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The osmotic coefficients of aqueous CsCl and CsCl + KCl mixtures at 298.15 K
M-845 J. Chem. Thrrmodynamtcs lW8, IO, 683-685
The osmotic coefficients and CsCl + KCI mixtures A. M. BAHIA,
T. H. LILLEY,
of aqueous CsCl at 298.15 K
and I. R. TAXER
Chemistry Department, The University, SheffieldS3 7HF, U.K. (Received24 October 1977; in revisedform I December1977) The osmotic coefficients of aqueous solutions containing CsCl and CsCl + KC1 at 298.15 K have been re-exarnined. The results have been analysed using a recent approach due to Pi&r. There is some discrepancy between the present results and an earlier investigation.
1. rIltrodllction A current
problem in electrolyte solutions is how to predict the thermodynamic properties of mixtures of electrolytes from the properties of single-component electrolyte solutions. Some progress has been made(‘) on the prediction of the properties of multi-component mixtures from the properties of single and binary systems but there is as yet no entirely satisfactory way of obtaining the properties of binary mixtures from the available information on single-component solutions. It is essential that before such a task is initiated the experimental data on both single and binary solutions should be reliable. With this in mind we have initiated a series of measurements aimed at cotiming the validity or otherwise of some early experimental work. In this paper the osmotic coefficients of CsCl and of CsCl + KC1 in water at 298.15 K over the approximate molality range 1 to 4.5 mol kg-’ are presented. 2. Experimental The isopiestic apparatus and procedure have been described elsewhere.@*‘) The KC1 and CsCl were high-quality analytical reagents of 99.9 moles per cent minimum purity. They were dried at 450 K for 48 h before use. 3. Results The experimental results obtained are given in tables 1 and 2. The agreement obtained between triplicate determinations on each solution investigated was always better than 0.1 per cent and the molalities presented in table 1 are each the mean of three determinations. 0021-9614/78/0701-0683
$01.00/O
0 1978 Academic Press Inc. (London)
Ltd.
684
A. M. BAHIA, T. H. LILLEY, AND I. R. TASKBR TABLE I. The molalities of CsCl (mCaCL)and KCl (mxOt) in isopiestic equilibrium
mscl mol kg-l
mol kg-l
mol kg-l
0.9939 1.0649 1.2366
0.9546 1.0234 1.1856
2.1705 2.3334 2.7953
-------
MXCl
ma01
mxCl
mol kg-l 2.0611 2.2111 2.6501
as01
mol kg-l 3.5326 3.5495 3.7867
mx01
mCsOl
mol kg-l
mol kg-l
3.3460 3.3499 3.5817
4.3112 4.4124
mxOl
mol kg-l 4.0634 4.1633
TABLE 2. Molalities of solutions of KC1 + CsCl in isopiestic equilibrium with KC1 solutions The total salt molality is m and yoscl is the electrolyte mole fraction of CsCl m
mol kg-’ 0.9546 0.9632 0.9757 0.9770 0.9831 0.9882
m Ycm
0 0.2107 0.4175 0.5118 0.6152 0.8067
~ mol kg-l
2.0611 2.0896 2.1086 2.1209 2.1305 2.1567
m YCSOl
0 0.2011 0.3970 0.4978 0.5920 0.7968
___ mol kg-’
3.3499 3.3974 3.4377 3.-1607 3.4767 3.5175
Y0801
0 0.2011 0.3970 0.4978 0.5920 0.7968
4. Discussion ft was decided to use the Pitzert4) approach to the thermodynamic properties of electrolytes rather than other approaches’5p 6, principally because of its simplicity and the relatively small number of coefficients necessary adequately to represent experimental results. The expression obtained from this procedure for the osmotic coefficient 4 of a solution containing a single electrolyte MX of the 1-l charge type is q5=l +fbi- B&xm+C$,m2, (1) where m is the molality of the electrolyte, f” is the modified Debye-Htickel expression for the osmotic coefficient, and B&x and C&x are coefficients representing, in an approximate manner at least, pairwise and triplet interactions between the ions Mf and X-. The analytical expression for f4 is given elsewhere,(‘) and that for Bcx is