Indi an Jo urn al of Chemi stry
Vol. 43A, September 2004, pp. 1872-1 875
'-
Densities and partial molal volumes of
sodium tetrafluoroborate aqueous
solutions at 20 0 e
Willi am J Crooks 111 *"
Westing ho use Savann ah Ri ver Co mpany,Savann ah River
Technology Center, A iken, SC 29808, USA
E mail: croo ks@ lanl. gov
and
Jerry D Christi an
3 122 Ho mes tead Lane, Id aho Fall s, ID 83404-7 195, US A
Emai l: j erryc @s rv. net
Received 19 A llg lls! 2003; revised 5 Jllll e 2004
Densities o f solutio ns o f NaBF4 in H20 have bee n determin ed
at 20.00 °C over th e co ncentrati o ll range 0.05 to 9.0 mo lal (0 to 50
wt%) NaBF4. T he result s are re presented by d (g/mL, 20 c C) =
9.726x I 0') 111 3 - 3.2 157x I 0.3 11/ 2 + 6.7447x 10·2 11/ + 0.99843, where
d is densit y and III is mo lality . Thi s equati o n has been used to
derive cO llcentrati ve properti es fo r NaBF4 solu tio ns. The raw
density data have bee n used to deri ve parti al molal vo lumes. T he
part ial mo lal vo lume at infinite diluti o n is 37.6 ± 2.7 mLimo l at
20°e. The pa rti al molal vo lume at 20°C is represe nted by y, =
37.5 + 9.22111 "2 - 2.92111 fro m 0 to 2.5 11/ NaB F4 and II, = 44 .6 +
0.08 1111 fro m 2.5 to 9 11/ NaBF4 .
7
IPC Code: Int C I. GOI N 9/04
An alytical data and pl a nt solution co mpos iti o ns are
ofte n reported in mo larity units. Dens iti es of sa lt
soluti ons are needed to convert the co ncentrati ons to
molal basis in order to lI ~ :!i ze physical property data
th at have been es tabli shed on a nlv : ~d basis, for
exa mpl e, solution reacti o n equilibrium co nstants or
acti vity coeffi cients. W e report he re the dens iti es at
20.00°C of sodium tetrafluoroborate (N aBF4)
so luti ons from 0 .05 molal to 9 .0 molal, near saturati on
of 9.2 mo lal.
Experimental
Sodium tetraflu oroborate, 98%, Chemi cal Abstracts
Service Registry Number 13755-29-8, a n off-grey
solid obtained from ACROS , was purifi ed by
recrystalli zati on from water, according to the
procedure of Platford ' . The NaBF4 (1 25 .8 g) was
added to 60 mL of hot Millipore wate r to dissolve it.
"Present address: Los Al amos Nati onal Laborato ry, MS G-7 30,
Los A lamos, NM 87545 , USA
The cooled solution was separated from the
precipitated crystals by suction filtration . A bl ack
solid depos ited o n the surface of the filter paper and
white NaBF4 crystals were on top of them . The white
crystal s (74. 1 g, 59 % recovery) were phys icall y
separated from the mixture of bl ack solie! and white
c rystals. Thi s NaBF4 was dri ed to a cons tant weiato ht in
a dryin g ove n at 120°C and stored in a desiccator until
use.
Soluti ons of NaBF4 were prepa red by weighin g th e
dri ed cry stals and adding degassed Millipore H20 by
weight. M asses were dete rmin ed o n an analyti cal
balance of 0 .1 mg sensiti vity that was calibrated
against NIST-traceabl e standard weights and were
co rrec ted for air bouya ncy. The NaB F4 masses ranged
from 0 .28 g to 5.93 g in 50 to 6. 0 g of H2 0 ,
respecti ve ly. Thus, the so luti on mo lal concentrat ions
were measured to an accuracy of 0 .04% at th e lowest
concentrati on to 0.003% at the hi ghes t conce ntra ti o n.
The indi vidual soluti on concentrati o n uncertainti es
are re ported w ith the res ults.
Densiti es were dete rmined w ith an Anton Parr
2
DNA 4500 osc illating U-tube de nsity meter . T he
techni cal specificati on for standard dev iati on in
re peatability is stated to be 0.0000 ] g/cm 3 . So urces
a nd magnitudes of error are di scussed by Fitzgeral d
fo r th e Anton Paar DMA 5000 de nsity meter3 . For
so luti o ns w ith a limited viscos ity range of less th an 30
mPaes, the maximum error is less th an 0 .000015
g/c m 3 . The DMA 5000 has a techn ical spec ifi cat ion
6
for standard dev iati on in repeatabili l:Y of I x I 0- g/c m"
a n order of magnitude less th an for the DM A 4500.
