Self-diffusion of chromate ion in agar gel

rwnurionul Journul of ,inted in Great Britain.

Applied Rudiurion

und Iw‘oropes

Vol.32. pp. 631 to 635.

I

0020-708x/8 l/O9063 -0s802.00/0 Pergamon Press Ltd

1981

Self-Diffusion of Chromate Ion in Agar Gel S. F. PATIL

and

N. G. ADHYAPAK

Department of Chemistry, University of Poona, Pune, 411 007, India (Receiued 1 December 1980; in revisedform 16 January 1981) The self-diffusion coefficient of the chromate ion is determined in agar gel media over the concentration range 10m5 to 0.25M at 25°C. Comparison of the experimental results and the theoretical values indicates failure in the application of ONSAGER-FUOSS theory to the ion diffusion in swollen gel system at all the concentrations studied. The observed results are explained on the basis of water-gel, ion-water and ion-ion interactions and the obstruction effect. Diffusion rates are also determined at various gel percentages and at different temperatures, keeping the electrolyte concentration constant. The obstruction effect is found to depend on the concentration of the electrolyte and the activation energy is found to decrease with increasing gel concentration. The results are discussed in the light of transition state theory of diffusion.

Introduction OURPREVIOUScommunication”) the obstruction 8ct due to the gel matrix, and the activation energy : the process of electrolyte diffusion and self-diffum of the chromate ion was reported. The present per deals with the measurement of the self-&fusion efficient of the chromate ion over a wide range of ncentrations at 25°C in a medium of constant gel ntent. Further, the variation of the self-diffusion zfficient with gel percentage keeping the electrolyte ncentration constant (5 x lo-‘M) was studied :r the temperature range of 25-50°C with a view to derstand how the activation energy for the difion process varies with the gel concentration.

In self-diffusion, the tracer ion moves in a medium of uniform composition of electrolyte solution, and the electrophoretic effect is negligible. However, the migrating ion has a velocity relative to other ions; its atmosphere is asymmetric and hence the relaxation effect becomes important. Taking into consideration the relaxation effect, ONSAGER derived a quantitative relationship which gives the concentration dependence of trace ion diffusion at low ionic strengths. The practical formula of the ONSAGER expression derived by GOSING and HARNED@)for the diffusion coefficient of jth ion (Df) in the case of an electrolyte solution is given by ‘i’

Experimental tadioactive “Cr in the form of chromic chloride lained from the Bhabha Atomic Research Centre, mbay, was converted into potassium chromate. : diffusion coefficient under different conditions is ermined using the zone diffusion technique. The ails of the experimenta! set up and the procedure owed for the calculation of diffusion coefficients ‘e reported earlier.“)

Results and Discussion

RTl? J = jZ,lFz

1q(Z,(F

- I.

X

3Ne

2.694 x lOi

(1)

where R is the gas constant in J K-l mol-‘, T is the temperature, 2: is equivalent conductivity of the jth ion at infinite dilution, Zj is the charge in electronic units, C, is the concentration in moles per litre of ion i, E dielectric constant of the solvent, F the Faraday constant and d(w,) is a complex function of concentration, charge and limiting conductance of the ions participating in the diffusion. For potassium chromate labelled with ‘lCr, this simplifies to

rheoretical value of D*

‘he theoretical values of self-diffusion coefficients :hromate ion at various concentrations are calcud by the GOSTINGand HARIVED equation derived n the ONSAGER-FUO@ and ONSAGER theory of diffusion. The theoretical and observed values for diffusion coefficient (D*) are presented in Fig. 1.

where $ and $’ are the limiting ionic conductances of potassium and chromate ions, respectively. Substituting the values of all the functions and constants in equation (1) we get the expression for self631

632

S. F. Patil and N. G. Adhyapak

---. 0Q

0

I

0.2

0.1

Limiting law Extended limitinglaw Experimental

03

XI(mal

1%

I

04

-

FIG. 1. Variation of self-diffusion coefficient of the chromate ion with concentration chromate in 1% agar gel at 25°C.

diffusion coefficient of the chromate

ion at

D&o:m x lo5 = 1.104 - 1.562s

25”C, (3)