B&,= j?Ei+fi& exp{ -2(m/me)'/'}, (2) where #$A and &$ are unknown coefficients, as is C&, above, and where me = 1 mol kg-‘. In treating experimental results all that is necessary is to fit the results to the combination of equations (1) and (2) with three unknown coefficients /3&, p& and C&x. The results obtained from a least-squares procedure to the present experimental results on solutions containing only CsCl are: B&t&, = 3.1310 x 10m2 mol-’ kg, /3&i& = 6.5925 x 10m2 mol- 1 kg, and C&r = 3.0705 x low4 mole2 kg’. Using these coefficients gives an average deviation from the experimental osmotic coefficients of 9 x 10B4. A comparison of the present results with those presented in Robinson and Stokes’ monograph(*) (which would appear to come from earlier work(g)) indicates that in the molality range investigated differences of up to 0.6 per cent are found. That the present results are correct is indicated by the agreement we find (0.1 per cent
AQUEOUS TABLE
685
CsCl + KC1
3. The osmotic coefficient &b,cI of CsCl at some round values1 of molahty
mo.4mol kg-’ 4”CaCL
CsCl AND
1 0.862
1.5 0.862
2.0 0.866
2.5 0.813
3.0 0.882
3.5 0.893
4.0 0.904
4.5 0.917
or better) with work by Jones”‘) and Kirgintsev and Luk’yanov.(“) In table 3 we present osmotic coefficients for CsCl solutions at round values of molality. We suggest that this table should replace that given elsewhere.“’ In the analysis of the mixed-electrolyte results we have also used the approach of Pitzer.(12) The osmotic coefficient rjmix of a solution containing CsCl +KCl is related to the osmotic coefficients of solutions containing only CsCl (&c,) and only KC1 (&-,) at the same modality as those of the mixture by(“) 4miX
= YCsC&sC*
+YKC&Cl+(eK,Cs
+m~K,Cs,C3mYx~CIYKCl~
(3)
where m is the sum of the molalities of CsCl and KCl, ycsci and YKct are the electrolyte mole fraction@ in a salt mixture, and t+cCs and $x, cs,c, are Coefficients which give a measure of interactions between the subscripted species. Analysis of the experimental results on the electrolyte mixtures, using the above coefficients for CsCl and those given earlier(‘) for KCl, indicated that only one coefficient in equation (3) was necessary to represent them adequately, namely t&& = - 6.5 x 10d3 mol-’ kg. Using this value the average deviation between the observed and calculated osmotic coefficients was 1.0 x 10T3. In the analysis (12) of some earlier(“) data on CsCl + KC1 mixtures it was concluded that only the lfik, cs, Cl term, with a value 0.0013 molV2 kg2, was needed. This conclusion, and one other(14) analysis of the older experimental results, is incorrect since it is based on the erroneous osmotic coefficients for CsCl solutions referred to earlier. We acknowledge financial support from the Iraqi Government
and S.R.C.
REFERENCES 1. See Lilley, T. H. Electrochemistry Vol. 5, Chapter 1. Chemical Society Specialist Periodical Report. 1975. for a summary and references. 2. Briggs, C. C.; Charlton, R.; Lilley, T. H. J. Chem. Thermouynamics 1973, 5, 445. 3. Lilley, T. H. ; Scott, R. P. J. Chem. Sot. Far&y Trans. Z 1976, 72, 184. 4. A summary is given in Pitzer, K. S. Ace. Chem. Res. 1977, 10, 371. 5. Wu, Y. C.; Rush, R. M.; Scatchard, G. J. Phys. Chem. 1968, 72, 4048. 6. Scatchard, G.; Rush, R. M.; Johnson, 3. S. J. Phys. Chem. 1970, 74, 3876. 7. Pitzer, K. S.; Mayorga, G. J. Phys. Chem. 1973, 77, 2200. 8. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions. Revised edition. Butterworths: London. 1965. 9. Robinson, R. A. J. Am. Gem. Sot. 1952, 74, 6035. 10. Jones, R. A. Thesis, University of Reading. 1969. 11. Kirgintsev, A. N. ; Luk’yanov, A. V. Russ. J. Phys. Chem. 1966, 40, 686. 12. Pitzer, K. S.; Kim, J. J. J. Am. Chem. Sue. 1974, 96, 5701. 13. Robinson, R. A. Trans. Faraday Sot. 1953, 49, 1147. 14. Rush, R. M. Oak Ridge National L&oratory Report No. ORNL4402. 1969.
