Osmometry in Vapour Phase. I.
Osmotic Coefficients of Some Electrolytes at 40°C
F . K O P E C K Ý a n d A. D Y M E Š
Department of Physical
Chemistry,
Faculty of Pharmacy,
Bratislava 1
Komenský
University,
Received S e p t e m b e r 24, 1971
The scope of t h e applicability of o s m o m e t r y in v a p o u r p h a s e t o t h e s t u d y
of aqueous solutions w a s t e s t e d b y d e t e r m i n i n g t h e osmotic coefficients
of six electrolytes of different t y p e a t 40°C.
It is the c o m p a r a t i v e isopiestic m e t h o d [ 1 , 2 ] which w a s m o s t l y used for t h e d e t e r m i n a tion of the osmotic coefficients of electrolytes a n d non-electrolytes h i t h e r t o listed a t t h e
temperatures differing from t h e freezing p o i n t or boiling p o i n t of a q u e o u s solutions.
The solutions of NaCl a n d KCl are usually u s e d as reference s t a n d a r d s . T h e osmotic a n d
activity coefficients of t h e s e s t a n d a r d s h a v e been established b y a direct b u t difficult
determination of w a t e r a c t i v i t y or c a l c u l a t e d from e l e c t r o m o t i v e forces. T h e a c c u r a t e
isopiestic m e t h o d is generally applicable over t h e whole t e m p e r a t u r e r a n g e b e t w e e n
the freezing a n d t h e boiling p o i n t s of solution. Nevertheless, a t lower c o n c e n t r a t i o n s
some difficulties a p p e a r a n d t h e molality m = 0.1 is considered t o be t h e lower limit
of applicability for b i n a r y electrolytes [1]. T h e c o m m o n c o n c e n t r a t i o n s of physiological
solutions, however, v a r y j u s t a t t h e p r o x i m i t y of t h a t limit.
In the cases of t h e solutions of similar or g r e a t e r dilution only osmotic d a t a d e t e r m i n e d
from freezing p o i n t depression or boiling p o i n t elevation a t n o r m a l pressure are often
available a n d practically used. D a t a o b t a i n e d a t o t h e r t e m p e r a t u r e s are r a t h e r scarce.
The osmotic coefficients of a limited n u m b e r of electrolytes calculated from t h e a c t i v i t y
coefficients on t h e basis of t h e Gibbs — D u h e m e q u a t i o n m a k e e x c e p t i o n [1] (p. 53).
The activity coefficients a r e o b t a i n e d b y m e a s u r i n g t h e electromotive force of corresponding galvanic cells t h e realization of w h i c h is n o t practically feasible w i t h a n u m b e r of
other electrolytes. Conversely, it w o u l d be useful t o o b t a i n t h e a c t i v i t y coefficients b y
calculation from t h e osmotic coefficients in t h i s case [2] (p. 263).
The aim of t h i s s t u d y w a s t o t e s t t h e possibility of using o s m o m e t r y in v a p o u r p h a s e
for the determination of osmotic coefficients of s u b s t a n c e s in dilute a q u e o u s solutions
at 40°C. Since t h e m e t h o d is of c o m p a r a t i v e c h a r a c t e r , t h e s u b s t a n c e s selected for t h e
first experimental s t u d y involved some electrolytes of different t y p e s ; a m o n g t h e m
a suitable s t a n d a r d s u b s t a n c e could b e found. O s m o m e t r y in v a p o u r p h a s e w a s described
mainly as a r a p i d a n d simple m e t h o d for t h e d e t e r m i n a t i o n of molecular weights of t h e
substances dissolved in n o n - a q u e o u s solvents, e.g. b e n z e n e [3, 4]. I t h a s n o t often b e e n
used for aqueous solutions [9, 5] because of t h e necessity of m o r e c o m p l i c a t e d i n s t r u m e n t a l
e
quipment.
Experimental
Chemicals
The anal, g r a d e salts w i t h o u t further purification were used e x c e p t e p h e d r i n e chloride
(EPHC1) which w a s recrystallized from a q u e o u s e t h a n o l a n d dried carefully a t a b o u t
Wem. zvesti 26, 327-332 (1972)
327
F . K O P E C K Ý , A. DYME;
110°C. I n a similar w a y , s o d i u m a n d p o t a s s i u m salts w e r e dried. T h e concentration of
M g S 0 4 a n d Z n S 0 4 solutions w a s d e t e r m i n e d c h e l a t o m e t r i c a l l y (eriochrome black T
while t h e w e i g h t e d a m o u n t w a s used for t h e calculation of t h e c o n c e n t r a t i o n of other
salts.
