the appearance of oxides of nitrogen in the oven. It was therefore necessary to prepare a stock solution of the nickel nitrate and to base the measurements on the analysis of this stock solution by precipitation of nickel ions as the dimethylglyoxime salt. A description of the experimental procedure follows and is similar to that described in reference 3. A solution was prepared containing dimethylglyoxime at a mass concentration of 10 g. dm 3 in a solvent composed of 95 volume per cent ethanol and 5 volume per cent water. Nickel nitrate stock solution containing about 0.60 g of nickel was diluted to a total volume of 200 cm3 ; 5 cm3 of 0.05 mol.dmP3 HCl was added to this solution which was then heated to about 350 K. The dimethylglyoxime solution, calculated to be in excess by about 10 per cent of the amount required to ensure complete precipitation, was added slowly to the nickel nitrate solution with stirring followed by the dropwise addition of aqueous NH, solution (z 7.4mol.dmm3) which was continued until the solution was basic as evidenced by the odour of ammonia from the solutions. The precipitate was allowed to settle for 1 h and a few additional drops of dimethylglyoxime solution was then added to confirm complete precipitation. The solution was filtered through grade 4 porosity sintered glass crucibles which had been dried to constant mass at 413 K, the precipitate rinsed very carefully with acetone to remove excess dimethylglyoxime, and then dried to constant mass at 413 K (drying for periods of longer than 18 h proved to be more than adequate). Six replicate analyses on the nickel nitrate stock solution yielded a molality of (4.833 f 0.015) mol. kg- ‘. Throughout this paper, numbers in parentheses denote the estimated standard deviations of the measurements and numbers following “i” denote estimates of random error obtained by multiplying the estimated standard deviations of the means by the appropriate factor in the t-distribution for 95 per cent confidence limits. The molality of the CaCl, stock solution was measured by six replicate gravimetric chloride analysest4’ and was (5.7709 ~0.0015) mol. kg-‘. The NaCl was dried at 423 K for 2 d and stored in a desiccator over solid calcium chloride and “Drierite”. Both the CaCl, and the NaCl were highly purified reagents having indicated purities of 99.86 and 99.97 mass per cent, respectively. The major impurities in the CaCl, were arsenic, strontium, lead, and barium, while in the NaCl the major impurity was potassium. Freshly degassed doubly distilled water was used for the preparation of all solutions used in the isopiestic measurements. Molar masses used in calculations were Ni(N03)*. 182.72; CaCl,; 110.99; and NaCl, 58.4428 g.mol-‘. SOLUBILITY
MEASUREMENT
A gravimetric dimethylglyoxime analysis was also performed on a saturated solution of aqueous nickel nitrate which had been allowed to equilibrate over solid Ni(NO,), *6H,O for 14 d at 298.15 K. The results of six replicate analyses yielded a
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
solubility of (5.386 f 0.010) mol. kg-‘. Linke and Seidell(5) report a solubility on the measurements of Sieverts and Schreiner@j’ of 5.413 mol. kg- l. ISOPIESTIC
539 based
MEASUREMENTS
The isopiestic measurements were performed using a conventional apparatus.“’ The cups or dishes were of the “flip-lid” type which could be closed rapidly and were fabricated from silver, with approximately two-thirds of the available cups having been gold-plated. Nickel nitrate solutions were contained only in the gold-plated cups, while the NaCl and CaCl, solutions were placed into either the plated or unplated ones. The possibility of reaction of the Ni(NO& solutions with the cups was tested by the addition of a few drops of concentrated hydrochloric acid to some of the solutions which had been in contact with the cups for 14 d ; the tests showed no detectable AgCl precipitate. Solutions of Ni(NO,), and the reference electrolyte(s), having molalities estimated to be approximately