Potmtlometrlc Sensors
Normalizing y as the fraction f of its maximum value, the general formula of all the hyperbolas under consideration may be written as f = xl(1lb x), where b is the slope of the hyperhola a t x = 0, while the asymptotes are y = 1and x = -(lib). Often y is a concentration and f = € i s the degree of conversion. - y)lymm Since the choice to define f as yly,, or as Cy,, is an arbitrary one, in some cases the hyperbola will decrease with increasing x and the fraction f and its derivative will take the form f = (llb)l(llb x) and -(df/dx) = kf2, respectivelv. The slooe will be nepative, but still proportional to the square of the distance from the curve to the asymptote x = 0,that is, to y2.
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To the Editor:
Selig's entertaining article on potentiometric sensors gives the impression, inadvertently perhaps, that the glass electrode has only just been discovered as a sensor for fluoride titrations (I).In fact its use goes hack a t least as far as the 1940's when quick methods for fluorine determination were being sought in the Manhattan project. More recently a detailed comparison of the glass with the fluoride I.S.E. has shown that the former is a perfectly adequate substitute for fluoride determination on the milligram scale (2). In these titrations i t is easy to understand how the glass electrode works. The fluorides usually titrated are alkaline in solution because of the weakness of aqueous hydrogen fluoride. The acidity increases as flnoride is precipitated and replaced by anions of stronger acids, and finally by excess of acidic reagent. I t may he that the aluminum electrode, presumably the hydrated oxide surface layer, is also responding to pH variations in flnoride titrations.
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Gawll Nlac lnstnutul Politehnlc Str. Emil lsac 15 3400 Cluj-Napoca. Romania
Llterature Cited 1. Selig, W. S. J , Cham. Educ. 1985.62,431. 2. Cartwight, M.;Wwlf, A. A. J. Fluorine Cham. 1979.13,501
A. A. Woolf Brlstol Polytechnic Coldharbour Lane. Frenchay Bristol. BSl6 1QY Englan6
Some OpportunRles for Reinforcement of Learnlng among the Subdlsclpllnes of Chemistry To the Editor:
T o the list of hyperbolic relationships encountered in chemistry, as discussed by A. L. Underwood [1984,61,143], a very important hyperbolic law can he added: the kinetics of .second-order homogeneous chemical reactions, with one reactant or with two reactants having identical initial concentrations. The integrated rate equation may he written as c = ca/(l kcat) or = tl(llkco t), co being the initial concentration, k the specific rate, and t = (co - c)/co the degree of conversion. I t should be added that all the discussed hyperholas have parallel asymptotes to the coordinate axes. Furthermore, such hyperbolas have slopes, at any point of the curves, proportional to the square of the distance from that point to the asymptote parallel to the x-axis. Specifically for secondorder kinetics this statement is equivalent to the rate law -(dcldt) = kc201 (dtldt) = kcoz(1- Q2.
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384
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Journal of Chemical Education
Whence the Copper 10117 To the Editor:
The article by Ron DeLorenzo (J.Chem. Educ. 1985,62, 424) about corrosion that can occur when dissimilar metals areiu contact is worthwhile information, hut the reactions s likelv to be misleadused to exolain the listed e x a m ~ l e are ing andlor confusing to the uninitiated. ~orkxample,in the case of the Cn/Fe system, Cu2+ is shown as oxidizing Fe, which raises the question, "Whence the copper ion?" In fact there are a variety of mechanisms for the corrosion that occurs in himetall; systems. Typically the more noble metal serves as a conductor for the electrons from the oxidized metal to the oxidizing agent, which is usually a constituent (e.g., oxygen or the oxides of nitrogen or sulfur) of the environment. Often the more noble metal serves as a catalyst if the electron transfer occurs more rapidly on it than on the less nohle metal. Admittedly the more nohle metal may sometimes he oxidized first by the environmental oxidizing agent, and the oxidized form of that metal in turn oxidizes the less nohle metal, hut the environmental oxidant is the ultimate oxidizing agent. Thus in each of the examples given, it would have been more appropriate to have shown oxygen as the oxidizing agent. For example, 4Hf 2Fe Oz 2Fe2+ 2H20, or 2H20 0 2 2Fe 2Fe(OH)2.
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Lawrence F. Koons Twkegee Institute Tuskegee Institute. AL 36088
