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Diffusion studies of some electrolytes in agar gel
0020-708X/82/020105-04SO3.00/0 Pcrgamon Press Ltd
Inremurionol Journal of Applied Rudiarion and 1sorop.v Vol. 33. pp. 105 10 108. 1982 Printed in Great Britain
Diffusion Studies of Some Electrolytes in Agar Gel S. F. PATIL
and N. G. ADHYAPAK
Department of Chemistry, University of Poona. Pune-411 007, India (Received 1 June 1981; in reoisedform 30 June 1981) The diffusion coefficients of KCI, K2Cr04, ZnCl, and Cd(CH3C00)2 were studied at various concentrations in agar gel medium at 25°C by the zone-diffusion technique. A minimum in the D vs JC curve is characteristic of all the four systems. The experimental results are compared with the values obtained by the Onsager-Fuoss theory. An attempt has been made to explain the divergence from the theory in terms of the different types of interactions occurring in the gel-water-electrolyte system.
Introduction THE DIFFUSIONof a number of alkali,“-4) alkaline earthcse7) and transition’8.9’ metal salts has been done by several workers both in pure aqueous solutions and in agar gel medium. In most of the cases the measured diffusion coefficient deviates from the theory for unsymmetrical and higher valence type electrolytes. For example, in the diffusion of CaC12,‘5’ K4[Fe(CN)6]‘L’ and Na2S04(4) in the aqueous solution a large divergence was observed. The present paper deals with the diffusion studies of KCI as well as unsymmetrical electrolytes K2Cr04, ZnCll and Cd(CH,C00)2. The results are compared with the theoretical values of diffusion coefficients to see whether the ONSAGER-FUOSS(“)theory is applicable over a wide range of concentrations.
:olumn contains a labelled electrolyte and pure gel :olumns on either side of the zone. When an electrolyte diffuses into the solvent, electrical neutrality requires that both ions move with the same average velocity. Under these conditions the ionic atmos pheres suffer no deformation, and the time of relaxition which is proportional to the difference between the velocities of the two ions vanishes. In this process, however, the electrolyte and solvent move in opposite directions and an electrophoretic effect occurs. Further, since the chemical potential of the electrolyte varies throughout the solution, a thermodynamic term will occur in the theoretical equation for the diffusion coefficient. Taking into consideration the :lectrophoretic effect and the chemical potential, ONSAGERand Fuoss derived the following expression Tar the diffusion coefficient:
Experimental Radioactive 36C1-, 5’Cr3+, 65Zn2+ and ’ 15mCd2+ were obtained from the Bhabha Atomic Research Centre, Bombay, in the form of HCI, CrCl,, ZnCl, and Cd(N03)2 respectively. ZnCl, was used in the same form, while chlorine. chromium and cadmium isotopes were converted into KCI, K2Cr04 and Cd(CHJCOO)2, respectively. Electrolyte diffusion of KCI, K2Cr04 and Cd(CH3COO)z was carried out in 1% agar gel while that of ZnCl, in 1.5% agar gel at 25°C using the zone-diffusion technique, over a concentration range of 10S5 to 2.0 M for different electrolytes. The details of the experimental setup and procedure followed for the calculations of the diffusion coefficient were reported earlier.“”
D = 1000 RT(vl + v2) where
IG -
C
C
- (lz,liy - lzllly AM’ = C ~021z111z21h + vz) 3.111 x lo-‘9 X
Ir0fl AM” -=
.