isopiestic, were prepared freshly on the day the equilibrations were to begin. The empty cups were weighed and 2.0 cm’ of the Ni(N03)2 solutions and the reference solutions were placed into their respective cups which were then rapidly closed and weighed again. Three nearly identical cups of Ni(N03)2 and reference solution (six cups total) were placed on a brass plate (2.5 cm thick and 19.7 cm in diameter) mounted in each glass desiccator and held in place, and thermally insulated from the glass walls of the desiccator by rubber mounts. The cups containing Ni(NOJ)* solutions and the reference solutions were alternately placed on to the brass plate so as to reduce effects on the measurements due to temperature gradients on the brass plate. The desiccators were sealed with Apiezon type L grease and evacuated to a pressure of about 2300 Pa by means of a water aspirator followed by a mechanical pump. When doing this, care was taken to remove any bubbles formed in the solutions so as to eliminate essentially the possibility of spattering of solutions which might be caused by formation of bubbles during the equilibrations. The evacuated desiccators were then placed in a large water bath, the temperature of which was regulated by a Haake type E3 proportional thermoregulator to within kO.01 K. The room temperature was generally maintained in the range 293 to 297 K. The temperature of the bath was set at 298.15 K as determined by a mercury-in-glass thermometer which had been calibrated at the National Physical Laboratory. The desiccators were rocked laterally back and forth at a rate of 20 min-‘. Following the equilibrations, which lasted from 8 to 35 d, the desiccators were removed from the bath, opened, and the cups rapidly closed and weighed within 5 min. All weighings were performed on a Mettler type A30 automatic balance having an imprecision of 0.1 mg. The automatic balance permitted the weighings to be performed very rapidly, thus reducing any evaporative losses from the cups. The evaporative loss rate was measured and found to vary from 0.0005 to 0.0010 mg . s- 1 for an individual cup; thus this effect was considered to be negligible and was not corrected for. All weighings were done relative to a standard weight which served as a tare and the accuracy of the balance itself was checked by comparison with a set of calibrated weights from the National Physical laboratory.
540
M. SARBAR
ET ,41
A test of the accuracy of the apparatus and of the procedures was performed by doing an intercomparison of KCI and NaCl solutions. The results yielded two sets of isopiestic molalities. In the first set. the molalities were KCl. 1.1139 (0.00072) and NaCl, 1.0678 (0.00097) mol. kg - ‘, while in the second set the molalities were KCl, 1.3162 (0.00084) and NaCl, 1.2544 (0.0010) mol. kg I. These yielded isopiestic ratios of (1.0432 f 0.0049) and (1.0493 I 0.0050). respectively. The evaluated measurements of Hamer and Wu@’ yield isopiestic ratios of 1.0437 and 1.0502, respectively, and so the results are in satisfactory agreement with the “best” literature values.
3. Results The results of the isopiestic measurements are given in table 1. In each case, the given molality is the mean value obtained from three cups contained in a given TABLE
(0.00038)” (0.00008) (0.00131) (0.ooo4) (O.ooO3)
mW(NW21 mol.kg-r 2.8106 3.1832 3.3889 3.8459
(0.0024) (0.0024) (0.0026) (0.0004)
molalities
m(NaC1) ___~ mol,kg-’
mWWGi mol.kg-r 0.05260 0.12630 0.2807 0.4477 0.8359
1. Isopiestic
0.07453 0.17858 0.4100 0.6739 1.3550
(0.00027) (0.00015) (0.0013) (0.0004) (0.0003)
t
m(Ni(N03),i
d
mol.kg-‘--
35 29 1: 20
-__
1.2560 1.7790 2.2394 2.7130 2.7188
I
m(CaC1,; ~.. mol.kg-’ 2.7384 3.0764 3.2619 3.6717
at 298.15 K with equilibration
mlNiW0d21 mol. kg-r
d
(0.0019) (0.0032) (0.0035) (0.0016)
14 14 19 19
(0.0013) (0.0006) (0.0028) (0.0029)b (0.0043)
4.3018 4.7937 5.1587 5.5105
” Numbers in ( ) are estimated standard deviations. b This point was given zero weight in our final correlation ’ Super-saturated solution.
