ANALYTICAL CHEMISTRY
910 The following example illustrates the use of these equations: Using pure nickel, the torsion suspension of the magnetic balance vias found to twist 22.5” per gram of nickel. As urn = 56.2 c.g.s./gram for nickel at room temperature, k = 22.5”/56.2 c.g.s. = 0.4004”/c.g.s.
A catalyst sample having a ratio of a-Fe:FeaOl = 76:24-that is, 7n2/(rn2 ma) = 0.76-as found by x-rayodiffraction, showed a deflertion a t room temFerature, J!I = 8.20 . At T = 330” C., the deflection was 5.85 ; hence, ( d i d 3 ) ~= 5.85/8.20 = 0.713. Furthermore, it has been found that, under the conditions of measurement, the specific magnetizations of metallic iron and of magnetite a t 330” C. are 96.5 and 76%, respectively, of their specific magnetization a t room temperature. Hence, from Equation (5B), d2 d3 = 0.713 (218 X 0.76 95.3 X 0.24)/ (210.4 X 0.76 72.4 X 0.24) = 0.758. From (SA), 0.758 = 0.4004(m~ m3)(218 X 0.76 95.3 X 0.24)/8.20, and m~ m3 = 0.0824 gram. Thus m2 = 0.76 X 0.0824 = 0.0626 gram and m3 = 0.24 X 0.0824 = 0.0198 gram. Also from Equation 6, d, = 1 - 0.758 = 0.242, and from (4A), 0.242 = 0.4004 X 140 X m1/8.20, ml = 0.0354 gram. From Equation 7, ?itm = 0.9030 X 0.0354 0.0626 0.7236 X 0.0198 = 0.109 gram of iron. The chemically determined mass of iron was 0.140 gram. Hence, from (SA to D),
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$’& iron in FelC = 90.30 X 0.0354/0.140 = 22.9% % iron in a-Fe = 100 X 0.0626/0.140 = 44.8% yo iron in F& = 72.36 X 0.0198/0.140 = 10.3% % nondetectable iron = lOO(0.140 - 0.109)/0.140 = 22.0% The errors in this type of analysis are those of sampling and of the chemical, x-ray, and magnetic analyses. The chemical analysis determines the accuracy of m, and the x-ray analysis that ma) only. Sampling errors beof mz/(ml m3) and ma/(ml come apparent from the reproducibility of the shape of thermomagnetic curves obtained with two or more samples of the same preparation. The mean total error-that is, those errors just described plus errors in k , UT, D, (dz errors caused by
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remanent magnetization, and errors caused by promoter-iron complexes (such as, magnesiof&rite)-is estimated to be about &8$& of the calculated percentages. In the case of fluidized beds, the sampling error is probably much less, and the mean error may thus be reduced considerably, The largest error, however, is that caused by the use of a low field strength. As a result, the saturation values of the specific magnetizations are probably not attained, and the degree of unsaturation may be different for each phase. The error from this source is included in the magnetically nondetectable fraction, the composition of which is unknown. By the use of a more powerful magnet, this error should be considerably decreased. LITERATURE CITED
(1) Austin, J. B., “Metals Handbook,” pp. 1181-2,Cleveland, Ohio,
Am. SOC.Metals, 1948. (2)BBnard, Jacques, Bull. S O C . chim. France, D109-16 (March-April 1949). A possible magnetic method using low temperatures. (3) Darken, L. S., and Gurry, R. W., “Metals Handbook,” pp. 121213, Cleveland, Ohio, Am. SOC.Metals, 1948. (4) Eisenhut, O.,and Kaupp, E., 2.Elektrochem., 36,392-404(1930). ( 5 ) Lehrer. E..Ibid.. 37.460-73 (1930).
