CONCLUSION
ACKNOWLEDGMENT
The infrared spectrometer described herein can provide good quality spectra of gas chromatographic fractions at levels of 20 micrograms or more. Frequently, observable bands occur at the microgram level. Variable scan speeds of 5 to 20 seconds and the small sample cell allow the spectrometer to be used with either SCOT or packed columns.
H. D. Raymond contributed significantly to the mechanical design and construction. H. C. Tsien and J. A. Wilson also assisted on various Phases of the Project. Laboratory measurements were carried out by T. H. Sara.
RECEIVED for review September 8, 1970. Accepted December 18, 1970.
Simple and Inexpensive Electronic Conductivity Manometer for Monitoring Pressure Changes Application to Pressuremetric Titrations of Iodate and Ammonium Ions D. J. Curran and S . J. Swarin Department of Chemistry, Unicersity of Massachusetts, Amherst, Mass. 01002
A novel pressure transducer system based on the electronic monitoring of the electrolyte level in a manometer with linear conductance circuitry has been developed. The instrument has a multirange capability and a high level dc output. I t is simple in design and construction and can be built with readily available electronic units. Its response to the quantity of gas generated in a closed system is linear to within 2-4 parts per thousand. It has been applied to the pressuremetric titrations of iodate with hydrazine sulfate and ammonium ion with electrogenerated hypobromite. Accuracies and precisions of a few parts per thousand have been obtained, down to the concentration level where only 12 pmoles of gas are evolved.
a multirange capability and a high level dc output suitable for recording. It appears to be suitable for use in all of the applications cited previously. Modular construction has been utilized to take maximum advantage of the economy and versatility of commercially available electronic units. We have demonstrated the applicability of this instrument as an end-point detection device in pressuremetric titrations of 14.33and 1.433-mg samples of iodate with hydrazine sulfate and 4.737- and 0.4737-mg samples of ammonium ion with electrogenerated hypobromite. In the first case nitrogen is generated according to: 103-
IN RECENTYEARS there has been renewed interest in the applications of pressure measurements in chemistry. This undoubtedly is due to the availability of accurate, sensitive, and precise modern pressure transducer systems (1). Typical applications of these instruments include: monitoring gas evolution or absorption in reaction kinetics (2-4), end point detection in pressuremetric titrations (5, 6),and monitoring analytical hydrogenations (7-9). Simple, inexpensive transducer systems are commercially available, but they lack multirange capability. Systems possessing the latter feature are also commercially available, but at a considerable increase in complexity and cost. The manometer has always been a common instrument for pressure measurements because of its simplicity in principle and construction, and its low cost. However, manometry requires numerous readings and constant operator attention. As part of our studies of applications of pressure transducers in chemical analysis, we have developed a simple and inexpensive pressure transducer system, based on a U-tube manometer, which is sensitive, precise, and compact. This instrument has ( I ) D. J. Curran, J. Chem. Educ., 41, A465 (1969). (2) L. R. Mahoney, ANAL.CHEM., 36,2516 (1964). (3) T. G . Traylor and C . A. Russel, J. Amer. Chem. SOC.,87, 3698 (1965). (4) W. K. Rohwedder,J . Cutul., 10,47 (1968). ( 5 ) D. J. Curran and J. L. Driscoll, ANAL.CHEM., 38,1746 (1966). (6) D. J. Curran and J . E. Curley, ibid., 42, 373 (1970). (7) A. Reuter,Z. Aiial. Chem., 231,356 (1967). (8) D. J. Curran and J. L. Driscoll, ANAL.CHEM., 42,1414 (1970). (9) D. J. Curran and J. E. Curley, ibid., 43, 118 (1971). 358
212
+ 51- + 6Hf
+ NZH4 .H?S04
+
Nz
t
+ 3Hz0 + so42-+ 6H+ + 41+
312
(1) (2)
And in the second case : Br2NH4+
+ 20H-
+ 3 BrO-
+ H 2 0 + 2e+ 3 Br- + 2H+ + 3H20
+ BrO-
(3)
f
(4)
+ N2
PRINCIPLE OF OPERATION
In 1926, I. B. Smith (10) described a liquid-level detector based on the conductivity bridge principle. By placing two pairs of identical platinum electrodes in the arms of a U-tube manometer containing an electrolyte, and placing the resistance between each pair of electrodes in a Wheatstone bridge circuit, it was found that the difference in the height of the liquid in the two arms could be determined. Smith’s work was based on the conductivity equation:
L = - 1= - - L,A
R
d
where L is the conductance, R is the resistance, L, is the specific conductance, A is the area of each electrode, and d is the distance between the electrodes. Since, for rectangular electrodes, the area is the product of length (I> and width ( w ) , Equation 5 becomes : 1 LS.Z.W L=-=--R d (10) I. B. Smith, J . Opr. SOC.Amer., 12,655 (1926).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
(6)
and k = 2. In either case, Equations 6 and 7 can be combined to yield : 1 L=R
=
KlAP
where Kl is a constant combining L,, w,d, p, g, and k . Thus, the conductance is linearly related to pressure changes in the manometer. In 1963 C. F. Morrison (11) reported the first linear conductance circuit using operational amplifiers. This circuit was based on the simple inverter amplifier where:
11
Ih
‘!