The osmotic coefficients and CsCl + KCI mixtures A. M. BAHIA,
T. H. LILLEY,
of aqueous CsCl at 298.15 K
and I. R. TAXER
Chemistry Department, The University, SheffieldS3 7HF, U.K. (Received24 October 1977; in revisedform I December1977) The osmotic coefficients of aqueous solutions containing CsCl and CsCl + KC1 at 298.15 K have been re-exarnined. The results have been analysed using a recent approach due to Pi&r. There is some discrepancy between the present results and an earlier investigation.
1. rIltrodllction A current
problem in electrolyte solutions is how to predict the thermodynamic properties of mixtures of electrolytes from the properties of single-component electrolyte solutions. Some progress has been made(‘) on the prediction of the properties of multi-component mixtures from the properties of single and binary systems but there is as yet no entirely satisfactory way of obtaining the properties of binary mixtures from the available information on single-component solutions. It is essential that before such a task is initiated the experimental data on both single and binary solutions should be reliable. With this in mind we have initiated a series of measurements aimed at cotiming the validity or otherwise of some early experimental work. In this paper the osmotic coefficients of CsCl and of CsCl + KC1 in water at 298.15 K over the approximate molality range 1 to 4.5 mol kg-’ are presented. 2. Experimental The isopiestic apparatus and procedure have been described elsewhere.@*‘) The KC1 and CsCl were high-quality analytical reagents of 99.9 moles per cent minimum purity. They were dried at 450 K for 48 h before use. 3. Results The experimental results obtained are given in tables 1 and 2. The agreement obtained between triplicate determinations on each solution investigated was always better than 0.1 per cent and the molalities presented in table 1 are each the mean of three determinations. 0021-9614/78/0701-0683
$01.00/O
0 1978 Academic Press Inc. (London)
Ltd.
684
A. M. BAHIA, T. H. LILLEY, AND I. R. TASKBR TABLE I. The molalities of CsCl (mCaCL)and KCl (mxOt) in isopiestic equilibrium
mscl mol kg-l
mol kg-l
mol kg-l
0.9939 1.0649 1.2366
0.9546 1.0234 1.1856
2.1705 2.3334 2.7953
-------
MXCl
ma01
mxCl
mol kg-l 2.0611 2.2111 2.6501
as01
mol kg-l 3.5326 3.5495 3.7867
mx01
mCsOl
mol kg-l
mol kg-l
3.3460 3.3499 3.5817
4.3112 4.4124
mxOl
mol kg-l 4.0634 4.1633
TABLE 2. Molalities of solutions of KC1 + CsCl in isopiestic equilibrium with KC1 solutions The total salt molality is m and yoscl is the electrolyte mole fraction of CsCl m
mol kg-’ 0.9546 0.9632 0.9757 0.9770 0.9831 0.9882
m Ycm
0 0.2107 0.4175 0.5118 0.6152 0.8067
~ mol kg-l
2.0611 2.0896 2.1086 2.1209 2.1305 2.1567
m YCSOl
0 0.2011 0.3970 0.4978 0.5920 0.7968
___ mol kg-’
3.3499 3.3974 3.4377 3.-1607 3.4767 3.5175
Y0801
0 0.2011 0.3970 0.4978 0.5920 0.7968
4. Discussion ft was decided to use the Pitzert4) approach to the thermodynamic properties of electrolytes rather than other approaches’5p 6, principally because of its simplicity and the relatively small number of coefficients necessary adequately to represent experimental results. The expression obtained from this procedure for the osmotic coefficient 4 of a solution containing a single electrolyte MX of the 1-l charge type is q5=l +fbi- B&xm+C$,m2, (1) where m is the molality of the electrolyte, f” is the modified Debye-Htickel expression for the osmotic coefficient, and B&x and C&x are coefficients representing, in an approximate manner at least, pairwise and triplet interactions between the ions Mf and X-. The analytical expression for f4 is given elsewhere,(‘) and that for Bcx is B&,= j?Ei+fi& exp{ -2(m/me)'/'}, (2) where #$A and &$ are unknown coefficients, as is C&, above, and