Thus, a max imum e rror for the DMA 4500 of
approxim ately 0 .00015 g/c m 3 mi ght be co nservatively
assumed (less th an 0 .015 % fo r the curre nt
meas ure ments). The foll owing precisi ons reflect
actu al measure me nt vari abilities, w hich are sli ghtl y
greater than these best poss ible specifications.
Three measureme nts were taken at each
concentrati on and ave raged for solu tions up to 1.5
mol al NaBF4 and two measure ments were averaged
for hi gher concentrati ons. The maxi mum vari ability
of an individu al measure ment from the average was
0 .02% or less for all but one o f the 23 data po ints,
which had a maximum variability of 0.04%. Th e
average standard deviation of meas ure me nts was
0 .00016 g/mL (0 .013 %). The instrument calibrati on
NOTES
was checked with boiled (degassed) Millipore H 2 0
«18 MOhms) (density at 20°C, 0.998204 g/mL)4,5
after each series of measurements at a concentration.
The calibration correction thus determined started at
-0.0 I % and gradually changed in a reg ul ar fashion to
+0. 13 % as the measurements progressed from th e
lowest co ncentratio n to the hi ghest in order. Thi s may
be due to a slight co rrosio n of the cell by the Na BF4
soluti ons. The calibration correcti ons are considered
to be good to 0.0 I % of the meas ured value.
The results of the instrument were checked by
determining the densities of the nomin al 1.0 and 9.0
molal NaBF4 so luti o ns fro m the mass of soluti o n
contai ned in a 10 mL Gay-Lussac spec ific gravity
bottl e at 20.00 °C and by measurin g the mass of
so luti o n delivered from a I mL pipette. The vo lumes
of the bottle and pipette we re calibrated with water
(standard dev iation of 5 measurements, 0 .003 % for
the bottle and 0.025 % for the pipette). Five
determinati o ns were made by each method for each
so lution, except that o nl y o ne measurement was made
o n the 9 mo lal soluti on w ith the specific gravity
bottl e. The results agreed with the density meter
measure ments within 0 .04% in a ll cases as follows: I
III
NaBF4 (pipette 0 .01 % differe nce, standard
deviati o n 0.06 %; specific g ravity bottle 0 .04%
difference, standard deviation 0.03 % ); 9 /II NaBF4
(pipette 0.02 % difference, standard deviat io n 0.09%;
specific g ravi ty bottle 0.02 % difference, sin gle point).
In all th e cases, the density meter read hi ghe r th an the
o thers . These results validate the density mete r
measure ments th at are used in the a na ly sis and data
reducti o n.
Temperature (lTS-90) was controll ed and measured
to within O.OI °C w ith two integrated NIST-traceab le
100 ohm platinum resistance thermo me ters. The
temperature was controlled to 20.00±0.0 I
This
correspo nds to an uncertai nty in den si ty of ±0.0002%.
The overall uncertainty in the averaged densi ty
measure ments is judged to be less than 0.03 %, based
o n the pooling of 2 times the average standard
deviation of meas urement (0.02%) and 2 times the
estimated error of calibrati o n correcti on (0.02%) . The
combined uncertainties in individual measure ments of
molality and de nsity (pooled) are less than 0 .05 % at
the lowest concentration to less than 0.03 % at the
highest concentration.
0c.
1873
Table I-Experimental values of NaBF4 solution de nsities at
20.00°C
NaBF4
Cone. , molal
Uncertainty
in Cone.,"
molal
Density,
g/mL
Uncertainty
in Density,b
g/mL
0.05018
0. 10020
0. 19960
0.29953
0.39971
0.49934
0.99611
1.4947
1.9909
2.4885
2.9927
3.4955
4.0035
4.4898
4.9857
5.4797
5.9982
6.4785
6.9477
7.4944
7.9971
8.4896
8.9823
0.00002
0.00002
0.00004
0.00004
0.00004
0.00004
0.00004
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
1.0018
1.0053
1.0121
1.0186
1.0252
1.0316
1.0629
1.0915
1.11 87
1.1485
1.1744
1.1995
1.2232
1.2462
1.2670
1.288 1
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
"Based on 0.000 I g un certainty in measured masses of NaBF4 and
H 20.
bBased on the pooled errors of 2 times average standard deviation
of measurement and 2 times the estimated error of instrumen t
calibration correction.
The data are well fitted by the equ ation
The experimental data are summarized in Table 1.