fi
l+A’&
(Zsj.7 + Z:;1!)’ AQ2
9.18 x 10-13 X
In electrolyte diffusion, the central zone of the gel A.R.I. 33,2--8 105
C
(2)
Results and Discussion calculations of dijiision coejkient
+!!L+!YL
l~lll&l~”
C
Theoretical
I,
Lyi;
= 1.074 x lo-z0
MT)*
A0 = i.: + 1.;
c4A’J;;
(3)
106
S. F. Patil und N. G. Adhytrpuk TABLE
1. The values ofdifferent
Parameters sJ
A’ B [I0
constants
and functions
required
KCI
K2Cr04
ZnCl,
0.509 I 1.4076 - 0.00484 4.284 1
I .7636 2.0865 - 0.02629 3.666 2 1 1 2 73.5 83 8.314 x 10’ 78.54 8.949 x 10-j
1.7636 2.8869 +‘0.08255 5.072 1
1 1 I 73.5 76.35 8.314 x 10’ 78.54 8.949 x lO-3
where AM’ and AM” are the first and second order electrophoretic effects: V, and \v2 are the number of cations and anions for the given electrolyte with charge Z, and Z2 : i.7 and ;.‘j are the limiting equivalent conductances of cations and anions. respectively: &A’, c is the exponential integral function: and all other symbols have their usual meanings. The thermodynamic term in equation (1) is given by
2 1 53 76.35 8.314 x 10’ 78.54 8.949 x 10-j
(
4.955 x 10’3 40.22 - 0.005812
+ 18.726~41.4076, ;
[
D KzcCrOr=
l-
- 0.1211c
(1 + 2.0865,$ D znC,> =
x
16.7985 - 5.5099 1
_ \c 1 + 1.4076, ;
1
x 1O-2o
0.5862, ;
- 0.02229~
(1 + 1.4076, ;)’
7.4321 x 10” ,; 1 + 2.0865, ; + 108.67c$~2.0865, ;
1
x 1O-2o
1
(6)
(7)
V’ 1 + 2.8869;:
1
x lo-”
2.0306 $
+ 0.3802~
(1 + 2.8869,::)’ DCd,Ac,z =
1
7.4327 x lOI
1(8)
7.4327 x 1013 ,C
1 + 3.&37\ ; + 98.455c$13.6437;;
The values of the different constants and the functions required for the diffusion coefficient are given in Table I. Substituting these values in equation (1). we get an expression of D for different electrolytes at 25’C as
x
1 54 40.9 8.314 x 10’ 78.54 8.949 x IO-’
(5)
HARNEDand OWEN.“”
x
4
L
+ 1.4376~$2.8869,‘:
+ 4.606 Br
where 5, is the hmiting function of the Debye-Huckel theory. B is the salting constant whose positive value causes a minimum in the curve and A’ is another empirical constant depending upon the nature of the electrolytes. The constants A’ and B are computed from the values of the activity coefficients of the electrolytes at two different concentrations. The values of &A’, c. a0 and S, are given in the tabular form by
D Kc-, =
1.7636 3.6437 -0.5086 6.401 1 2
2.0306 J
_
l+!
(1) at 25 C
in equation
1
x lo-”
2.0306, ;; (1 + 3.6437, ‘c,’
- 2.3426~
1
(9)
It is seen from Fig. 1 that Drrp, values for chromate and chloride ions are higher than Dlhoo at all the concentrations studied. while for zinc and cadmium (Fig. 2) ions the values observed are lower than DFXP,up to 5 x 1O-3 and 2.5 x 10e3 M, respectively. However, beyond these concentrations, the experimental values of diffusion coefficients were found to be higher than that of the theoretically expected values. A noteworthy feature common to all the four systems is the characteristic minimum which was observed at lo- 3 M for ZnCIz and cadmium acetate, and at 0.1 M for K2Cr04 and KCI. On the other hand. theoretical calculations show a minimum only for ZnCl, at 0.05 M concentration. as salting constant is positive for ZnCI, while all the other systems have a negative salting constant. These observed deviations may be attributed to different types of interactions occurring in the gel-water-electrolyte system.
Electrolyte
107
diffusion in agur gel
2.3
I.7
0.2
0.4
0.6
0.6
1.0
1.2
1.4
1.6
-(a)
I.11 0
0.