where me = 1 mol kg-‘. In treating experimental results all that is necessary is to fit the results to the combination of equations (1) and (2) with three unknown coefficients /3&, p& and C&x. The results obtained from a least-squares procedure to the present experimental results on solutions containing only CsCl are: B&t&, = 3.1310 x 10m2 mol-’ kg, /3&i& = 6.5925 x 10m2 mol- 1 kg, and C&r = 3.0705 x low4 mole2 kg’. Using these coefficients gives an average deviation from the experimental osmotic coefficients of 9 x 10B4. A comparison of the present results with those presented in Robinson and Stokes’ monograph(*) (which would appear to come from earlier work(g)) indicates that in the molality range investigated differences of up to 0.6 per cent are found. That the present results are correct is indicated by the agreement we find (0.1 per cent
AQUEOUS TABLE
685
CsCl + KC1
3. The osmotic coefficient &b,cI of CsCl at some round values1 of molahty
mo.4mol kg-’ 4”CaCL
CsCl AND
1 0.862
1.5 0.862
2.0 0.866
2.5 0.813
3.0 0.882
3.5 0.893
4.0 0.904
4.5 0.917
or better) with work by Jones”‘) and Kirgintsev and Luk’yanov.(“) In table 3 we present osmotic coefficients for CsCl solutions at round values of molality. We suggest that this table should replace that given elsewhere.“’ In the analysis of the mixed-electrolyte results we have also used the approach of Pitzer.(12) The osmotic coefficient rjmix of a solution containing CsCl +KCl is related to the osmotic coefficients of solutions containing only CsCl (&c,) and only KC1 (&-,) at the same modality as those of the mixture by(“) 4miX
= YCsC&sC*
+YKC&Cl+(eK,Cs
+m~K,Cs,C3mYx~CIYKCl~
(3)
where m is the sum of the molalities of CsCl and KCl, ycsci and YKct are the electrolyte mole fraction@ in a salt mixture, and t+cCs and $x, cs,c, are Coefficients which give a measure of interactions between the subscripted species. Analysis of the experimental results on the electrolyte mixtures, using the above coefficients for CsCl and those given earlier(‘) for KCl, indicated that only one coefficient in equation (3) was necessary to represent them adequately, namely t&& = - 6.5 x 10d3 mol-’ kg. Using this value the average deviation between the observed and calculated osmotic coefficients was 1.0 x 10T3. In the analysis (12) of some earlier(“) data on CsCl + KC1 mixtures it was concluded that only the lfik, cs, Cl term, with a value 0.0013 molV2 kg2, was needed. This conclusion, and one other(14) analysis of the older experimental results, is incorrect since it is based on the erroneous osmotic coefficients for CsCl solutions referred to earlier. We acknowledge financial support from the Iraqi Government
and S.R.C.
REFERENCES 1. See Lilley, T. H. Electrochemistry Vol. 5, Chapter 1. Chemical Society Specialist Periodical Report. 1975. for a summary and references. 2. Briggs, C. C.; Charlton, R.; Lilley, T. H. J. Chem. Thermouynamics 1973, 5, 445. 3. Lilley, T. H. ; Scott, R. P. J. Chem. Sot. Far&y Trans. Z 1976, 72, 184. 4. A summary is given in Pitzer, K. S. Ace. Chem. Res. 1977, 10, 371. 5. Wu, Y. C.; Rush, R. M.; Scatchard, G. J. Phys. Chem. 1968, 72, 4048. 6. Scatchard, G.; Rush, R. M.; Johnson, 3. S. J. Phys. Chem. 1970, 74, 3876. 7. Pitzer, K. S.; Mayorga, G. J. Phys. Chem. 1973, 77, 2200. 8. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions. Revised edition. Butterworths: London. 1965. 9. Robinson, R. A. J. Am. Gem. Sot. 1952, 74, 6035. 10. Jones, R. A. Thesis, University of Reading. 1969. 11. Kirgintsev, A. N. ; Luk’yanov, A. V. Russ. J. Phys. Chem. 1966, 40, 686. 12. Pitzer, K. S.; Kim, J. J. J. Am. Chem. Sue. 1974, 96, 5701. 13. Robinson, R. A. Trans. Faraday Sot. 1953, 49, 1147. 14. Rush, R. M. Oak Ridge National L&oratory Report No. ORNL4402. 1969.