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Determination of the dissociation constant and limiting equivalent conductance of a weak electrolyte from conductance measurements on the weak electrolyte
Analytica Chimica Acta, 125 (1981) 219-220 Elsevier Scientific Publishing Company, Amsterdam -
Printed in The Netherlands
Short Communication
DETERMINATION OF THE DISSOCIATION CONSTANT AND LIMITING EQUIVALENT CONDUCTANCE OF A WEAK ELECTROLYTE FROM CONDUCTANCE MEASUREMENTS ON THE WEAK ELECTROLYTE
LEONARD
Chemistry
S. LEVITT
Department.
College of Science. ‘The University of Texas at El Paso, El Paso,
TX 79968 +Y.S.A.) (Received 27th October 1980) A method is described for computing the dissociation constant and equivalent conductance at infinite dilution, ~~ , for a weak electrolyte from as few as two conductance measurements at different concentrations_ The iterative procedure applied to acetic and an average value (n = 4) of acid data yielded a dissociation constant of 1.80 x lo-’ A, of 389.5 compared with an expected value of 390.7.
Summary.
It is well known that a plot of the equivalent conductance, A, vs. cl’* for a strong electrolyte gives a straight line (Kohlrausch’s Law) which can readily be extrapolated to zero concentration to obtain AO, the equivalent conductance at infinite dilution. For a weak electrolyte the same plot is curved and approaches the A axis asymptotically, thus making it impossible to determine A0 by extrapolation. Consequently, A, for a weak electrolyte is computed as the sum of the individual ionic conductances at infinite dilution, X0, which in turn are determined from conductance measurements on strong electrolytes by the application of Kohlrausch’s second Law (X0+, + X,-) = A,,)_ It is shown below that both A0 and the concentration dissociation constant, K,, can be calculated accurately for weak electrolytes from as few as two conductance measurements at two different concentrations. Neither graphical extrapolation nor individual ionic conductivities at infinite dilution are required for these calculations. The accuracy of the method is limited by the accuracy of the Ostwald-Arrhenius dilution law [l] Kc= A*C/A,,(A,,-A)
(1)
In principle it is necessary only to solve two equations for two unknowns (A0 and Z!&j which seems trivial and obvious enough, except for the fact that it is never done. Equation (1) can be solved for A0 to yield Ao = (A/2)
[l + (1 + 4c K,-‘)‘p-]
(2)
Substituting A 1 and A2 at concentrations c, and c2, respectively, it is shown that Kc= {[li2(++
KJ”2-A1(4cl
0003-2670/81/000~000/$02_50
+ K,)“*]/[AI-_A,]}* 0 1981 Elsevier Scientific Publishing Company
(3)
Equation (3) can be solved for numerical data by an iterative procedure in which it is assumed that 4c > K,, or by regression methods. When K, has been determined in this manner, it can be used to calculate A0 with eqn. (2). The values obtained for A,, for two or more experimental concentrations should agree. The equilibrium constant and conductance at one concentration can also be used to compute the conductance at any other concentration using eqn. (2). The applicability of these relations was evaiuated using the conductance data of MacInnes and Shedlovsky [2] for acetic acid at 25°C. From the data for two low concentrations (c, = 2.801 X lo-‘; A 1 = 210.4; and c2 = 1.028 X IO”; A2 = 48.15), the iterative procedure yielded ;i, = 1.80 X lo-‘. This is the usual value for acetic acid when K, is not corrected for activity coefficients [ 33 . Values of A0 computed with K, = 1.80 X lo-’ and c = 2.801 X 10m5, 1.028 X 10m3, 5.911 X lo”, and 1.0 X 10-l M were 388, 389,391, and 390, respectively, compared with the accepted thermodynamic value of 390.7 for acetic acid [3] _ It should be clear that for higher concentrations, where 4c/K, 9 1, eqn. (2) can be simplified [4] to A JA2 5 (c~/c~)‘~‘, which gives quite accurate results at alI concentrations [4] above 0.01 M. REFERENCES 1 2 3 4
L. D. G. L.
S. Levitt and H. Widing, Chem. Ind., (1974) 781. A. MacInnes and T_ Shedlovsky, J. Am. Chem. Sot., 54 (1932) 1429. M. Barrow, Physical Chemistry, McGraw-Hill, 2nd edn., 1966, p_ 652. S_ Levitt, Chem. Ind., (1961) 1621.