Equipment
and
measurements
T h e m e a s u r e m e n t s were m a d e w i t h a D a m p f d r u c k o s m o m e t e r K n a u e r Model Щ
i n s t r u m e n t using a t w o - t h e r m i s t o r p r o b e s u i t e d for all k i n d s of solutions. A t t h e terminal
p o i n t s of t h e p r o b e t h e t h e r m i s t o r s w e r e isolated b y sealing t h e m i n t o t h e glass capillaries
r o u n d w h i c h a m i n i a t u r e corrosion r e s i s t a n t m e t a l spiral w a s coiled. Consequently.
a s a m p l e of solution p u t o n t h e first t h e r m i s t o r b y m e a n s of a syringe a s well as рик
w a t e r p u t on t h e second o n e does n o t form a r o u n d e d d r o p b u t s p r e a d s along the spiral
on t h e whole surface of capillaries. T h e v a p o u r cell w h e r e t h e p r o b e w a s placed щ\
electronically t h e r m o s t a t e d .
Table 1
D e p e n d e n c e of t h e c h a n g e in t h e r m i s t o r resistances (AR) on t h e m o l a t i l y (m)
of NaCl solutions
AR
Q
I
II
0.04
0.07
0.10
0.14
0.17
0.20
41.0
73.0
101.5
144.0
173.5
205.0
k\
1024.3 ± 6.7
41.0
72.0
104.5
145.5 *
175.0
205.0
1031.0 ± 8.1
k\ — co3rficie:it in e q u a t i o n (1).
T h e t h e r m o m e t r y device of t h e o s m o m e t e r ( T e m p e r a t u r - M e ß g e r ä t Knauer) was
c o n n e c t e d w i t h a n electronic line recorder e K B T 1 ( V E B ) . T h e r e c o r d e d deflection
c o r r e s p o n d e d t o t h e arisen difference b e t w e e n t h e t h e r m i s t o r resistances AR. In the
circuit b e t w e e n t h e , p r o b e a n d t h e t h e r m o m e t r i c device a d e c a d e resistance was placed
b y m e a n s of w h i c h t h e deflection w a s c a l i b r a t e d a n d t h e r a n g e of t h e recorder changed.
P r o v i d e d a q u e o u s solutions were u s e d a t t h e t e m p e r a t u r e of t h e v a p o u r cell (40°C)
a b i t h e r m a l distillation e q u i l i b r i u m w a s e s t a b l i s h e d b e t w e e n t h e s a m p l e of solution
o n t h e first t h e r m i s t o r a n d w a t e r on t h e second one in 2 — 3 m i n u t e s . F o r t h e higher
c o n c e n t r a t i o n s used, t h e arisen difference b e t w e e n t h e resistances of t h e r m i s t o r s AR w«
a s m u c h as 250 Q. a n d it d i d n o t u s u a l l y v a r y b y m o r e t h a n ± 1 Q . T h e zero position ot
b l a n k t e s t (water o n b o t h t h e r m i s t o r s ) d i d n o t c h a n g e in r e p e a t e d measurements with
s t e a d y - s t a t e i n s t r u m e n t b y m o r e t h a n 3 Q in one h o u r .
T h e long t e r m s t a b i l i t y of t h e r m i s t o r s w a s e x a m i n e d b y occasional measurement;
of t h e NaCl solutions w h i c h were used as s t a n d a r d for t h e d e t e r m i n a t i o n of osmotic
328
Chem. zvesti 26, 327-332 (197i)
OSMOMETRY IN VAPOUR PHASE. I
Fig. 1. D e p e n d e n c e of t h e c h a n g e in t h e r m i s t o r
resistances (AR) on t h e m o l a l i t y of solution (га)S o l u t i o n s : o NaCl, A Na2SC>4, D CuSC>4.