Values of 1’ at 25°C are taken from the literaturej5’ For higher concentrations a semi-empirical correction@) is to be introduced in the limiting law equation which takes into consideration the ion size parameter a. The $ in equation (3) is replaced by ,/c/(1 + ka)(l + ka/$?) where k is the reciprocal radius of the ion atmosphere and a is the closest distance of approach between oppositely charged ions. The value of a is determined from the data of activity coefficients”.‘) of potassium chromate at two concentrations and is found to be 0.366 nm. 2. Concentration

variation:

a comparison

with the

theory

Figure 1 shows the variation of the self-diffusion coefficient of chromate ion with concentration of potassium chromate in 1% agar gel at 25°C. The solid line and the dashed line are obtained by using the limiting law and the extended limiting law, while the curve with open circles indicates our experimental results. It can be seen from Fig. 1 that the experimental values of diffusion coefficients are greater than the theoretical values at all the concentrations studied, indicating the quantitative failure in the application of the ONSAGER-FUOSS theory. However, the rate of diffusion is found to decrease with increasing concentration up to 0.005 M, which is qualitatively in agreement with the ONSAGER-FUOSS(~) theory. Beyond this concentration, the self-diffusion coefficient of chromate ion increases with increasing concentration. The discrepancies in the observed and theoretical diffusion rates over the entire concentration range may be explained by considering the gel-water, ion-water and ion-ion interactions and the obstruction effect.

1

0.5

of potassium

In the lower concentration range, according to are fully hydrated, as they are at infinite dilution, and any distortion present in “solvent” water surrounding the ion is nearly the same as that at infinite dilution. Hence one should expect agreement with the theory at least in the lower concentration range. In the present work, the rate of diffusion even at 10e5 M concentration (Fig. 1) is found to be higher (by 31%) than the NERNST(“) limiting value expected in aqueous solution. Our observation is supported by SINGH et al., u’) who reported the diffusion coefficient of Na+ ion in different electrolytes and found that diffusion coefficients for Na+ ion are distinctly higher than the Nernst limiting value. For example, the diffusion coefficient of Na+ ion in CsCl electrolyte at a concentration as low as 10F6 M is found to be 23% higher than that obtained from the Nernst limiting value. This unexpected high value of the diffusion coefficient even at low concentrations suggests that the ion-solvent structure in aqueous solution and that in the gel medium are not the same. This may be attributed to water-gel interaction. In the gel medium the water molecules are held up in the fibres of the agar gel network by hydrogen bonding, adsorption”‘) and dipole-dipole interactions.‘13) Thus in the presence of the gel the dipole association in water is affected (water-gel interaction), causing a distortion in the short-range crystalline structure of water which leads to an increase in the mobility of the ion (14*’ 5, thus giving rise to a higher diffusion coefficieit as observed. On the other hand, macromolecules present in the agar gel are known to lengthen the path of the diffusing ion because of the three-dimensional network which causes a lowering of D* in the gel medium, as an obstruction eflect, provided other effects are absent. The gei-water interaction and the obstruction in the diffusion path of ion due to gel macromolecules WANG~‘~, ions

633

Self-diffusion of chromate ion

ppose each other, and hence the experimental difision coefficient will be determined by the relative agnitude of the two effects. The observed results dicate that the gel-water interaction dominates over e obstruction effect, thus giving higher D* value in :l media than in pure aqueous solution. It may be lticed that even at the highest gel concentration Jdied (2.5%) (Fig. 2), the D* value is found to be gher than the theoretical value, which supports the love view that the obstruction effect is less prolunced than the gel-water interaction in the present stem. Further, it may be seen from Fig. 1 that the viations in observed and theoretical diffusion coeffints decrease with increasing concentration (up to 05 M). This is thought to be due to an increase in : obstruction effect with the concentration of elecjlyte. Independent experiments in our laboratory rformed at 5 x 10e5 M and 10m3 M chromate ion ncentration do suggest that the obstruction effect :reases with concentration, at least in the above ige of concentration. l%e entire concentration curve can be explained alitatively by considering (i) the relaxation effect VSAGER-FUMES theory) for the initial decrease as eady considered and (ii) ion-ion interactions ANG’Smodel) and the structure-breaking properties :he ion (HERTZet al. model) for the subsequent rise D*. The subsequent increase after the minimum in the ve is consistent with the models of WANG(‘) and of RTZ et Al. According to WANG, as the concen.ion of the electrolyte increases, the mean distance vell as the number of water molecules between two bositely charged ions decreases, and it becomes .easingly difficult for water molecules to orient nselves to maintain a stable semi-crystalline struc: of water. This results in a decrease in the local

dielectric constant of the medium, which in it; turn increases the self-energy of the ion. To that extent, then, the energy barrier to be overcome for the process of diffusion is reduced. The overall effect is thus an increase in the D* with concentration above 0.005 M as observed. The increase in D* over the higher concentration range is also consistent with the model of HERTZet al. The central ion is envisaged in this model as surrounded by a first hydration and a second hydration sphere. The formation of water/ion aggregates of varying sizes determines the overall D*. The sizes of the aggregates at different concentrations depend on the structure-breaking or structure-forming properties of the approaching ion. Thus, at higher concentrations of potassium chromate, the structure-breaking effects of the diffusing ions dominate due to the increase of the probability of formation of smaller aggregates by the decoupling of hydrogen bonds. This results in an increase of D* with concentration beyond the minimum at 0.005 M as observed. 3. Variation of the difJirsion coefJicient with gel concentration and temperature

