Simple Square-Law Computer - Analytical Chemistry (ACS Publications)

Simple Square-Law Computer. Robert Muller. Anal. Chem. , 1951, 23 (10), pp 1494–1495. DOI: 10.1021/ac60058a039. Publication Date: October 1951. ACS ...
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directly proportional to the square of the shaft rotation. This swamping circuit entails an error of 1 part in 10,000 as a consequence of this approximation, which is ten times smaller than the rated precision of the Helipot (linearity, 0.1%) and still smaller than the reproducibility of the recorder. The function of the right branch of the circuit is almost selfevident. As the normal zero position of the computer Helipot is mid-center, there i d be a finite signal a t this position. This can be canceled exactly by means of the 15-ohm slide-Tire designated as “zero sct.” By this means, the recorder pen can be set to zero or to any desired up-scale reference position.

Simple Square4aw Computer RALPH H. M e L L E R ’ .Yew I-ork University, New York 3, X.

Y.

URIKG extensive studies on the rate of diffusion of liquids D through filter paper, semiautomatic equipment was developed to record the kinetics of the phenomenon. The rise of liq-

+

uids in paper strips was followed by a traveling low-power microscope, the elevation shaft of which n-as coupled with a preci.cion potentiometer (Helipot). The potential drop across the potentiometer Tyas automatically and pcriodically connected to :L Brown Elcctronik recorder a t exactly 1-minute intervals. The final record exhibited the capillary rise as a function of elapsed time. This turned out to be a square-law relationship. To evaluate diffusion coefficients, it was necessary to compute the square of each recorded height and replot it as a funrtion of time. Although the instrument was precise and rapid and eliminated t.he confusion element, it n-as deceptive, in that the operator n-as likely to forget the tedious computations following data so e a d y and rapidly acquired (3). K i t h very little modification, a circuit has been devised which develops potentials proportional t o the square of the microscope trawl, v-hich cnn lie recorded, ns before, at stated time intervalq. Several electrical and electronic means 101~squai,irig 01’ olitaiiiiiig the quadratic function are linon-n. One of these ~ w chosen s 11crause its requirements imposed the lrnst change in cyui~)nient.

22.5 V

100K

-J n

1-

.L Figure 2

To check thc perforiixtnce of this computer element, thc of which mas coupled to the Helipot,, scale mounted in the vertical plane. onnected to the recorder through the intermittent timer. .cvailing height was therefore drawn by the recorder a t exactly 1-minute intervals, the duration of the writing intcrv:il being 5 secontls in eac:h case. Figure 3, A , is n trariny of a tj.i)irnl recording in which uniform 5-mm. increments of height wcrv srt in on the microscope. The recorded ordinates show the c q c ~ r t r t lresponse proportional to h*. A more direct inierforniancc is shown in Figure 3, B, in \rhjch pc settings IYRS computcti such that successive thr, squnrc root of h . Khcn thcw were sct

Figure 1

If the extremities of the winding of a uniform potmtionietcr are connected together as shown in Figure I , then the net resistance, R, measured between the slider and the shorted ends is a quadratic function of the displacement, of the slider from the midpoint of the winding. Thus, if Ro is the total resistance, and the linear displncenient of tht, slider from the mid-poiiit is 2, the latter can vary brtn.cen zcrn arid TT = + l . It (‘an be shown ( 1 ) thnt Ro/4 X (1

It

- 2’) li

For the vai,ious possible values of x, the niasimum and minimum valueP of R will be R0/4 and 0, respectively, with a quadratic variation of R between these limits. This computer element has been widely used for squaring a n d in ti,iangle solvers ( g ) . For the present purpose the square-law variation of R in this circuit was not directly applicable. There were two requirement9: a potential varying as the square of shaft rotation and lon- output impedance to match the input of the Brown recorder. This was solved b>- means of the simple circuit illustrated i l l 1;iyure 2.