I
0.2 &
(mol
0.3
0.4
0.5
C’)!+
FIG. I. Variation of (a) DKfro, with concentration of K,CrO, and (b) DK,-,with concentration of KCl. in 17; agar gel at 25’C. theoretical. -G-Gexperimental. Adsorption of ions on the gel and obstruction in the diffusion path by agar macromolecules cause a lowering of diffusion coefficient in the gel medium, while gel-water interaction enhances the diffusivity in the medium. All these effects are described in detail in our previous paper. (13) It is seen from Fig. 1 that the water-gel interaction is the dominating factor which leads to higher values of Dexp, than predicted by the theory at all the concentrations in potassium chromate and potassium chloride systems. On the other hand, in the diffusion of Zn2+ and Cd*+ (Fig. 2X adsorption along with the obstruction effect dominates over the water-gel interaction, giving lower diffusivities in the lower concentration range. However, at
0
0.1
the higher concentrations, adsorption effect becomes negligible, and it can be seen from the results (Fig. 2) that water-gel interaction along with other interactions occurring at higher concentrations dominates over the obstruction effect showing higher values of D cxp, than the theoretical diffusion coefficient. It can be seen from Figs 1 and 2 that diffusion coefficient decreases and then increases with concentration, giving rise to a minimum in the D vs concentration curve. This can be explained by considering the change in hydration of ion with concentration due to ion-ion interactions which is not taken into account by the Onsager-Fuoss theory. As the concentration increases, self-energy of the
0.2 d?!
(mol
0.3
0.4
0.5
l-‘)h
FIG. 2. Variation of (a) DZ,,,-,,with concentration of ZnCll in 1.57; agar gel and (b) Dcd(CH,cOO)a with concentration of Cd(CH3C00)2 in l?,; agar gel at 25T. -theoretical, -O--O-experimental.
108
S. F. Patil
und N. G. AdhJapak
central ion also increases.‘14’ This is to be expected since in more concentrated solutions the electric field ne;Lr the central ion is reduced by the opposing field of the ionic cloud, and the central ion becomes effectively desolvated. This reduction of the primary solvation interaction is accompanied by an increase of lateral repulsions between the dipoles of solvent molecules as these are forced against one another by interactions with nearby ions. This results in an increase of the activity coefficient of the electrolyte in real solution. hence the thermodynamic term in the diffusion coefficient equation also increases giving a higher value of D as observed. and we get increase of D with concentration though theoretically there should be no minimum in the D vs v’c curve. Also the observed minimum in the ZnCl, curve shifts to the lower concentration side. suggesting that the above effect influences the minimum in the curve.
References
2. 3. 4. 5. 6.
76, 2064 (1954).
8. 9. 10. II.
Ackrlolcl~~/~~et~?~~~lr.s-We are deeply indebted to Professor Emeritus H. J. Arnikar for his valuable discussions. We would like to express our thanks to Professor V. K. Phan-
salkar for providing the facilities. One of us (NGA) is thankful to the University Grants Commission for a Junior Research Fellowship.
HARNED H. S. and HUD~~N R. M. J. Am. Chem. Sot. 73, 5083 (19.51). JANZ C. J.. OLIVER B. G.. LAKSHMINARAYANAN. G. R. and MAYER G. E. J. Phys. Chem. 74, 1285 (1970). SOOD M. L. and KAUR G. 2. Phys. Chem. (Leipzig) 259, 585 (1978). %WD M. L., KAUR G. and CHOPRA S. L. Indian J. Chem. ISA, I81 (1979). ROBIN~QNR. A. and CHIA C. L. J. Am. Chem. SW. 74, 2776 (1952). HARNED H. S. and POLESTRAF. M. J. Am. Chem. Sot.
12. 13. 14.
GUPTA R. P.. Z. Phys. Chum. (Neue Folge) 81, 286 (1972). REILLY P. J. and STOKESR. H. Ausr. J. Chem. 24, II36 (1971). LUK Y.. NANIS L. and LITT M. Ind. Eny. Chem. Fundam. 14, 92 (1975). ONSAGER L. and Fuoss R. M. J. Phys. Chem. 36, 2689 (1932). ARNIKAR H. J.. PATIL S. F.. ADHYAPAK N. G. and POTDAR J. K. Z. Phys. Chem. (Neue Folge) 120, 51 (1980). HARNED H. S. and OWEN B. B. The Physicul Chemistr) qf‘E/rctrolJfic Solutions. (Reinhold. New York. 1950). PATIL S. F. and ADHYAPAK N. G. Inr. J. Appl. Radiar. Isot. (In press). BENNETTOH. P. and SPITZER J. J. J. C. S. Farad+ Twits.
