only this theory, but also the possibility that cellular mechanisms play a role in the development of immunity. Dr. Miller's experiments using gamma-irradiated treponemes have provided more information on the possible nature of the immunogenic antigens. Gamma irradiation of treponemes with 520,200 roentgens results in the serological inactivation of heatlabile antigens. Since organisms irradiated with 650,000 roentgens can stimulate complete protection, it's conceivable that radiation-resistant, heat-stable antigens, presumably polysaccharide in nature, play a dominant role in stimulating the treponemicidal antibodies. Preliminary attempts have been made to extract relatively pure, im-
munogenic polysaccharide antigens from the Nichols strain. These tries have resulted in the isolation of a homogeneous polysaccharidee— acts with homologous rabbit—but not human—syphilitic sera. These results provide additional support to a concept suggested by Dr. J. H. Bekker and Dr. J. H. DeBruijn of the National Institute of Public Health, Bilthoven, the Netherlands, and Dr. Miller. They believe that either antigenic differences exist between the rabbitadapted Nichols and human strains of T. pallidum or that there are differences in the host response to certain of the treponemal antigens. Cousins. Dr. John Knox at Baylor medical school in Houston, Tex., has tried to develop a vaccine against
syphilis by injecting harmless treponemes (commonly found, for example, in the mouths of humans). These treponemes do not cause syphilis or any other disease. Dr. Knox's theory is that the related treponemes could offer some protection against their bacteriological cousin, the treponeme that causes syphilis. One of the problems that confronts all venereal disease research workers is the risk that the vaccine can produce positive blood tests for syphilis in immunized patients who have never had the disease, points out Dr. Leslie C. Norins, a specialist at CDC on the immunology of venereal disease. These false positive results could destroy the reliability of the test to diagnose syphilis and could hinder
New function gives quantitative determination of acid strengths A new quantitative determination of acid strengths is made possible by use of a mathematical function developed by Dr. Leonard S. Levitt and Harry F. Widing (who has just obtained a B.S. in physics) of the University of Texas at El Paso. Based on the Ostwald dilution law, the function describes the ability of any Bronsted acidic solute to transfer a proton to any solvent and the reverse—the ability of any base to abstract a proton from a Bronsted acidic solvent. This function can give much more information to chemists than can the customary comparison of the ratio of the ionization constants of two different acids. Such a conventional comparison is especially meaningless if a strong acid such as hydrochloric acid is considered; in water, its ionization constant is practically infinite, Dr. Levitt points out. The usual form of the Ostwald dilution law, K = a2c/(1—a), where K is the ionization constant, a is the fraction of a weak acid or base ionized in a given solvent, and c is the molar concentration of the acid or base, can be plotted as a family of curves (which intersect only at c = O), with K as the parameter. To eliminate any arbitrary choice of concentration at which the fraction of acids or bases ionized will be compared, the comparisons are made at concentrations between 0 and 1M. This can be done, Dr. Levitt says, by integrating to find the areas under the curves. However, because the curves are asymptotic to the "c" axis, integration between zero and infinity is not practical. If the axes are transposed and the Ostwald equation is converted to the 50 C&EN JUNE 21, 1971
form where concentration is obtained as a function of the fraction ionized, then c(a) = K(1-a)/a2. This function, when integrated over the limits of a between zero and one, becomes equivalent to a sum of two areas—those on either side of the fraction («i) of the acid or base ionized at unit concentration. Upon evaluating the integrals and noting that K is constant, Dr. Levitt and Mr. Widing obtain the area (S):
S = ai + K(1/«i — 1 + In ai). When the equivalent for K from Ostwald's law is substituted into this expression, the final equation becomes:
S =
ai[2 +
ai(1
ai) _1 lnai].
The second term in the brackets of the equation approaches minus one as ai nears unity, and therefore S approaches
one. This would be the situation for a strong acid, for instance, Dr. Levitt points out. For a weak acid, S can be considered as nearly 2ai, or 2V/C For a very weak acid, ax approaches zero and, therefore, S approaches zero. Relative strengths of two different acids can be calculated easily using data obtained from conductivity and spectroscopic measurements. If, for example, one of the acids is strong, then Ss is one. The relative strength, Ss/Sw, of a strong and a weak acid becomes nearly equal to 1/(2V/C). If both of the acids are weak, then the relative strength is nearly equivalent to VK1/K2, where the subscripts identify the acids. If applied to benzoic and acetic acids, the relative strength as calculated from the simplified equation is two, not four as would be found from comparing ionization constants.
Dr. Levitt (left) and Mr. Widing base function on Ostwald dilution law
