N o tizen 903 T h e V is c o s ity o f A q u eo u s B a C l2 + N a C l
S o lu t io n s *
A nim esh K u m ar Rakshit
D e p a rtm e n t o f C h em istry , F acu lty o f Science, M. S. U n iversity o f B aroda, B aroda, India Z. N atu rfo rsch . 4 2 a , 9 0 3 - 9 0 4 (1987);
received A pril 23, 1987
V iscosities o f th e title solution w ere m easu red at 35, 40, 45 and 50 °C for 0.2, 0.3 and 0.4 M N a C l and 7 B a C l2 concentrations. C o n sid erin g the N a C l solutions as the solvents for B aC l2, the results w ere co m p ared w ith the Jo n es-D o le eq u atio n , the M oulik e q u atio n and the Vand e q u atio n .
A ccording to Jones and D ole [1,2] the viscosity rj o f electrolyte solutions follows the em p irical relatio n
T ab le 1. Viscosities (cp) o f a q u eo u s so d iu m c h lo rid e so lu tions at differen t tem p e ra tu res.
%
= 1 + A ^ C + B C, (1)
w h ere C is the co n cen tratio n o f th e solute and rj0 the viscosity o f the solvent. T he constant A is a th eo retically ju s tifia b le ion — ion in teractio n p a ram eter, and B is an em p irica l ion - solvent in teractio n constant w hich can not be calculated from a m odel [3]. M any single salts have been stu d ied in a q u eo u s m ed iu m [1, 2, 4, 5] and also in m ix ed solvents, b u t th ere are very few studies o f m ixed electrolytes in aq u eo u s so lution [6, 7],
In existing viscosity studies on m ixed aq u eo u s electro lytes th e ratio o f the co ncentrations o f the electrolytes was k e p t constant [6, 7], In the present study, so d iu m ch lo rid e- w a ter m ixtures w ere considered as solvents and the effect o f B aC l2 was stu d ied . T h e solvents used w ere 0.2, 0.3 and 0.4 m o la r in N aC l.
B arium chloride (G R ) and so d iu m ch lo rid e (A R ) w ere fro m BDH , India, and w ere used w ith o u t fu rth e r p u rific a tion. T he w ater used was d o u b le distilled. An O stw ald visco m eter w ith a flow tim e o f 213 sec for w ater at 30 °C was used. T he v iscom eter and the 10 ml p y k n o m eter w ere cleaned with alkali, su lp h u ric acid and d istilled w ater, in th a t o rd er, before use. T h e tem p e ra tu re o f the b a th was co n tro lled to ± 0.02 °C.
T ab les 1 and 2 show the exp erim en tal results. O n fitting (1) to these, in accordance w ith [8] very low positiv e values o f A w here found, show ing th at the solute - solute in te r
actio n s are small. T h e B values o b tain ed by fitting a s tra ig h t line to the d a ta are presen ted in T ab le 3. T h e B v alu e for B aC l2 in w ater at 35 °C was found to be 0.282 1/mole (lite ratu re value 0.285 [9, 10]).
* A m ajo r p a rt o f th is w ork was done at the C h em istry S ection. U D C T , th e U niversity o f B om bay, B om bay, India.
R e p rin t request to Dr. A. K. R akshit, D e p a rtm e n t o f C h em istry , F aculty o f Science, M .S. U n iversity o f B aroda, B aro d a, India.
Solvent o n 40 °C o U O o U
0.0 M 0.719 0.653 0.596 0.547
0.2 M 0.733 0.660 0.598 0.556
0.3 M 0.738 0.665 0.603 0.561
0.4 M 0.752 0.672 0.617 0.568
T able 2. R elativ e viscosities w /«0 o f solutions o f BaCl-> in a q u eo u s N aC l at d iffere n t tem p eratu res.