Including the 0 molal data point of 0.99820 glmL,
= 9 .726xlO· 511l 3
3.2 157x lO·311 ? +
6.7447xlO,2 m + 0.99843, R2 = 0.99997
d (g/mL, 20°C)
-
where m is molality and d is density. This equation
was used to deri ve concentrative properties for NaBF.j
soluti o ns in tabul ar form (see T able 2) ide ntica l to
those provided for solutions in the CRC Handbook of
6
Chemistry and Physics . The heading notation s are
identical to the CRC Handbook: (p = dens ity, g/mL =
O.99997x D;o, D;~ = specific grav ity at 20°C =
D;o /0.99823,
Results and discussion
1.3090
1.3244
1.3437
1.3648
1.3822
1.3991
1.4152
C.
= NaBF4
concentration, giL, M =
molar concentration, g-moIlL, C w = tota l water
concentration, giL and (Co - C w) = water displaced by
anhydrous solute, giL)
INDIAN J CHEM, SEC A, SEPTEMBER 2004
1874
Table 2-Concentrative properties of NaBF4 aqueous solutions at 20°C
NaBF/fo
p, g/mL
20
D20
C,.g/L
M, g-mollL
Cw.g/L
(Co - C w )
giL
1.0014
1.0045
1.0077
1.0109
1.0141
1.0173
1.0206
1.0238
1.0271
1.0303
1.0336
1.0369
1.0402
1.0436
1.0469
1.0503
1.0536
1.057 1
1.0605
1.0639
1.0708
1.0778
1.0848
1.0920
1.0991
1.1 065
1.1138
1.1213
1.1288
1.1 365
1.1520
1.1679
1.1843
1.2010
1.21 82
1.2359
1.2540
1.2727
1.2918
1.3115
1.3317
1.3526
1.3740
1.3960
1.4186
1.0031
1.0063
1.0095
1.0127
1.0159
1.0191
1.0224
1.0256
1.0289
1.0322
1.0355
1.0388
1.0421
1.0454
1.0488
1.052 1
1.0555
1.0589
1.0623
1.0658
1.0727
1.0797
1.0868
1.0939
5.007
10.05
15 .12
20.22
25. 35
30.52
35.72
40.95
46.22
51.52
56.85
62.22
67.62
73.05
78.52
84.02
89.56
95.13
100.74
106.39
117 .79
129.33
141.03
152.87
164.9
177.0
189.4
201.8
21 4.5
227.3
253.4
280.3
307.9
336.3
365.5
395.5
426.4
458.2
490.9
524.6
559.3
595.1
632.0
670.1
709.3
0.04560
0.09 149
0.1 377
0.184 1
0.2309
0.2780
0.3253
0.3730
0.4209
0.4692
0.5178
0.5667
0.6158
0.6653
0.7151
0.7653
0.8157
0.8665
0.9 176
0.9690
l.0728
1.1780
1.2845
1.3924
1.5017
1.6124
1.7246
1.8383
1.9534
2.0702
2.3083
2.5530
2.8044
3.0629
3.3286
3.6020
3.8833
4.1729
4.4710
4.7780
5.0943
5.4203
5.7564
6.1029
6.4603
996.4
994.5
992.6
990.7
988.8
986.8
984.8
982.9
980.8
978.8
976.8
974.7
972.6
970.5
968.4
966.3
964.1
961.9
959 .7
957.5
953.0
948.4
943.8
939.1
934.3
929.4
924.5
919.5
914.3
909.2
898.6
887.6
876.4
864.7
852.8
840.4
827. 7
814.5
800.9
786.9
772.4
757.4
74 1.9
725 .9
709.3
1.9
3.8
5.7
7.6
9.5
II.5
13.5
15 .4
17.5
19.5
21.5
23.6
25.7
27.8
29.9
32.0
34.2
36.4
38.6
40.8
45.3
49.9
54.5
59.2
64.0
68.9
73.8
78.8
83 .9
89.1
99.7
110.7
121.9
133.6
145.5
157.9
170.6
183.8
197.4
2 11.4
225 .9
240.9
256.4
272.4
289.0
by wt.
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
10.00
11 .00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00
22.00
24.00
26.00
28 .00
30.00
32.00
34.00
36.00
38.00
40.00
42.00
44.00
46.00
48.00
50.00
I. lOll
1.1084
1.1158
1.1233
1.1308
1.1385
1.1540
1.1700
1.1864
1.2031
1.2204
1.238 1
1.2562
1.2749
1.294 1
1.3138
1.334 1
1.3549
1.3764
1.3984
1.4211
Partial molal vol umes were determined from the
density data as follows . The apparent molal
volume, ~v, was first derived from the raw den sity
values 7 :
¢V
=[ 1000 (do _ d ) + M 2 ]
mddo
d
.. . (1)
where do is the solvent (H 20) density, 0.998204 g/mL
at 20 o e, and M2 is the molecular weight of the solute
NaBF4, 109.794 g/mol. Extrapolation of the apparent
mo lal volume data from 0.05 to 0.5 m NaBF4 to
infinite dilution yielded <l>V<>, the value of <l>V at infinite
dilution, of 37.6 mLimol. This is also the value of
partial molal volume of NaBF4 at infinite dilution , V~I
(ref. 7).