-h

Considering for a moment the left branch of the circuit, the shorted 50-ohm Helipot, is connected in series with a large swamping resistor of 100,000 ohms. \Vith the fixed potential of 22.5 volts applied to these resistors, the current t,hrough them is practically independent of the position of the slider, Thich can produce a change of resistance no greater than 12.5 ohms out of n total of some 100,OOO ohms. However, the drop in potential Iiet~wenthe top connection of the Helipot and ground nil1 be 1

ZERO SET

50

I

=

I RECORDER

R

12

I

EL EVATl0 N

increasinp

decreasinq

c--.

Figure 4

I’rcicnt address, 1.0s Alamos PrientiIic Laboratory. 1.0s hlanios. S . 11.

1494

V O L U M E 23, N 0.

OCTOBER 1951

in with the microscope drive, one after another, up to the maximum and then removed successively, the recorder drew the pattern shown in B , in which the ordinates rise and fall in uniform increments-Le., proportibnal to h. The range or proportionality factor in this network can be varied by changing the applied potential or by the choice of swamping resistors. If the latter method is chosen, the only practical requirement is to keep the magnitude of the swamping resistors a t least 1000 times greater than the maximal value of the squaring element. In this application, no elaborate precautions were taken to ensure the maximum attainable precision. The battery source was permanently connected to the network, wherein the drain was a constant 450 Fa. Temperature coefficients of resistance and source e.m.f. were ignored and under these circumstances the reproducibility over weeks a t a time was of the order of 0.09 chart divisions, which corresponds to an error signal a t the input of the recorder of 2 pv. Any doubt about the absolute response is easily checked by setting the microscope drive to an arbitrarily chosen height. If the indicated response differs detectably from the correct value, the operator may restore the original deflection electrically or use a small correction factor in computing the slope of the square-law plot. In anv case the quadratic response is rig-

1495 orously maintained-only the slope factor is subject to change. For anyone interested in precision beyond these high levels, or in very long-term stability, the conventional potentiometric methods of checking against a standard cell can be used. The literature ( 1 , 4, 6) on related computer elements iq extensive. Any instrumental development which eliminates tedium and fatigue, and which increases the speed and precision with which data can be accumulated, may well defeat its purpose if it does not include means for the rapid calculation and assimilation of the data. LITER4TURE CITED (1) Greenwood, I. A., H o l d a m , J. V., Jr., a n d MacRae, D., Jr., “ E l e c t r o n i c I n s t r u m e n t s , ” R a d i a t i o n L a b o r a t o r y Series, Vol. 21, p. 121, N e w Y o r k . M c G r a w - H i l l B o o k Co., 1948. (2) Ibid., p. 139. (3) Muller, R. H., a n d Clegg, D. L., AXAL. CHEM., 23, 396-411 (1951). (4) M u r r a y , F. J., “ T h e o r y of h l a t h e n i a t i c a l Machines." 2 n d ed., X e w Y o r k , King’s C r o w n P r e s s , 1948. ( 5 ) S v o b o d a , “ C o m p u t i n g M e c h a n i s m s a n d Linkages,” M.I.T. Radia t i o n L a b o r a t o r y Series, V o l u m e 27, K e w Tork. McGraw-Hi11 B o o k Co., 1947. RECEIVED February 6 , 1961.