In the second part of the work, we have studied the obstruction effect on the diffusion rate by varying the gel concentration. The study also covers the determination of the energy of activation for self-diffusion of the chromate ion. (i) The obstruction efict. The ion exchange properties”‘) of the gel, adsorption”‘) and surface migration of the ions along the three-dimensional network of the gel affect the self-diffusion rate of an ion. ALLENet uL,(‘~’ KELE~~AN et al., GO) SCHANTZand LAKER and SLADEet aP2” found that the obstructing effect of the gel on the diffusion rate as gel concentration is increased, obeying the relation D,*=D:-a’o

27r

2.5 , P

1F-Z

where w is the weight fraction of the gel, 0: is the diffusion coefficient in gel medium, 0: is the extrapolated value of D,* to zero agar content for the given concentration of electrolyte and a’ is the slope of the plot of D: versus w. Figure 2 shows the variation of D,* of the chromate ion at 5 x lo-‘M concentration with the weight fraction of gel UJat different temperatures. It can be seen that 0: decreases with gel concentration at all the temperatures studied. LANGD~N and THOMAS expressed the obstruction effect in terms of the formation factor F observed in the diffusion of Na+, Cland I- ions by the following expression: 0:/D;

00 0.005 0.010 0.015 0.020 0.025 0.030 wt fraction of agar w -

(4)

1 -l+C%X 1 - uo

= F = -

(5)

where a is the slope of the plot of D,* us w divided by 0:.

Obstruction effect in the self-diffusion of CrO:- in 5 x lo-’ M K,CrO, solution.

According to SLADEet a/.,(22’ the formation factor is independent of the solute character, concentration

S. F. Patil and N. G. Adhyapak

634

-

-464

-

-4.66

-

* m-4.72 cl

-

0 o

T/K

-476-

-MO-

-464

-

-466-

-492

3.0

3.1

3.2 h/T)

3.3

3.36

K x IO+’ -

FIG. 3. Activation energy for self-diffusion of CrO:-

in 5 x 10m5M K2Cr0, solution at different gel concentrations.

and temperature. It is a constant for a given content where of macromolecules, while LANGDON and THOMAS cz3) AH: = E - RT+ PAV: (8) showed that a changes with the concentration of the electrolyte. The value of a obtained from the plots in As the diffusion is accompanied by a negligible Fig. 2 for 5 x 10-s M K2Cr04 is 5 10.96 and is indevolume change, it follows that pendent of temperature. The corresponding value D* = e ,42kT/h e&s ,-sJRr (9) reported by us at 0.001 M for the same electrolyte was 21.“) Thus the formation factor is independent of the where E is the observed activation energy for diftemperature but it does depend upon the concenfusion and I is the jump length, i.e. the distance tration of the electrolyte. The differences in a values between two equilibrium positions in the direction of may be attributed to the different degrees of interacdiffusion, and AS: is the entropy of activation. A comtion between gel and electrolyte at the two concenparison of the equations (6) and (9) gives D$: trations. Further, it should be noted that the extrapoDl: = e A2 kT/h eAdlR (10) lated value 0: is greater than that obtained from the ONSAGERlimiting equation (ii) Variation of activation energy with ge/ concentration. The variation of the self-diffusion coefficient of the CrO:- ion with temperature at different gel 7.0 concentrations are presented in Fig. 3. The energies of activation (E) are calculated from the slopes of the t 6.0 plots, and Dt values are obtained from the equation 0; = Do*e-EIRT

(6)

which are tabulated in Table 1. The EYRING(~~)equation for self-diffusion is given by D* = J.‘(kT/h) exp(ASt/R) exp( -AH:/RT) (7) TABLE1. Variation of Dt and E for self-diffusion of chro-

To

so-

“5 %

4.0 -

i *p”

3.0 -

2.0 -

mate ion with gel percentage IO-

Gel percentage 1.0

1.5 2.0 2.5

DE/10e3 cm* s-l 6.886 3.473 1.392 0.596

E/kJ mol-

15.4 13.8 11.7 9.6

1 00

0.2

04

06

FIG. 4. Variation of Dt with w-“~

0.6

IO

for 5 x lo-’ M chromate ion concentration.

Self-difision of chromate ion

ssuming ASt to be independent of the agar content, e decrease in DO+with gel percentage
rtnowledgements-We are grateful to Dr H. J. Amikar, jfessor Emeritus, for his keen interest and valuable dissions and to Professor V. K. Phantilkar for providing !lities. One of us (NGA) is thankful to the University ints Commission for a Junior Research Fellowship.

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