eout =
i
- ei,
R,
-
Ri,
Here eoutis the output voltage, ei, is the input voltage, R , is the feedback resistance, and R,, is the input resistance. If ei, and Rf are constant and Ri, is the resistance of the conductivity cell, then (10)
Figure 1. Electrolyte-filled manometer
---__
E
where K2 is a constant and Li, is the conductance. A modification of this circuit utilizes a differential design so that any initial conductance can be nulled (12, 13). We report the construction of suitable linear conductance circuitry using operational amplifiers and its application to liquid-level detection in a manometer, in order to obtain a pressure transducer system with linear output. The circuit, shown schematically in Figure 2, consists of an alternating current source (sine wave oscillator), an impedance isolator (voltage follower), and a signal conditioner (linear conductance monitor with null offset). Amplifier 2 is an amplitude stabilized Twin-Tee Sine Wave Generator (14) which produces a very pure sine wave when R/2 is properly adjusted. In this application, a 500-Hz 18-volt peak-to-peak sine wave is produced. This signal is then attenuated to 1-volt peak-to-peak and impedance isolated from the signal conditioning circuitry
Initial level of manometer fluid Final level of manometer fluid Conductivity electrodes
Thus, the resistance is inversely related to the length of the electrodes immersed. Although Smith gave no data on the measurement of pressure with his special monometer, it is obvious that this is possible since the pressure difference between the arms of a manometer is given by:
PL - Pi
=
AP
= pgh
(7)
where p is the density of the manometer liquid, g is the acceleration due to gravity, and h is the height difference between the two arms of the manometer. Figure 1 shows the relationship between h and I for the case where only one pair of electrodes is used. Since the electrode assembly occupies some volume, I is greater than 1’. However, if the horizontal cross-sectional area of the electrode assembly is constant in the vertical plane, then the volume of electrolyte displaced by the assembly must be proportional to the depth of immersion of the assembly, and hence h = kl. For the case in which the volume displacement of the electrodes is negligible, I = I’
I C
-
(11) C . F. Morrison, ANAL.CHEM., 35, 1820 (1963). (12) G. W. Ewing and T. H. Brayden, Jr., ibid., 35, 1826 (1963). (13) T. R. Mueller, R. W. Stelzner, D. J. Fisher, and H. C . Jones, ibid., 37, 13 (1965). (14) Tektronix, Inc., Beaverton, Ore., “Operational Amplifiers and Their Applications”, p 6-2 (1965).
c l
Figure 2. Schematic diagram of pressure transducer system
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
359
I
1
I/
kl.
G52
1
I
LLz?---
FS2
FS4
4,
Scope
Manometer
s
b
Lirear Corduc:snce
P
AC O u t p u t
output
Figure 3. Circuit diagram of pressure transducer system Starting at ground, the Heath EUW-19A amplifiers have pins numbered clockwise as 4, 5, 1, 2, and 3. They are, respectively: ground, noninverting input, inverting input, balance supply, and output by a voltage follower (Amplifier 1). Tuning of the wave shape and amplitude is accomplished through oscilloscope connections placed after the follower. Alternatively, the potentiometers Rj2 and R , could be replaced by fixed value resistors. This would improve the reproducibility and ease of tuning and adjusting the alternating current source, but would decrease the overall flexibility of the instrument. From Amplifier 1, the sine wave is applied as the excitation signal for the manometer electrodes (cell resistance = Rm)and for the null adjust potentiometer, R,. Amplifiers 3 and 4 perform the function of a null offset linear conductance monitor. Considering first the pathway through the manometer, the signal developed at point A is given by : eouts=
-
ei,
(z)
Now considering this signal as an input to Amplifier 4, along with the signal developed through R,,we obtain :
D1 D2 Z c1 c2 c3
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 Rl1 R12 P1 P2
P3 FS
GS MS M
Following this amplification, the output signal of Amplifier 4 is rectified and filtered so that a high level dc output is produced. Thus, the output of the instrument is proportional to the conductance across the manometer electrodes, Lm, according to: eoutde = einRK(Lm - L,)
(14)
where K is a constant to take into account the ac t o dc conversion. Since from Equation 8, the conductance is directly related to the pressure change sensed by the manometer, the output voltage is directly related to this pressure change. The potentiometer R,, whose conductance is L,, can be used to offset any initial conductance across the manometer elec360
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