0.00
0.05
0.10
020 m
0.15
coefficients. T w o series of m e a s u r e m e n t s m a d e o n e b y o n e in a half-year p e r i o d of t i m e
are given in T a b l e 1. T h e observed difference b e t w e e n t h e series / a n d II is still w i t h i n
the limits of e r r o r s c a u s e d b y o t h e r factors.
The solutions of o t h e r e l e c t r o l y t e s w e r e m e a s u r e d a t e q u a l or similar c o n c e n t r a t i o n s
as the NaCl solutions. T h e r e a r e t h r e e t y p i c a l d e p e n d e n c e s of AR o n t e m p e r a t u r e w h i c h
are presented in F i g . 1. Considering t h e p i c t u r e d form, t h e r e l a t i o n s h i p b e t w e e n AR a n d
molality ra w a s t e s t e d b y t h e least-square m e t h o d u s i n g b o t h linear (1) a n d q u a d r a t i c (2)
functions:
AR =
kirn,
(1)
2
AR = kirn -f & 2 ra .
(2)
The suitability of t h e s e expressions w a s j u d g e d a c c o r d i n g t o t h e m a g n i t u d e of t h e
calculated s t a n d a r d errors of coefficients k\ a n d k^. I t w a s f o u n d t h a t t h e linear f u n c t i o n
(l)was convenient for t h e s t u d i e d electrolytes of u n i - u n i v a l e n t t y p e / — / i n t h e investi­
gated c o n c e n t r a t i o n r a n g e while t h e q u a d r a t i c f u n c t i o n (2) h a d t o b e u s e d for o t h e r
electrolytes. T h e coefficients k\ a s well as t h e s t a n d a r d e r r o r s for N a C l a r e given i n T a b l e 1
while these values t o g e t h e r w i t h coefficients кг for o t h e r electrolytes a r e p r e s e n t e d in Ta­
ble 2.
Table 2
Coefficients of t h e r e l a t i o n s h i p b e t w e e n AR a n d m o l a l i t y
E q u a t i o n s (1) a n d (2)
Electrolyte
*i
KCl
KC104
KNO,
EPHC1
1004
996
997
972
^n. zvesti 26, 327-332 (1972)
±8
13
8
14
14
Electrolyte
ki
CuS04
MgS0 4
ZnS04
Na2S04
679
685
623
1402
±8
К
±8
14
20
30
25
-490
-609
-160
-950
210
190
200
290
329
Г. KOPECKÝ, A. DYMES
Calculation
of activity
coefficients
T h e molal a c t i v i t y coefficient q? of a q u e o u s electrolyte is defined [1] (p. 48) by the
-expression
1000
<p =
—
In ow
(3)
vmMy,
w h e r e a w a n d iWw a r e t h e a c t i v i t y a n d molecular weight of w a t e r respectively, m denotes
t h e m o l a l i t y of electrolyte a n d v is t h e n u m b e r of ions i n t o w h i c h a molecule of electrolyte
is dissociated in solution.
T h e calculation of osmotic coefficients is b a s e d on t h e a s s u m p t i o n t h a t t w o solutions
w h i c h show e q u a l difference b e t w e e n t h e resistances of t h e r m i s t o r s AR h a v e t h e equal
a c t i v i t y of w a t e r a t a given t e m p e r a t u r e . If one of t h e m is considered t o b e a reference
s t a n d a r d a n d d e n o t e d b y i n d e x s, it holds a c c o r d i n g t o e q u a t i o n (3)
M
vgrm = v3 (ps m>s-
T h e solutions of NaCl were chosen as reference s t a n d a r d . H o w e v e r , t h e values of у
found in l i t e r a t u r e d o n o t cover sufficiently t h e i n v e s t i g a t e d c o n c e n t r a t i o n range from
0.04 t o 0.02 m solutions a t 4 0 ° C e v e n if a t e m p e r a t u r e i n t e r p o l a t i o n i n c o r p o r a t e d in Table 3
is u s e d . F o r t h i s r e a s o n t h e c a l c u l a t i o n of q? w a s c a r r i e d o u t b y m e a n s of t h e activity
coefficients of NaCl p u b l i s h e d in a m o r e r e c e n t p a p e r [6] w h i c h covers a considerable
r a n g e of t e m p e r a t u r e a n d c o n c e n t r a t i o n . T h e a c t i v i t y coefficients p r e s e n t e d in t h a t paper
a n d r e l a t e d t o 38°C were a d a p t e d b y i n t e r p o l a t i o n for 40°C. T h e y a r e listed in Table 3.
