Interdiffusion coefficients of thallous sulphate and orthophosphoric acid in H2O and D2O at 35°C by a radioactive tracer technique

Vol. 45. No. 3, pp. 335-339, 1994 Copyright G 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0969-8043194 $6.00 + 0.00

Appl. Radial. hr.

Pergamon

Interdiffusion Coefficients of Thallous Acid in Sulphate and Orthophosphoric Hz0 and D,O at 35°C by a Radioactive Tracer Technique A. DAS Department

of Physics, (Received

and S. N. CHANGDAR*

Bose Institute, 8 October

93/l,

A.P.C.

Road,

1992; in revised form

Calcutta

23 July

700009,

India

1993)

Interdiffusion coefficients of T&SO, and H,PO, solutions into H,O and D,O media with (2@‘TI)TIzSOa and H,j2P0, respectively as tracers have been measured using a sliding cell mechanism, developed in our laboratory, at 35°C. The changes of the diffusion coefficient with increasing concentration are explained by considering the fact that the dielectric constant of the aqueous medium is changed by the introduction of the inorganic salt. The comparison of the values of D in H,O and D,O media in both the cases, at the same temperature, indicates that the addition of the electrolyte affects the two solvent structures differently. The experiments with H,PO, showed the effect of hydration at a particular concentration in H,O and D,O. Some experiments were performed to observe the coupling flow by introducing CaHPO, in the H,PO,-H,O system.

1. Introduction

system for a few concentrations with CaH3*P0, as a tracer by the method developed in our laboratory.

use of inelastic neutron scattering, pulsed N.M.R. techniques, optical measurements and various forms of radioactive tracer techniques has resulted in the accumulation of extensive data on diffusion processes in aqueous solutions (Tyrrell and Harris, 1984) in recent years. The closed capillary method for the determination of self-diffusion coefficients of ions in electrolyte solutions has been developed by Liukkonen, Passiniemi and coworkers (Passiniemi, 1978, 1983; Noszticzius et al., 1976) and has an increase in reliability and precision compared to the diaphragm cell techniques (Mills and Woolf, 1968). The sliding cell technique developed in our laboratory (Changdar, 1970) is also consistent and its reliability can be comparable with any other method developed so far (Changdar, 1973). It has been employed, among other applications, for a systematic study of diffusion in various aqueous solutions using different radioactive isotopes as tracers (Chakrabarti and Changdar, 1992). In this paper we present our results for diffusion measurements in three systems: solutions of thallous sulphate and orthophosphoric acid in water and heavy water with (*““Tl) Tl,SO, and HJ3*P0, as the tracers over a wide range of concentrations and the H, PO,-CaHPO,-H, 0 The

2. Theory and Working Formula for the Present

Method The starting point of the present method of measuring diffusion coefficients in liquids is Fick’s second law of diffusion for unidirectional flow

ac(xJ)_ *

(1)

ax*

In our experiment the non-radioactive part (solvent) of the diffusion column is superimposed on the radioactive part (solute) of equal length and cross sectional area with radioactive isotope concentration c0 at time t = 0. Hence for

t=O c = co for x = 0 to x = I

(2)

c=Oforx=Itox=21

(3)

and

and

acw *Author

a*C(x,t )

at

ax

for correspondence. 335

=- ackt ) c =0

ax

I=0 r;=*

(4)

A. DAS and S. N. CHANGDAR

336

3. Experimental

and for t + cc C = $j for all values of x.

(5)

These boundary conditions reduce (Chakrabarti and Changdar, 1992), the general solution of Fick’s second law to

C(X,t)=++?

1&T

1 n=

n

1.3.5

x cos y

exp{

eniyfD’}](6)

If n ‘Dt

-

412

> 0.5,

all higher order terms in (6) are negligible first approximation. C(x,t)=qCosFlexp(--Kt)

and to a

(7)

where K=n2D/412.