I. 74. 2385 (1978).
Inremurionol Journal of Applied Rudiarion and 1sorop.v Vol. 33. pp. 105 10 108. 1982 Printed in Great Britain
Diffusion Studies of Some Electrolytes in Agar Gel S. F. PATIL
and N. G. ADHYAPAK
Department of Chemistry, University of Poona. Pune-411 007, India (Received 1 June 1981; in reoisedform 30 June 1981) The diffusion coefficients of KCI, K2Cr04, ZnCl, and Cd(CH3C00)2 were studied at various concentrations in agar gel medium at 25°C by the zone-diffusion technique. A minimum in the D vs JC curve is characteristic of all the four systems. The experimental results are compared with the values obtained by the Onsager-Fuoss theory. An attempt has been made to explain the divergence from the theory in terms of the different types of interactions occurring in the gel-water-electrolyte system.
Introduction THE DIFFUSIONof a number of alkali,“-4) alkaline earthcse7) and transition’8.9’ metal salts has been done by several workers both in pure aqueous solutions and in agar gel medium. In most of the cases the measured diffusion coefficient deviates from the theory for unsymmetrical and higher valence type electrolytes. For example, in the diffusion of CaC12,‘5’ K4[Fe(CN)6]‘L’ and Na2S04(4) in the aqueous solution a large divergence was observed. The present paper deals with the diffusion studies of KCI as well as unsymmetrical electrolytes K2Cr04, ZnCll and Cd(CH,C00)2. The results are compared with the theoretical values of diffusion coefficients to see whether the ONSAGER-FUOSS(“)theory is applicable over a wide range of concentrations.
:olumn contains a labelled electrolyte and pure gel :olumns on either side of the zone. When an electrolyte diffuses into the solvent, electrical neutrality requires that both ions move with the same average velocity. Under these conditions the ionic atmos pheres suffer no deformation, and the time of relaxition which is proportional to the difference between the velocities of the two ions vanishes. In this process, however, the electrolyte and solvent move in opposite directions and an electrophoretic effect occurs. Further, since the chemical potential of the electrolyte varies throughout the solution, a thermodynamic term will occur in the theoretical equation for the diffusion coefficient. Taking into consideration the :lectrophoretic effect and the chemical potential, ONSAGERand Fuoss derived the following expression Tar the diffusion coefficient:
Experimental Radioactive 36C1-, 5’Cr3+, 65Zn2+ and ’ 15mCd2+ were obtained from the Bhabha Atomic Research Centre, Bombay, in the form of HCI, CrCl,, ZnCl, and Cd(N03)2 respectively. ZnCl, was used in the same form, while chlorine. chromium and cadmium isotopes were converted into KCI, K2Cr04 and Cd(CHJCOO)2, respectively. Electrolyte diffusion of KCI, K2Cr04 and Cd(CH3COO)z was carried out in 1% agar gel while that of ZnCl, in 1.5% agar gel at 25°C using the zone-diffusion technique, over a concentration range of 10S5 to 2.0 M for different electrolytes. The details of the experimental setup and procedure followed for the calculations of the diffusion coefficient were reported earlier.“”
D = 1000 RT(vl + v2) where
IG -
C
C
- (lz,liy - lzllly AM’ = C ~021z111z21h + vz) 3.111 x lo-‘9 X
Ir0fl AM” -=
.