T h e osmotic coefficients h a v e b e e n c a l c u l a t e d from t h e s e a c t i v i t y coefficients b y a n appro­
x i m a t e n u m e r i c m e t h o d [7] w h i c h is sufficiently a c c u r a t e a n d does n o t r e q u i r e a com­
p l i c a t e d c o m p u t a t i o n a l t e c h n i q u e . All t h e o s m o t i c coefficients o b t a i n e d h a v e been graphi­
cally s m o o t h e d b y p l o t t i n g t h e m a g a i n s t y m a n d t h e s m o o t h e d v a l u e s s o m e of which are
Table 3
O s m o t i c (<p) a n d a c t i v i t y (y) coefficients of NaCl in a q u e o u s solutions a t 40°C
<P
a)
b)
c)
d)
330
0.01
0.02
0.0256
0.04
0.05
0.0576
0.10
0.1024
0.15
0.900
0.870
0.967«
0.959«
0.9536"
0.819
0.943«
0.9400"
0.931«; 0.931*
0.9307*
0.2
0.3
0.726
0.774
0.919«; 0.923*
0.916c
0.958
0.947
0.943
0.932
0.925
0.921
0.916
c a l c u l a t e d from t h e p r e s e n t e d a c t i v i t y coefficients.
i n t e r p o l a t i o n 3 5 - 4 5 ° C ; see [1] (p. 557).
i n t e r p o l a t i o n 25 —60°C; see [1] (p. 550 a n d 556).
s m o o t h e d values.
Chem. zvesti 26, 327-332(197"
OSMOMETRY m VAPOUR PHASE. I
presented in T a b l e 3 h a v e been u s e d for f u r t h e r calculations. I n general, t h e values t h u s
obtained are in good a g r e e m e n t w i t h t h o s e c a l c u l a t e d from t h e a c t i v i t y coefficients
ofNaCl published in a n t e r i o r p a p e r s [8].
The relationship b e t w e e n t h e p r o d u c t <ps ras a n d AR of NaCl solution was expressed
in a simple q u a d r a t i c form
2
AR = Ki <ps ms + K2(cps ms) .
(-5)
The values of coefficients a n d t h e i r s t a n d a r d errors c a l c u l a t e d b y t h e least-square m e t h o d
are
X i = 1086.8 ± 8 . 1 ; K2 = 166 + 66.
By solving e q u a t i o n (J) w i t h respect t o (ps ms a n d s u b s t i t u t i n g i n t o (4) we o b t a i n t h e
expression for t h e calculation of cp of a n a r b i t r a r y electrolyte
9
= ±(-*vm
\
+ )/Ж^Ж').
2K2
V
4Jt2
K2
(в)
J
ÚR of an e x a m i n e d electrolyte c a n b e c a l c u l a t e d for c o r r e s p o n d i n g m from e q u a t i o n (1)
or (2). The osmotic coefficients o b t a i n e d a r e listed in T a b l e 4.
Table 4
Osmotic coefficients of electrolytes d e t e r m i n e d b y o s m o m e t r y in v a p o u r p h a s e a t 40°C
<P
0.04
0.10
0.15
0.20
KCl
KC10 4
KN03
EPHC1
CuS0 4
MgS0 4
ZnS04
Na 2 S0 4
0.919
0.911
0.905
0.900
0.911
0.904
0.898
0.892
0.912
0.905
0.899
0.893
0.889
0.882
0.877
0.871
0.604
0.574
0.550
0.526
0.606
0.569
0.540
0.510
0.566
0.554
0.544
0.535
0.830
0.788
0.753
0.720
EPHC1 — e p h e d r i n e chloride.
Discussion
From the p o i n t of view of t h e factors influencing t h e a p p l i c a b i l i t y of o s m o m e t r y in v a pour phase [3] w a t e r h a s several d i s a d v a n t a g e s w h e n c o m p a r e d w i t h organic s o l v e n t s ,
«•</. benzene. I n p a r t i c u l a r , it is electric c o n d u c t a n c e , a p p r o x i m a t e l y twofold specific
heat, fivefold h e a t of e v a p o r a t i o n , a n d lower p r e s s u r e of s a t u r a t e d v a p o u r .