(8)

In our experimental geometry (Fig. l), the tracer part of the solution is in the aqueous radioactive solution of the chosen salt and the detector is placed vertically above the diffusion column, consisting of both the radioactive and nonradioactive part. The count rate observed by the detector at any time t is proportional to the integrated weighted average of c (x,t ) over the variables. Let us consider an element of layer defined by x and x + dx. The count rate dN (x,t ) as recorded by the scaler coupled to counter placed above the diffusion column at time t may be written, dN (x,t) =

~c(X,t)~@I-x)~ +(d-x)

In the sliding cell arrangement, two stainless steel slabs (2.5” x 2” x 1”) are placed one above the other and in turn the cell pair are kept within a brass vessel. The lower slab, which is kept fixed to the brass vessel, contains a central cavity (dia: 0.4-0.6 cm and length: l-2cm) filled up with the aqueous radioactive solution of the chosen salt. The upper slab consists of two cavities of same dimension as above, one of which is used to fill the radioactive solution. The other cavity, filled up with unradioactive solution together with the central cavity of the lower slab form the diffusion column. At time t = 0, the two liquid columns are superimposed by sliding one cell above the other with the help of a screw and spring arrangement. Proper precautions are taken to maintain the mechanical and thermal equilibrium throughout the experiment. As the diffusion starts, it first occurs in between the boundary layers of two columns and with time it continues to occur throughout the liquid column. The RCA 5819 type of photomultiplier coupled with anthracene crystal is placed vertically above the diffusion column and this in turn is connected with amplifier-analysercounter system. The movements of the labelled species are detected by the detector and corresponding integrated weighted averages of counts are taken.

4. Present Investigation (a) Systems studied For a part of the present set of measurements (2MT1)Tl, SO, is the tracer and the solution of Tl, SO., in H,O and D,O is the liquid system (Das and Changdar, 1992). Tl,SO, solution has been used over a concentration range of 0.0024079 mol/L and the temperature was kept constant at (35 + O.l)C. For

PI (9)

where, t is a constant representing the overall counting efficiency of the detector and 4{(2 I -x), p}/t+J~(d - x)) is the weight factor involving geometry, absorption and scattering of radiations from the layers. As shown in our previous communications (Changdar, 1973; Chakrabarti and Changdar, 1992), if we integrate over both the spatial and time part of equation (9) to get the count observed by the scaler from the contribution of isotopes over the whole liquid column 2 I and a time interval (say T), the generalized expression for the observed number of counts N, during experiment can be written as, No-N,=Bexp(-kt) where, N, is the total saturation count taken over the time interval r, N, is the total count taken at a time t over the same interval and B characterizes a constant involving geometrical factors.

dx

I I I I

Radioactive

IdI

Fig. 1. Geometry

of the diffusion

system.

Diffusion

coefficients of T&SO, and H,PO, at 35°C

Table I. Diffusion coefficients of thallous sulphate in Hz0 and D,O media at 35°C at different concentrations using (2MTl) T&SO, as tracer D x IO5 (cm2s-‘)

Concentration (m&m3 )

fi

WW-)

(mol/L)

0.079 0.059 0.040 0.030 0.020 0.010 0.008 0.004 0.002

0.282 0.244 0.199 0.172 0.141 0.100 0.089 0.063 0.044

40 30 20 I5 IO 5 4 L

DH200 I .37 * 0.004

1.40 I .44 I.51 I.55 1.60 I .67 I .73 I.81

D0*0 I.11 1.15 I.19 I.21 I .25 1.39 I .43 I.51 I.61

the other set of measurements, Hj32P0, has been used as tracer for the solution of H,PO, in H,O and D,O for a very wide range of concentrations (0.05 to 10 mol/L) at the same temperature. An aqueous solution of H,PO,CaHPO, system was another experimental liquid where CaH3*P0, has been used as the tracer. A U-10 thermostat was used to keep the temperature constant. @) Procedure The solution of the experimental electrolyte was prepared for any chosen concentration by the weighing method using both H,O and D,O as solvent. The radioactive part of the solution was prepared by introducing labelled species within it. The diffusion experiment was performed by superposing the upper column of water or heavy water over the radioactive part. The measured D values are thus interdiffusion coefficients for the systems studied.