(0.0021) (0.0007) (0.0039) (0.0061)’
times
t
m(NaC1)
t
mol. kg- r
il
2.1712 3.2612 4.2648 5.3452 5.3383
(0.0034) (0.0021) (0.0029) (0.0150) (0.0025)
m(CaCI,; mol,kg-’ 4.0824 4.5272 4.8701 5.2032
(0.0023) (0.0012) (0.0022) (0.0033)
11 10 9 12 11 I d 19 22 22 22
of results,
desiccator. The estimated standard deviations of the three measurements and the equilibration times are also given. In performing the calculations, we have adopted four different correlating equations for the osmotic coefficients : f$ = 1+A,B-3(I/me))‘[+l/{l
il +B(l/me)“2)
+21n(l+B(l/me)‘i2\
+B(Z/me)'~2)]+~C(m/me)+~D(m/me)2+~~(m/me)3+~~~,
(la)
4 = 1-~A~(Z/me)1’2-)~2(I/me)~~+1n(Z/me)~ +C~~,Bi((i+1)/(i+3))(m/me)‘i+1”2,
(2a)
OSMOTIC
COEFFICIENTS
OF AQUEOUS
(fJ= 1 -+A, (Z/RI”)“* +Cyz, Bi((i+
c$ = 1+/z+:-
l)/(i+
NICKEL
3))(m!me)“+
541
NITRATE
I)‘*.
Ua)
If~+(m/m”){2(v+v~)/v)~ +(nt/m”)~{2(v+ \‘L)” *jv~C~+(nl/me)3(2(v+v~)2/v~D~+~“~
where A, and A, are theoretically fixed constants, (9) which for electrolytes of charge type 2--l in water at 298.15 K are 2.3525 and 0.92238 respectively, m is the molality, I is the ionic strength on a molality basis assuming complete dissociation, and me = 1 mol. kg-‘. B, C, D, E, etc. in equation (la) and the Bi’S in equations (2a) and (3a) are adjustable parameters. Equation (4a) is that used by Pitzer and Mayorga,“” for which f4 = -A~(l/rne)“*/~l
+h(l/rne)“2~.
and B” = 13(0)+~~1’exp[-cc(Z/me)1’Zj. We have followed Pitzer and Mayorga”” and kept b = 1.2 and o! = 2.0. The remaining coefficients are as follows: A, is a Debye-Htickel constant equal to iA, ; PO’, /J(l), C’@‘,D”, etc. are adjustable parameters; v = (v+ + v- ); and z+ and z- are the charge number of the ions. The corresponding equations for the mean ionic activity coefficients y? on a molality basis are: lny,
= -A,(Z/me)“Z,/{l
+B(Z/mft)*“f
+C(m/m”)+D(m/me)2 +E(m/me)3+...,
In y* = -A, (Z,/me)li2 -A2(Z;ma)ln(Z/rn”)
(lb)
+CF= ,Bi(m/me)“+‘“*.
(2b)
In?+ = -A,(Z/ms)“2+~~~1Bi(m/me)‘if1’~~,
(3b)
and In ;‘? = Iz+z-l.f’+(m/me){2(
v, \l.~)/~iBY+(mjrn~)‘12(~,+
v~)~‘~/v)cY
+(m,/mB)3j2(v+
v-)‘/v)Di’+.
. . . (4b)
For equation 4(b): f’ = -.4,(Z/me)112/{l
+b(Z/me)1’21 +(2/b)ln{l
BY = 2/r0’+{2f11)/~*(Z/me)j[1
-expj
+ b(ZlmY)“*).
-a(Z/me)“*~
I1 +~(Z~me)‘~*-~a2(Z/m”)11,
and
Using the isopiestic molalities from table 1 we have calculated osmotic coefficients for Ni(NO,), solutions using evaluated@,9’ values of 4 for the NaCl and CaCl, solutions and the values of the parameters in equations (1) to (4) using previously
M. SARBAR
542 TABLE
2. Coefficients
of correlating
equations; deviation
Equations (1): B, 0.2061 x lo+‘. 0.72x -0.121307, 0.36x 10-l; F, 0.295746x 0.18796x 10-3, 0.93 x 10-4.