NOTES
1875
As di scussed above, un certainty In individual
densi ty values is estimated to be approx imately
0.0003 g/mL, or less th an 0.03%. The corres ponding
uncertainty in Ijl V is obtained7 by differenti ating Eq.
(1 ) with res pect to d, yielding a probab le error in <P V of
would continue a slight increase, an adequ ate
representati on above 2.5 molal was obtained by fitting
a linear fun cti on to the two points of the 2.5 mol al
value fro m the Redli ch-M eyer equat ion and the 8
molal value from the qu adrati c equ ati on. This
approach yielded a smooth transitIOn between
equ ati ons. The res ulting representati on of the parti al
molal volume (mLimol at 20°C) is, thus,
Th is would correspo nd to an ex perimental uncertai nty
in apparent molal vo lume at the lower limit of 0.05 111
NaBF.j of 15 % (i5.7 mLimol) and 1.4% (i O.6
mLimol) at 0.5 111 Na BF4. (If one co nsiders the pooled
errors of density and molality meas urements of
0.05 %, th e total uncertainty in appare nt molal vo lume
fro m both sources of error becomes 26% and 2.2 % at
0.05 and 0.5 III NaBF4' res pecti vely.) Based on th e
unifo rmity of th e series of density values and th e good
ex trapo lati on to th e infinitely dilute value of 0.9982
g/mL, th e associated uncertainty fo r the extrapolated
apparent molal volume is judged to be approx imately
7% (i2.7 ml /l11ol), correspondin g to iO.O 14%
uncertainty in density at 0.05 111 NaBF4 .
In order to represe nt the apparent 11101al volumes
analyti cally, two regions of data were fitted in
overl apping ranges. The data from 0 to 6 molal NaBF4
were fitted to th e Red li ch-M eyer fun cti on7.8 to yield a
fun cti on suitable to 2.5 molal. To obtain a suitable
fun cti on above 2.5 molal, the data fro m 1 to 9 molal
were fitted to a qu ad ratic fun ction.
Parti al molal volume values, v2 , were then deri ved
from these fun cti ons using th e relati onship7,9
v2 = 3 7.5 +9 . 22 111 "~ -2.92 111
The parti al molal vo lume functi on deri ved from the
quadrati c parti al mo lal volume equati on had a
curvature th at did not quite match the Redli ch-M eyer
value at 2.5 molal and had a slight maximum at 8.5
molal NaBF4 . Considerin g th at the actu al valu es
fro m 0 to 2.5 III NaBF.j
and
v2 = 44.6+0.08 1111
fro m 2.5 to 9 11l NaBF4
Considerin g vari ability in indi vidual values and the
in accuracies of the fitted eq uati ons, the un certainty in
indiv idual calcul ated values is approx imately i 2.7
mLimol at the lower end of the concentrati on range
and i 1 mLimol beyond 2. 5 molal.
References
I Platfo rd , R F, Can J Chell/, 47 ( 1969) 227 1.
2 Anton Paa r G mbh, Anton Paar StraBe 20, A-805 4 Grnz.
Austri a/Europc.
3 Fitzgera ld D, Technical AssesslI/ent of th e AnIOn Poor DMA
5000 Density Meter, 10 Janu ary 2000, H& D Fi tzgera ld Ltd ..
CEfn Du , T remeirchi on, S t. Asaph, LL 17 OUS. UK;
de ni s@ densit y.co. uk.
4 Jones F E, JNMM , Febru ary (1990), 26.
5 Kell G S, J Chell/ Eng Data, 20 ( 1975) 97.
6 Wo lf A Y, Brow n M G & Prenti ss P G, Co ncent rati ve
Properti es o f Aq ueo us Solutio ns: Con version Tables. CRC
Handbook of Chell/ istry and Physics, 66 th Ed iti on, (C RC
Press, Inc ., Boca Rato n, Flori da), 1985, R. C Weast, Ed .-in C hi ef, M J Astl e & W H Beyer, Assoc. Eds., D-219
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Transport Processes, (Wi leyInterscience Di visio n of John Wiley & Sons, Inc., New York),
1972, Chapter 13.
8 Owe n B B & Bri nkl ey S R, Chelll Rev, 29 ( 194 1) 4 1.
9 Lewis G N, Randall M, Pitzer K S & Brewer L.
Therlllodynalllics, 2nd Editi on, (McGraw-HilI Book Compan y,
In c., Ne w Yo rk), 196 1, 207.