Printed in The Netherlands
Short Communication
DETERMINATION OF THE DISSOCIATION CONSTANT AND LIMITING EQUIVALENT CONDUCTANCE OF A WEAK ELECTROLYTE FROM CONDUCTANCE MEASUREMENTS ON THE WEAK ELECTROLYTE
LEONARD
Chemistry
S. LEVITT
Department.
College of Science. ‘The University of Texas at El Paso, El Paso,
TX 79968 +Y.S.A.) (Received 27th October 1980) A method is described for computing the dissociation constant and equivalent conductance at infinite dilution, ~~ , for a weak electrolyte from as few as two conductance measurements at different concentrations_ The iterative procedure applied to acetic and an average value (n = 4) of acid data yielded a dissociation constant of 1.80 x lo-’ A, of 389.5 compared with an expected value of 390.7.
Summary.
It is well known that a plot of the equivalent conductance, A, vs. cl’* for a strong electrolyte gives a straight line (Kohlrausch’s Law) which can readily be extrapolated to zero concentration to obtain AO, the equivalent conductance at infinite dilution. For a weak electrolyte the same plot is curved and approaches the A axis asymptotically, thus making it impossible to determine A0 by extrapolation. Consequently, A, for a weak electrolyte is computed as the sum of the individual ionic conductances at infinite dilution, X0, which in turn are determined from conductance measurements on strong electrolytes by the application of Kohlrausch’s second Law (X0+, + X,-) = A,,)_ It is shown below that both A0 and the concentration dissociation constant, K,, can be calculated accurately for weak electrolytes from as few as two conductance measurements at two different concentrations. Neither graphical extrapolation nor individual ionic conductivities at infinite dilution are required for these calculations. The accuracy of the method is limited by the accuracy of the Ostwald-Arrhenius dilution law [l] Kc= A*C/A,,(A,,-A)
(1)
In principle it is necessary only to solve two equations for two unknowns (A0 and Z!&j which seems trivial and obvious enough, except for the fact that it is never done. Equation (1) can be solved for A0 to yield Ao = (A/2)
[l + (1 + 4c K,-‘)‘p-]
(2)
Substituting A 1 and A2 at concentrations c, and c2, respectively, it is shown that Kc= {[li2(++
KJ”2-A1(4cl
0003-2670/81/000~000/$02_50
+ K,)“*]/[AI-_A,]}* 0 1981 Elsevier Scientific Publishing Company
(3)
Equation (3) can be solved for numerical data by an iterative procedure in which it is assumed that 4c > K,, or by regression methods. When K, has been determined in this manner, it can be used to calculate A0 with eqn. (2). The values obtained for A,, for two or more experimental concentrations should agree. The equilibrium constant and conductance at one concentration can also be used to compute the conductance at any other concentration using eqn. (2). The applicability of these relations was evaiuated using the conductance data of MacInnes and Shedlovsky [2] for acetic acid at 25°C. From the data for two low concentrations (c, = 2.801 X lo-‘; A 1 = 210.4; and c2 = 1.028 X IO”; A2 = 48.15), the iterative procedure yielded ;i, = 1.80 X lo-‘. This is the usual value for acetic acid when K, is not corrected for activity coefficients [ 33 . Values of A0 computed with K, = 1.80 X lo-’ and c = 2.801 X 10m5, 1.028 X 10m3, 5.911 X lo”, and 1.0 X 10-l M were 388, 389,391, and 390, respectively, compared with the accepted thermodynamic value of 390.7 for acetic acid [3] _ It should be clear that for higher concentrations, where 4c/K, 9 1, eqn. (2) can be simplified [4] to A JA2 5 (c~/c~)‘~‘, which gives quite accurate results at alI concentrations [4] above 0.01 M. REFERENCES 1 2 3 4
L. D. G. L.
S. Levitt and H. Widing, Chem. Ind., (1974) 781. A. MacInnes and T_ Shedlovsky, J. Am. Chem. Sot., 54 (1932) 1429. M. Barrow, Physical Chemistry, McGraw-Hill, 2nd edn., 1966, p_ 652. S_ Levitt, Chem. Ind., (1961) 1621.