lithium Aluminum Hydride as a Qualitative Test Reagent for Aromatic Nitro Compounds LLOYD S. NELSON’ AND DONALD E. LASKOWSKI Illinois Institute of Technology, Chicago 16, I l l . I X T R O M and Brown ( I O ) reported the reduction of nitrobenzene, p-nitrobromobenzene, and nitromesitylene directly to the corresponding symmetrical azo compounds in good yields with lithium aluminum hydride. Because of the distinct color changes which occurred, these workers suggested the possible applicability of lithium aluminum hydride as a reagent for determining aromatic nitro groups. This paper presents the results of a series of experiments designed to investigate the applicability and determine the sensitivity of lithium aluminum hydride as such a test reagent. -4fter its acceptance for publication a note on the same subject appeared (3). Several qualitative tests for the aromatic nitro group have heen reported. Reduction to the amine and subsequent identification appear in several laboratory texts ( 6 , 7 , 14.16). Reduction to the substituted hydroxylamine, .rvhich then gives a positive Tollens test, is also common practice ( 2 , 6,9,12,13,15). Bost and SichOlson ( 1 ) have reported the action of alkali on acetone solutions of aromatic nitro compounds as a color test. Olivier (11) states that, aromatic nitro compounds give a red color with aluminum bromide in benzene. Hearon and Gustavson (4)have explored the use of ferrous hydroxide as a color test reagent for nitro compounds in general. PROCEDURE

T w o materials are required. 1. Lithium aluminum hydride. The product of Metal Hydrides, Inc., was used. The same results are obtained whether the hydride is dark gray or practically white. 2. Absolute ethyl ether. Commercial anhydrous ethyl ether dried over sodium metal was used. Approximately 100 mg. of the unknown are dissolved in 5 ml. of anhydrous ethyl ether. About 10 mg. of lithium aluminum hydride are added to this solution. A change in (but not a disappearance of) the color of the solution, the formation of a colored precipitate, or both, within 5 minutes, is taken as a positive test. 1

Present address, General Elertric Co.. Waterford X Y

DISCUSSION AND CONCLUSIOY

Twenty-six aromatic nitro compounds containing a wide variety of functional groups were tested. These are listed in Table I

Table I Coinpound Solution Color 1-Nitronaphthalene Y tint I O Y normal tone Nitrobenzene 2,4-Dinitrophenylhydrazine Colorless VR shade 2 2-Nitrodiphenylamine YO tint 2 2,4,6-Trinitrotoluene m-Nitrobenzenesulfonic c acid Colorless 3,B-Dinitrobenzoic acid 2.4-Dinitro~henvlthio. ” R O - 0 shade 1 cyanate 0 shade 1 Picric acid o-Nitroiodobenaene c 2-Nitroresorcinol 4-Bromo-3-nitrobenzeneY tint 1-2 sulfonic acid 8-Nitroquinoline R-OR shade 2 o-Nitrobromobenzene YO normal tone e o-Kitroaniline c m-Xitrobenzaldehyde o-Nitrochlorobenzene VR normal tone p-Nitrobenzoic acid Y broken tone 2,4-Dinitrochlorobenzene e rn-Nitrobenzvl alcohol O Y tint 1 Green-brownd o-Xitroanisoie o-Ethylnitrobenzene OR-RO normdl tone 0 - Y O normal o-Nitrotoluene tone Y shade 2 n-Nitrochlorobenzene 0 tint 1 o-Nitrodiphenyl 2-Chloro-5-nitrobenzenesulfonic acid Colorless Abbreviations V. Violet R. Red 0. Orange RO. Red-orange Y. Yellow OR. Orange-red

Precipitate Color Y tint 2 YO shade 1

O Y shade 2 0 shade 1

T tint 2

Limit of Detection, G . / M . X 10 2 3 a

0.01 1

Brownd

2 0.7

R O - 0 shade 2 OR-RO shade 1 R O - 0 tint 1 V broken tone

0 2 8

I’ tint 1-2

R-OR shade 2 V broken tone OY tint 2 Y O shade 2 Y broken tone 0 - Y O shade 2 O Y tint 2

0 3 4 0 1 3 0 2 1 0.4

3

2

,

YO shade 1

0.4 3

YO normal tone

4

Y broken tone OY tint 1

8 3

White

e

b

OY. Orange-yellow YO. Yellow-orange VR. Violet-red

5 Only a saturated solution was tested because of insolubility of compound. b Color uncertain b u t similar to so1,ution color, C Suspended material made detection of solution color uncertain. d N o t adeauatelv described b y color standard. e Negative test.