fi
l+A’&
(Zsj.7 + Z:;1!)’ AQ2
9.18 x 10-13 X
In electrolyte diffusion, the central zone of the gel A.R.I. 33,2--8 105
C
(2)
Results and Discussion calculations of dijiision coejkient
+!!L+!YL
l~lll&l~”
C
Theoretical
I,
Lyi;
= 1.074 x lo-z0
MT)*
A0 = i.: + 1.;
c4A’J;;
(3)
106
S. F. Patil und N. G. Adhytrpuk TABLE
1. The values ofdifferent
Parameters sJ
A’ B [I0
constants
and functions
required
KCI
K2Cr04
ZnCl,
0.509 I 1.4076 - 0.00484 4.284 1
I .7636 2.0865 - 0.02629 3.666 2 1 1 2 73.5 83 8.314 x 10’ 78.54 8.949 x 10-j
1.7636 2.8869 +‘0.08255 5.072 1
1 1 I 73.5 76.35 8.314 x 10’ 78.54 8.949 x lO-3
where AM’ and AM” are the first and second order electrophoretic effects: V, and \v2 are the number of cations and anions for the given electrolyte with charge Z, and Z2 : i.7 and ;.‘j are the limiting equivalent conductances of cations and anions. respectively: &A’, c is the exponential integral function: and all other symbols have their usual meanings. The thermodynamic term in equation (1) is given by
2 1 53 76.35 8.314 x 10’ 78.54 8.949 x 10-j
(
4.955 x 10’3 40.22 - 0.005812
+ 18.726~41.4076, ;
[
D KzcCrOr=
l-
- 0.1211c
(1 + 2.0865,$ D znC,> =
x
16.7985 - 5.5099 1
_ \c 1 + 1.4076, ;
1
x 1O-2o
0.5862, ;
- 0.02229~
(1 + 1.4076, ;)’
7.4321 x 10” ,; 1 + 2.0865, ; + 108.67c$~2.0865, ;
1
x 1O-2o
1
(6)
(7)
V’ 1 + 2.8869;:
1
x lo-”
2.0306 $
+ 0.3802~
(1 + 2.8869,::)’ DCd,Ac,z =
1
7.4327 x lOI
1(8)
7.4327 x 1013 ,C
1 + 3.&37\ ; + 98.455c$13.6437;;
The values of the different constants and the functions required for the diffusion coefficient are given in Table I. Substituting these values in equation (1). we get an expression of D for different electrolytes at 25’C as
x
1 54 40.9 8.314 x 10’ 78.54 8.949 x IO-’
(5)
HARNEDand OWEN.“”
x
4
L
+ 1.4376~$2.8869,‘:
+ 4.606 Br
where 5, is the hmiting function of the Debye-Huckel theory. B is the salting constant whose positive value causes a minimum in the curve and A’ is another empirical constant depending upon the nature of the electrolytes. The constants A’ and B are computed from the values of the activity coefficients of the electrolytes at two different concentrations. The values of &A’, c. a0 and S, are given in the tabular form by
D Kc-, =
1.7636 3.6437 -0.5086 6.401 1 2
2.0306 J
_
l+!
(1) at 25 C
in equation
1
x lo-”
2.0306, ;; (1 + 3.6437, ‘c,’
- 2.3426~
1
(9)
It is seen from Fig. 1 that Drrp, values for chromate and chloride ions are higher than Dlhoo at all the concentrations studied. while for zinc and cadmium (Fig. 2) ions the values observed are lower than DFXP,up to 5 x 1O-3 and 2.5 x 10e3 M, respectively. However, beyond these concentrations, the experimental values of diffusion coefficients were found to be higher than that of the theoretically expected values. A noteworthy feature common to all the four systems is the characteristic minimum which was observed at lo- 3 M for ZnCIz and cadmium acetate, and at 0.1 M for K2Cr04 and KCI. On the other hand. theoretical calculations show a minimum only for ZnCl, at 0.05 M concentration. as salting constant is positive for ZnCI, while all the other systems have a negative salting constant. These observed deviations may be attributed to different types of interactions occurring in the gel-water-electrolyte system.
Electrolyte
107
diffusion in agur gel
2.3
I.7
0.2
0.4
0.6
0.6
1.0
1.2
1.4
1.6
-(a)
I.11 0
0.