10-l; lo-‘,
ET AL.
name of parameter, of parameter C, 0.1238. 0.11 x 10-l;
0.55x G,
Equations (2): E,, 0.210621 x lo+‘, 0.48 x 10-l ; B,, 0.601108 B4, 0.455068, 0.41 x10-l; B,, -0.48212x lo-‘, 0.60x lo-‘. Equations (3): B1, 0.127879 x lo+‘, 0.50; B,, -0.2878143 -0.41667483 x lo+‘, 0.80x lo+‘; 0.63 x lo+’ ; B4, -0.91255456 x lo+‘, 0.25 x lo+’ ; B,, 0.18490905 x lo+‘,
x lo+‘.
10-l; D. 0.29450, -0.373651 x lo-‘. 0.11;
1) = 0.0028;
TABLE
3. Mean
y*
4
m mol.kg-’ 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 0.200 0.300 0.400 0.500 0.600
0.8908 0.8548 0.8300 0.8108 0.7950 0.7815 0.7698 0.7594 0.7501 0.7416 0.6836 0.6491 0.6250 0.6067 0.5922 0.5802 0.5702 0.5617 0.5543 0.5137 0.4993 0.4959 0.4989 0.5064
0.9635 0.9516 0.9434 0.9372 0.9321 0.9278 0.9241 0.9208 0.9179 0.9153 0.8986 0.8897 0.8843 0.8808 0.8785 0.8771 0.8761 0.8757 0.8756 0.8839 0.8997 0.9191 0.9409 0.9644
s(equations
ionic
activity
a, 0.999948 0.999897 0.999847 0.999797 0.999748 0.999699 0.999650 0.999602 0.999554 0.999505 0.999029 0.998558 0.998090 0.997623 0.997155 0.996687 0.996219 0.995750 0.995279 0.990492 0.985518 0.980326 0.974895 0.969210
2) = 0.0020;
and osmotic
lo+*. B,,
n Saturated
coefficients
G”’
m ~mol.kg-’
of aqueous
0.700 0.800 0.900 1.000 1.250 1.500 1.750 2.000 2.250 2.500 2.750 3.000 3.250 3.500 3.750 4.000 4.250 4.500 4.750 5.000 5.250 5.386“ 5.500 5.510
m
m 44)
mol.kg-’ 0.001 0.010 0.100 l.CNIO
3) = 0.0032;
0.0002 0.0010 0.0019 0.0018 solution
s(ln
Yf )
0.0004 0.0023 0.0068 0.0068
4Yc)
0.0003 0.0017 0.0038 0.0038
mol.kg-’ 2.ooo 5.000 5.510
-0.196022
E, H.
x lo+*, 0.27 x lo+’ ; B,, 0.43593998‘x B,, 0.25006526~ lo+‘. 0.58 x lo+‘; 0.57; Es, -0.1594902, 0.54 x 10”.
J.kg-’ -1 -2 -3 -4 -6 -8 -10 -12 -14 -16 -41 -72 -105 - 142 -180 -219 -260 - 303 - 346 -818 -1326 - 1846 - 2366 - 2878
0.63x 10-l; 0.16x lo-‘:
0.10;
s(equations
&,
standard
x lo+‘.
Equations (4): t@“‘. 0.45006,0.54 x lo- * ; $$“, 0.2628 x lO+ ‘, 0.73 x 10-l 0.27 x lo-*; (8/3)D+, 0.2045 x lo-*, 0.33 x 10-3. s(equations
of parameter,
vdhe
; (2”*/3)C+, s(equations
Ni(NO,),
‘ii
9
0.5173 0.5311 0.5476 0.5664 0.6231 -0.6932 0.7773 0.8765 0.9929 1.1291 1.2885 1.4752 1.6941 1.9509 2.2520 2.6046 3.0165 3.4965 4.0547 4.7035 5.4593 5.9234 6.3458 6.3864
0.9894 1.0156 1.0426 1.0705 1.1425 1.2166 1.2921 1.3683 1.4451 1.5228 1.6013 1.6809 1.7616 1.8433 1.9258 2.0089 2.0920 2.1750 2.2573 2.3392 2.4209 2.4656 2.5034 2.5069
4#J) 0.0017 0.0021 0.0028
-0.25481
x 10-l.