The conductance of w a t e r a n d a q u e o u s solutions necessitates t h e isolation of t h e r mistors. The sensing e l e m e n t t o g e t h e r w i t h a d r o p of w a t e r or solution h a s t h e n a h i g h e r
heat capacity a n d also a g r e a t e r loss of h e a t . T h i s fact u s u a l l y r e d u c e s t h e so-called efficiency of the a p p a r a t u s [3] a n d e x t e n d s t o g e t h e r w i t h t h e lower v a p o u r p r e s s u r e t h e t i m e
necessary to r e a c h t h e b i t h e r m a l distillation e q u i l i b r i u m , w h i c h is a n y h o w o n l y t e m p o r a r y .
Moreover, t h e established t e m p e r a t u r e difference b e t w e e n t h e d r o p s of solution a n d s o l v e n t
13
much lower here b e c a u s e it is inversely p r o p o r t i o n a l t o t h e specific h e a t of e v a p o r a t i o n .
The shortcomings could n o t be o v e r c o m e q u i t e satisfactorily in m o s t e q u i p m e n t s of older
design [9].
c
b . zvesti 26, 327-332 (1972)'
331
F. KOPECKÝ, A. DÝMEJ
As to the described equipment, the time necessary for the establishment of equilibrium
(2 — 3 minutes) as well as the stability of equilibrium is on the level of the best results
obtained with organic solvents [3]. This fact is evidently due to a special design of thermistor sensing element and a perfect thermostating of vapour cell. Though the pressurt
of saturated vapour of water at 40°C is only about 55 Torr, the results obtained indicate
the possibility of measuring even at lower temperatures.
Owing to the high heat of evaporation, the optimum concentrations of solutions are
higher than those with organic solvents. The concentration range from 0.02 to 0.25 m
may be recommended for an electrolyte of the type I—I while the higher value quoted
does not represent the upper limit of applicability. The above range covers the region
of physiologically important concentrations and moreover it corresponds sufficiently to
the region of applicability of the isopiestic method.
The standard errors of the osmotic coefficients determined (Table 4) follow from
the standard errors of the cofficients ki, k2 or K\, Кг given in Table 3. Thus for the elec­
trolytes of the type I —I they amount to i 1 — 2%, for multivalent electrolytes to
± 3 — 4%. In the case of potassium chloride, this fact may also be verified by comparing
the results with the osmotic coefficients calculated from the activity coefficients [1]
(p. 558). The relatively less favourable results obtained with multivalent electrolytes are
likely due to lower values of the measured AR (except Na2S04, see Fig. 1) as well asto
different properties of their solutions.
The technically simple and rapid osmometry in vapour phase with the use of a modem
equipment is therefore without doubt a useful supplementary method of the determine
tion of osmotic coefficients, especially for those kinds of electrolytes and concentration
regions where neither the measurement of electromotive force nor isopiestic method may
be used. At the same time, the results presented illustrate the possibility of further applica­
tion of this method to the study of aqueous solutions at the temperature close to that of
physiological medium.
References
1. Robinson R. A., Stokes R. H., Electrolyte Solutions, p. 213. (Russian translation.) Izd.
inostrannoj literatury, Moscow, 1963.
2. Lewis G. N., Randall M., Thermodynamics, p. 320. McGraw-Hill, New York, 1961.
3. Biroš J., Chem. Listy 61, 1513 (1967).
4. Van Dam J., Rec. Chim. Pays-Bas 83, 129 (1964).
5. Johnson R. D., Goyan F . M., Tvek L. D., J> Pharm. Sei. 54, 1176 (1965).
6. Truesdell A. H., Science 161, 884 (1968).
7. Mikulin G. I., Voznesenskaja J . E., in the book: G. I. Mikulin (Editor), Voprosypceskoj chimii rastvorov elektrolitov. (Physicochemical Problems of the Solutions of Electrolytes.) P . 150. Chimija, Leningrad, 1968.
8. Lang A. R. G., Aust. J. Chem. 20, 2017 (1967).
9. Baldes E. J., Biodynamics 46, 8 (1939).
Translated by B f Domanský
332
Chem. zvesti 26, 327-332 (1^