5. Results To obtain consistent values of D, each experiment was repeated at least thrice for each particular concentration with different diffusion column lengths (24cm) and diameters (0.40.6cm). The diffusion coefficients are given in Table I,2 and 3. the accuracy of D lies within + I%, and our experimental investigaiton clearly shows a decrease of D with increasing concentration both in H,O and D,O media. The resulting (D - &) curves are shown in Figs 2 and 3

Table 3. Diffusion

331

coefficients of H,PO,-CaHPOrH,O 35°C using CaH’*PO, as tracer 10Scm’s~

D x

Concentration (moW (C) 9.00 5.94 2.90 1.60 0.57

Jc J(mol/U

DH,w~-H~o

3.00 2.44 I .70 I .26 0.75

0.81 0.81 0.91 0.92 0.94

system at

D,,mo;CaHPO-H,O 0.76 0.78 0.88 0.90 0.9 I

for the thallous sulphate and othophosphoric acid media. The data show that the diffusion coefficient of the same ion at same temperature is higher in the H,O medium compared to that in the D,O medium. Again, Fig. 2 shows a certain decrease in value of D in orthophosphoric acid at 0.84 mol/L in both the solvent systems.

6. Discussion curves show a decrease of diffusion co(D-A) efficient with increasing concentration in all the systems studied. The change in diffusion coefficient at lower concentrations obeys Nernst’s limiting law but the coefficients at higher concentrations can be explained only by Onsager’s phenomenological coefficients (Chakrabarti and Changdar, 1992). The diffusive motion of an ion (or an aggregate of ions) in solution depends both upon the interaction between ion and the neighbouring structured water molecules (ion-solvent interaction) and also on the interaction between ions of similar and opposite charges placed in the neighbourhood of the migrating ion (ion-ion interaction). All these electrostatic interactions are strongly governed by the change in dielectric constant of the aqueous medium by the introduction of ions in water and heavy water. It is known (Hasted et al., 1948) that introduction of ions in water shows a lowering of dielectric constant and shift in the relaxation time of water. Huckel (mentioned Hasted’s paper) showed that a variation of dielectric constant would have a significant effect on the properties of 2.0 r

Table 2. Diffusion coefficients of orthophosphoric acid in H,O and D,O media at 35°C at different concentrations usine H,‘2P0. as tracer Concentration (mow) (C) 0.089 0.110 0. I70 0.340 0.570 0.680 0.840 1.600 2.900 4.600 5.940

& ,/(mol/U 0.298 0.332 0.412 0.583 0.755 0.825 0.916 1.265 1.703 2.145 2.437

D x IO’ (cm2 SK’) &,o

D IhO

I .07 I .02 I .oo 0.96 0.94 0.93 0.82 0.92 0.91 0.88 0.81

0.78 0.71 0.67 0.67 0.61 0.66 0.66 0.63 0.61

0.8 0.0

0.1

0.2

0.3

C “2 (mol/L)“* Fig. 2. (D - A) curve for thallous sulphate solution using H,O and D,O as solvents at 35°C.

A. DAS and S. N. CHANGDAR

338 1.3

0 Hz0 as solvent l

_

1.1

0.5

0.0

D,O as solvent

0

0.5

I .5 1.0 c 0 5 (mot,t$l.’

2.0

2.5

Fig. 3. (D - fi) curve for orthophosphoric acid solution using H,O and D,O as solvents at 35°C.

