THE CA1,CULATION OF S--POTEKTIAL FROM A40BILITY MEASUREMENTS BYROBERT J. HEXTER C.X.I.R.O., Division of SotZ8, Canheria, Australka Racezved December 26, 1961
The calculation of f-potential from mobility measurements is a simple matter only when xa is very large ( 100) or very small (50.1). For intermediate values, a correction must be applied __ for the retardation and relaxation effects. The resulting equation for the mobility, U , takes the form of a power series in f . Overbeek' has calculated the coefficients of this series up to terms in (3, for both symmetrical and unsymmetrical electrolytes, while Booth2 has calculated the coefficients up to p4 for symmetrical electrolytes. Booth's equation takes the form
>
terms are of no value for the calculation of p because of the inherent limitations of eq. l. Booth's eq. 1 is actually an infinite series for which only coefficients up to C4 have been evaluated. To estimate the influence of the remaining terms on 1 we may introduce into (1) the next term in the series ( C b p 5 ) ; TIT then find, using the second procedure
[(gy- g](gy
+ 7 c12 csc4 (a) u + ... ..
(5)
Kow if we that eq. gives an estimate of Lr accurate to within 5% for (-50 mv. and xa=5, we find that C S - C ~(ie., assuming that the error in U is due solely to neglect of the term in p6). The coefficient of U5 in ( 5 ) then is dominated by the (unknown) value of C5 and there is no point in u = CIS+ car3 c4r4 (l) continuing the exDansion bevond U4. Even if we since C, = 0 for a symmetrical electrolyte. The assume &at Cg