I
0.2 &
(mol
0.3
0.4
0.5
C’)!+
FIG. I. Variation of (a) DKfro, with concentration of K,CrO, and (b) DK,-,with concentration of KCl. in 17; agar gel at 25’C. theoretical. -G-Gexperimental. Adsorption of ions on the gel and obstruction in the diffusion path by agar macromolecules cause a lowering of diffusion coefficient in the gel medium, while gel-water interaction enhances the diffusivity in the medium. All these effects are described in detail in our previous paper. (13) It is seen from Fig. 1 that the water-gel interaction is the dominating factor which leads to higher values of Dexp, than predicted by the theory at all the concentrations in potassium chromate and potassium chloride systems. On the other hand, in the diffusion of Zn2+ and Cd*+ (Fig. 2X adsorption along with the obstruction effect dominates over the water-gel interaction, giving lower diffusivities in the lower concentration range. However, at
0
0.1
the higher concentrations, adsorption effect becomes negligible, and it can be seen from the results (Fig. 2) that water-gel interaction along with other interactions occurring at higher concentrations dominates over the obstruction effect showing higher values of D cxp, than the theoretical diffusion coefficient. It can be seen from Figs 1 and 2 that diffusion coefficient decreases and then increases with concentration, giving rise to a minimum in the D vs concentration curve. This can be explained by considering the change in hydration of ion with concentration due to ion-ion interactions which is not taken into account by the Onsager-Fuoss theory. As the concentration increases, self-energy of the
0.2 d?!
(mol
0.3
0.4
0.5
l-‘)h
FIG. 2. Variation of (a) DZ,,,-,,with concentration of ZnCll in 1.57; agar gel and (b) Dcd(CH,cOO)a with concentration of Cd(CH3C00)2 in l?,; agar gel at 25T. -theoretical, -O--O-experimental.
108
S. F. Patil
und N. G. AdhJapak
central ion also increases.‘14’ This is to be expected since in more concentrated solutions the electric field ne;Lr the central ion is reduced by the opposing field of the ionic cloud, and the central ion becomes effectively desolvated. This reduction of the primary solvation interaction is accompanied by an increase of lateral repulsions between the dipoles of solvent molecules as these are forced against one another by interactions with nearby ions. This results in an increase of the activity coefficient of the electrolyte in real solution. hence the thermodynamic term in the diffusion coefficient equation also increases giving a higher value of D as observed. and we get increase of D with concentration though theoretically there should be no minimum in the D vs v’c curve. Also the observed minimum in the ZnCl, curve shifts to the lower concentration side. suggesting that the above effect influences the minimum in the curve.
References
2. 3. 4. 5. 6.
76, 2064 (1954).
8. 9. 10. II.
Ackrlolcl~~/~~et~?~~~lr.s-We are deeply indebted to Professor Emeritus H. J. Arnikar for his valuable discussions. We would like to express our thanks to Professor V. K. Phan-
salkar for providing the facilities. One of us (NGA) is thankful to the University Grants Commission for a Junior Research Fellowship.
HARNED H. S. and HUD~~N R. M. J. Am. Chem. Sot. 73, 5083 (19.51). JANZ C. J.. OLIVER B. G.. LAKSHMINARAYANAN. G. R. and MAYER G. E. J. Phys. Chem. 74, 1285 (1970). SOOD M. L. and KAUR G. 2. Phys. Chem. (Leipzig) 259, 585 (1978). %WD M. L., KAUR G. and CHOPRA S. L. Indian J. Chem. ISA, I81 (1979). ROBIN~QNR. A. and CHIA C. L. J. Am. Chem. SW. 74, 2776 (1952). HARNED H. S. and POLESTRAF. M. J. Am. Chem. Sot.
12. 13. 14.
GUPTA R. P.. Z. Phys. Chum. (Neue Folge) 81, 286 (1972). REILLY P. J. and STOKESR. H. Ausr. J. Chem. 24, II36 (1971). LUK Y.. NANIS L. and LITT M. Ind. Eny. Chem. Fundam. 14, 92 (1975). ONSAGER L. and Fuoss R. M. J. Phys. Chem. 36, 2689 (1932). ARNIKAR H. J.. PATIL S. F.. ADHYAPAK N. G. and POTDAR J. K. Z. Phys. Chem. (Neue Folge) 120, 51 (1980). HARNED H. S. and OWEN B. B. The Physicul Chemistr) qf‘E/rctrolJfic Solutions. (Reinhold. New York. 1950). PATIL S. F. and ADHYAPAK N. G. Inr. J. Appl. Radiar. Isot. (In press). BENNETTOH. P. and SPITZER J. J. J. C. S. Farad+ Twits.
I. 74. 2385 (1978).