concentrated salt solutions. Hasted ef al. also referred to the theoretical estimate of Sack about the lowering of dielectric constant that would be expected because of the saturation of the dielectric in the neighbourhood of an ion. It is found (Hasted et al., 1948) that the dielectric constant can be represented by a formula t, = t, +2&Z’ where eW is the dielectric constant water, C is the concentration in moles per litre and 6 has values between -7 and -IS for various salts in concentrations of up to 2 M. We think that this fact is reflected in our measured values of diffusion coefficients in different liquid systems, because with the lowering of the dielectric values, the interaction between ions increases with this retards the diffusive motion of the migrating particle, as demonstrated in all our experimental results. The resulting D - 8 curves for Tl,SO, and H,PO., solutions are given in Figs 2 and 3 respectively. The calculation of Nernst’s limiting value of diffusion coefficient of thallous sulphate solution using H,O and D,O as the solvents gives and DT,+oI D&SO& (H,O) = 2.050 x IO- 5cm’ss’ (D,O) = 1.945 x 10m5cm2 s ’ (Das and Changdar, 1992). The value of the diffusion coefficient at constant temperature is greater in the Hz0 medium than in the D,O medium in both the cases over the whole concentration range studied. The mass differences between the two solvent systems is partly responsible for causing such a difference (10%). The remaining differences (66-12% in case of Tl?SO, solution and 1417% in case of H,PO, solution) in D may be due to structural changes in the H,O and D,O systems. Thus the difference in diffusion coefficients of (204Tl) Tl,SO,, and H,‘2P0, in H,O and D,O media showed indications of fundamental changes in the structure of the soivent upon the dissolution of a salt. Actually, comparison of diffusion and viscosity (Ostroff et al., 1969) data of D,O and H,O solution provides insight into the effects of various ionic species on the structure of the solution.

Since pure D,O and Hz0 are considered to have different structural characteristics (Kirshenbaum, 1951) the introduction of ions should affect the structure differently. The neutron diffraction study (Powell et al., 1989) also shows that the mean scattering cross section and mean absorption cross section, which are in turn related to the structure factor and radial distribution function of the solution, are different for H,O and D20 solutions of the same ion. The diffusion data at various concentrations of the solute indicate that the molecular displacements are greater in H,O systems in comparison with D,O systems. This observation is also supported by the fact that the structure of DZO is more ordered than that of H,O. In electrolytic solutions, there is an effect of the electric field of the ion on the dipole molecules of the water. There may be some cases where some solvent molecules may get themselves attached to an ion durjng its diffusive motion, and this cluster, comprising the ion and the primary water shell, has an effective increased radius and hence the diffusion constant decreases. Our experiment with orthophosphoric acid showed this effect at a particular concentration of 0.84mol/L. Again there is an anomaly in the degree of dissociation of orthophosphoric acid near 1 mol/L (Edwards and Huffman, 1959). This fact helps us to conclude that at this particular concentration the hydration effect predominates and a drop in diffusion coefficient occurs. The earliest work (Anonymous, 1928) on the diffusion coefficient of orthophosphoric acid in water reported diffusion coefficients obtained by Graham’s method at 20 C, for the concentration range 0.25-3.0 N. Edwards and Huffman in 1959 used the two lens Gouy diffusiometer for the determination of diffusion coefficient of an aqueous solution of orthophosphoric range acid at 25°C over the concentration 0.03616mol/L. Rao and Rao (1971) measured the same at 35’C by the magnetically stirred porous diaphragm cell technique for the concentration range 0.082-I 3.4 N. The diffusion coefficient at infinite dilution obtained by Rao and Rao is 1.398 x 10~‘cm2s~‘. Rao and Rao also calculated the diffusion coefficient at infinite dilution, corrected for temperatures 35’ C, from the data of the previous values of obtained the workers, and and 1.820x 10m5cm’s ’ re1.740 x lO~‘cm’s~ spectively. Extrapolation of our experimental results gives D&,, (H,O) = 1.231 x lO~‘cm’s I_ Our experimental data show the same trend as found by Edwards and Huffman except for the dip in D-values at the concentration 0.84 mol/L. Rao and Rao’s work shows some inconsistency in the experimentally observed values. The diffusion of an ion in a medium may be drastically changed by the introduction of another ion. The diffusive motion of the ion is affected by the forces exerted on the diffusing ion by the new atoms introduced which are also in motion. This

Diffusion effect

of mutually

other

is termed

diffusing as coupled

ions flows,

coefficients

or atoms and

of T&SO, and H,PO,

on each

extensive

work

has been performed (Leaist and Wiens, 1986; Leaist, 1987). We tried to see the effect of introducing a new chemical species CaHPO, on the measured diffusion coefficient

of H,PO,-Hz0

data are given in Table

system,

and

the measured

3.

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at 35°C

339

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