C o f BaC l2 Lo o o O o U IT) o U un O o u (m o le s/lite r)
0.2 M a q u eo u s N aC l solution
1.173 1.353 1.374 1.393 1.403
0.9385 1.280 1.299 1.309 1.318
0.7508 1.224 1.242 1.251 1.259
0.6006 1.177 1.191 1.201 1.205
0.4805 1.141 1.155 1.161 1.164
0.2803 1.085 1.091 1.097 1.101
0.1730 1.053 1.056 1.060 1.065
0.3 M a q u eo u s N aC l so lution
1.173 1.355 1.371 1.377 1.389
0.9385 1.274 1.278 1.305 1.314
0.7508 1.222 1.224 1.247 1.255
0.6006 1.178 1.177 1.197 1.203
0.4805 1.142 1.146 1.158 1.162
0.2803 1.084 1.086 1.093 1.098
0.1730 1.053 1.054 1.058 1.061
0.4 M a q u eo u s N aC l so lution
1.173 1.310 1.333 1.337 1.356
0.9385 1.257 1.274 1.276 1.285
0.7508 1.207 1.220 1.224 1.229
0.6006 1.164 1.177 1.175 1.180
0.4805 1.130 1.141 1.144 1.144
0.2803 1.077 1.085 1.086 1.092
0.1730 1.048 1.051 1.052 1.056
T ab le 3. B values (1/m ole) fo r BaCl2 solutions in aqueo us N aC l at d ifferen t tem p eratu res.
Solvent 35 °C O o U O O O o U
0.2 M N aC l 0.301 0.318 0.333 0.344
0.3 M N aC l 0.283 0.301 0.315 0.327
0.4 M N aC l 0.260 0.279 0.293 0.306
T he results m ay be su m m ariz ed q u a litativ ely as follows:
(i) T he viscosities in crease w ith increasing N a C l and B aC l2 co n cen tratio n s, w hich im plies rj > r/0, and d e crease w ith increasing tem p e ra tu re.
(ii) ij/ris increases w ith increasin g tem p eratu re.
(iii) T he increase o f rj w ith increasing B aC l2 co n cen tratio n is the sm aller the larg e r th e N a C l concentration.
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904 N o tizen T ab le 4. P aram eters o f (2) and (4) for a q u e o u s B aC l2- N aC l solutions.
T em p. °C M ou lik Eq. (2)
/ M
[(1/m ole)2]
V an d Eq. (4)
V° (extrapolated) [cm V m ole]
B aC l2-0.2 M N aC l
35 1.158 0.522 120.38
40 1.174 0.556 129.60
45 1.182 0.585 138.34
50 1.189 0.602 145.81
B aC l2-0.3 M N aC l
35 1.160 0.506 121.01
40 1.160 0.522 123.15
45 1.181 0.560 134.15
50 1.189 0.579 140.55
B aC l2-0.4 M N aC l
35 1.152 0.449 109.80
40 1.164 0.485 118.48
45 1.166 0.491 121.11
50 1.168 0.521 127.49
Possible exp lan atio n : T h e viscosity increases w ith in creasing solvation o f th e ions. T h en (ii) w ould show th at th e solvation o f B a2+ is less te m p e ra tu re d e p en d e n t th an th e solvation o f N a +, and (iii) w ould show th a t the solva
tio n o f the ions decreases w ith increasing co n ce n tra tio n o f the ions.
A ccording to M oulik [11], for c o n cen trated so lutions
(.r,/ri0) 2 = I + M C2 , (2)
w here / and M are constants. Plots o f rj2x vs. C 2 w ere d one, and the com p u ted values o f / and M are g iven in T ab le 4.
T h e correlatio n coefficients (0.96 - 0.98) w ere fo u n d to be not as good as for rj vs. C plots (0.992 — 0.996).
Vand [12] suggested th e e q u atio n
In 2.5 0
\ - Q 0 ' (3)
w h ere Q is a g eneralized p a rticle in te ra c tio n coefficient a nd 0 the volum e fractio n o f the solute. A re a rra n g e m e n t o f (3) gives
2.5 C 1
2.303 l o gW vo) (4)
w here V is the p a rtial m o lar v olum e o f th e solute. O n p lo ttin g the 1. h.s. o f (4) vs. C, re aso n ab le stra ig h t lines w ere o b tain ed (co rrelatio n coefficient 0.95 to 0.996). T h e in tercepts with the o rd in ate gave the F° v alu es o f T ab le 4.
B values calculated w ith th e e q u atio n
B [1/mole] = 2.5 • 10~3 K° [cmVmole] (5) did not tally w ith the B values o f T ab le 3 b u t w ere o f the sam e o rd er o f m ag n itu d e, as has b een fo u n d for o th e r system s [14] too.
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