4) = 0.0046.
at 298.15
a,
K G’” ___. J.kg-’
0.963260 0.957041 0.950549 0.943787 0.925722 0.906076 0.884968 0.862518 0.838840 0.814036 0.788203 0.761443 0.733869 0.705617 0.676843 0.647725 0.618453 0.589214 0.560176 0.531462 0.503130 0.487869 0.475145 0.473975
- 3376 - 3857 -4316 -4752 - 5722 - 6504 - 7080 - 7438 -7568 - 7462 -7114 - 6517 - 5666 -4555 -3180 - 1535 381 2570 5035 7776 10793 12551 14088 14233
sOnY+)
SC?*)
0.0074 0.0071 0.0075
o.cQ65 0.0335 0.0481
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
543
documented least-squares procedures. (g*l ‘) These values are given in table 2 together with their standard deviations s and, at the bottom of the table, standard deviations for observations of unit weight for the four different correlating equations. Table 3 contains a table of activity and osmotic coefficients, activities (a,, of H,O and excess Gibbs energies G’” calculated at selected molalities using equations (1) and the coefficients given in table 2. Standard deviations of calculated values of 4, In Ye, and y+ at selected molalities are given at the bottom of table 3. -Since the calculation of y* involves some uncertainty concerning the extrapolation from zero to the lowest measured molality, the values of y-+ calculated from the four different correlating equations will differ. At m = 5.5105 mol. kg- ‘, y* is calculated to be 6.386,6.488,6.349, and 6.292 using equations (l), (2), (3), and (4) respectively. 4. Estimates
of error and comparison
with previous results
The random error associated with a measured osmotic coefficient is proportional to the quantity {(sSm"/m,)2+(s,me/mr)2)1'2, where s, and s, are, respectively, the standard deviations for the salt under investigation and the reference salt at the molalities, m, and m,, at which the salts are in isopiestic equilibrium. This quantity, as calculated using the estimated standard deviations given in table 1, is greatest at the lowest molalities (it is 0.008 at m{Ni(NO,),) = 0.0526 mol. kg-‘) and then steadily decreases to an approximate average value of 0.0012 for molalities greater than 1 mol. kg- ‘. A comparison of estimates of random error, as obtained from the above quantity, with the individual deviations of the measured osmotic coefficients from the fit shows that the scatter of the points about the fit is completely accounted for in terms of the random errors associated with the individual measurements. Estimates of systematic errors and their propagation to the osmotic coefficients are given in table 4. We make a final estimate of error, random plus systematic, of 0.009 for the osmotic coefficients over the entire molality range. The relation of earlier work to our measurements is shown in the deviation plot of figure 1. The work of Ryabov ef al. (12) had earlier”’ been taken to be the most TABLE 4. Estimates of systematic error
Quantity
Estimate of possible systematic Effect of estimate of systematic error on 4 error in quantity low molalities high molalities
molahty of Ni(NO,), stock solution molality. . of CaCI, stock solution impurities m Nt(NO,), impurities in CaCl, impurities in NaCl isopiestic technique : temperature gradients, non-equilibrium between solutions, vaporization effects, etc.
0.3 per cent 0.05 per cent 0.1 per cent 0.1 per cent 0.1 per cent 0.1 per cent at the highest molalities to 1.0 per cent at the lowest molalities
0.002 0.0004 O.CUO6 O.WO4 0.002 0.009
0.007 0.0006 o.ooo2 O.oool 0.002 0.002
total in quadrature
0.010
0.008
M. SARBAR ET Al..
544
0
AA 0
-0.02 - ‘,
o +
a -0.04 I 0
0 0
:
0 0
. .
0
0 :-:-L-~&--4 1
2
I 0
0 iJ-----d 3
! 4
5
6
m/(tnol~kg-‘)
FIGURE 1. Plot of {#(ohs.)-4(calc.)) for the various sets from our final fit, using equations (I), asa function of the molality. v’, Dieterici,“s) vapour-pressure measurements; + , Frolov et aI.,‘r3) isopiestic measurements (reference salt was not specified by the authors); A, Jones et 01.. t14) freezing-temperature depressions; A. Jones and Pearce,“” freezing-temperature depressions; +, King et al., (r6’ freezing-temperature depressions; 0, Ryabov et al.,(’ *) .rsopiestic measurements (reference salt was not specified by the authors); 0. Yakimov and Guzhavina,“” vapour-pressure measurements; x , this work, isopiestic measurements, reference salt is NaCl ; 0, this work, isopiestic measurements, reference salt is CaCI,.
reliable, but it is seen to differ by as much as 0.03 in 4 from our measurements. These workers(‘2) give few details about their experimental procedures and we are thus unable to explain the observed differences. M.S. thanks the University of Tabriz, Iran, for the award of a scholarship. R.L.N. and R.N.G. acknowledge support by the U.S. Department of Energy and the Office of Standard Reference Data of the National Bureau of Standards. These measurements were performed while R.N.G. was on secondment at the Department of Physical Chemistry, University of Newcastle-upon-Tyne, during 1980.
REFERENCES 1. Goldberg, R. N.; Staples, B. R.; Nuttall, R. L. J. P&x C/rem. Rej Data 1979, 8, 923. 2. Analar Standards for Loboratory Chemicals. Analar Standards: Poole, Dorset, England. 1977. 3. Charlot. G.; Bezier, D. Quanfitafive Inorganic Anulysb. Methuen: London. 1957. 4. Analytical Chemistry, Vol. II. Strouts, C. R. N.; GilfiJIan, J. H.; Wilson. H. N.: editors. Oxford University Press: London. 1955.
OSMOTIC
COEFFICIENTS
OF AQUEOUS
NICKEL
NITRATE
545
5. Linke, W. F.; Seidell, A. Solubilities: Inorganic and Metal Organic Compound--A Compilation oj Soluhility Data from the Periodical Literature. Vol. I : A-h, Vol. II: K-Z. Vol. I : Van Nostrand: Princeton, New Jersey. 1958; Vol. II: American Chemical Society: Washington, D.C. 1965. 6. Sieverts, A.; Schreiner. L. Z. Anorg. Chem. 1934, 219, 105. I. Platford, R. F. Activity Coeficients in Electrol.vte Solutions, Vol. I. Pytkowicz, R. M.: editor, CRC Press: Boca Raton, Florida. 1979. 8. Hamer. W. J.; Wu, Y. C. J. Phys. Chem. Ref. Data 1972, 1, 1047. 9. Staples, B. R.; Nuttall, R. L. J. Phys. Chem. Ref. Dara 1977, 6, 385. 10. Pitzer. K. S.; Mayorga, G. J. Phys. Chem. 1973,ll. 2300. 11. Staples, B. R.; Nuttall, R. L. Nafl. Bur. Stand. (U.S.) Tech. Note 928. 1976. 12. Ryabov. V. P.; Ageev. A. A.; Nikolaev, V. P.; Frolov, Yu. G. Tr. Mask. Khim.-Tekhnol. Inst. 1972. 71, 307. 13. Frolov, Yu. G.; Nikolaev, V. P.; Ryabov. V. P.; Ageev, A. A. Termodin. Str. Rastvorov. 1974, 2, 55. 14. Jones, H. C.; Getman, F. H.; Bassett, H. P.: McMaster. L.; Uhler. H. S. Carnegie Inst. Washington, Publ. No. 60. 1907. 15. Yakimov, M. A.; Guzhavina, E. I. Russ. J. Inorg. Chem. (Engl. Transl.) 1971, 16, 934.; Zh. ,h’mrR. Khim. 1971. 16, 1758. 16. King, H. J. S., Cruse, A. W.; Angell. F. C. J. Chem. Sot. 1932, 2928, 17. Jones, H. C.; Pearce, J. N. Am. Chem. J. 1907, 38, 683. 18. Dieterici. C. Ann. Phys. (Leipzig) 1923, 375. 617.