Table I. Components for Figure 3 IN4002 Texas Instruments IN 538 Texas Instruments 9.0 Volt, 1-watt Zener diode 0.0022 pF, lo%, paper 0.0047 pF, l o % , paper 0.22 pF, lo%, paper 154 Kn All are 1/2 watt, 1 %, carbon film loOn 1 KR lOKn l00Kn 1 Me@
20Kn l00KR 200Kn 300KR
992Kn 3.9 KR 100Kn, 0.5 % linear, 10-turn wire wound potentiometer 20Kn, 0.5 % linear, IO-turn wire wound potentiometer 250KR, lo%, 2 watt carbon potentiometer Function Switch, ceramic rotary, 5P5T Gain Switch, ceramic rotary, 6P5T Meter Switch, ceramic rotary, SP6T 0-50 p A meter, Lafayette Radio No. 99-R-5042
trodes so that the initial output is zero, provided there is n o phase shift in the manometer and the phase shift through Amplifier 3 is exactly 180". To improve this null adjusting capability, a variable capacitor may be added in parallel to R, in order to null any initial capacitance of the conductivity cell. EXPERIMENTAL Apparatus. The complete circuit diagram of the pressure transducer system is given in Figure 3 ; and the components are listed in Table I. The Heath EUW-19A Operational Amplifier System (Heath Co., Benton Harbor, Mich.) was used. The components necessary to use these amplifiers in the circuit described were wired in a blank chassis (Heath
Model EUW-19A-I) which is made to plug directly onto the operational amplifier system. The manometer used was a U-tube type constructed of 15mm i.d. borosilicate glass. Connections t o the reference and working pressure cells were made through 3 1215 ball joints as shown in Figure 1. The electrode assembly was fitted to the low pressure arm of the manometer by means of a f 29/42 inner member joint. The electrode assembly consisted of two 5 X 100 X 0.076 mm sheets of platinum foil (E. H. Sargent and Co., Chicago) which were each cemented to a 9 X 190 X 2 mm section of glass plate using epoxy (2-Ton Epoxy, Devcon Co., Danvers, Mass,), The electrodes were mounted facing each other and spaced 5 mm apart by cementing glass tubing between the glass plates. Platinum lead wires were spot welded to the tops of the electrodes. This assembly was cemented into a 7 29,42 outer member joint for connection into the manometer. The electrical leads passed through the epoxy seal at the top of the 29/42 outer member joint. Pressure signals for testing the linearity and reproducibility of the transducer were supplied in two ways: a Sargent Model C Automatic Constant Rate Buret with plunger driven assemblies of 50-, lo-, and 2.5-ml capacities; and a hydrogennitrogen coulometer designed according to the recommendations of Page and Lingane (15) and operated with a Sargent Model IV Constant Current Source. The recorder, constant temperature bath, submersible magnetic stirring motor, micrometer burets, potentiometer, and Ampot used in this study have all been previously described (6, 8). Pressuremetric titrations were conducted in all-glass reactors similar to those previously described by this laboratory. For volumetric titrations, the reactor described by Curran and Driscoll ( 8 ) was used. However, one of the microburets had a short glass stem so it would not withdraw solution when it was used to compensate the volume compression due t o titrant addition. For titrations in which the titrant was generated electrochemically, the modified H-cell described by Curran and Curley (6) was used with a 12- and 25-cmZplatinum anode and cathode, respectively. Reagents and Solutions. All chemicals were reagent grade except as noted. Potassium iodate was primary standard grade. Hydrazine sulfate was Eastman White Label No. 575. Triton X-100 was obtained from Analabs, Inc. Laboratory distilled water which was redistilled from alkaline permanganate was used for all solutions. Manometer fluid was 0.50 X 10-3M in potassium chloride and 0.03 wt in Triton X-100. It was prepared by appropriate dilution of a stock 0.100M potassium chloride solution. The surfactant was added to ensure smooth, frictionless flow. It had no noticeable effect o n the conductivity. Stock potassium iodate solution, 8.192 X 10-3M, was prepared by dissolving 0.8765 gram of the dried material in a 500nil volumetric flask. A 10-fold dilution of this stock solution was taken as 8.192 X 10-4M. Hydrazine sulfate solutions, approximately 1.0 and 0.10M, were prepared as described previously ( 5 ) . The phosphate buffer was prepared by making a solution 0.5M in potassium monohydrogen phosphate, then adding sufficient potassium dihydrogen phosphate to bring the solution p H to 7.2 as determined with a Corning Model 7 pH meter. The starch indicator solution was prepared according to the procedure of Koltoff and Belcher (16). Stock ammonium sulfate solution, 2.642 X 10-2M in ammonium ion, was prepared by dissolving 0.8729 gram of the dried material in a 500-ml volumetric flask. A 10-fold dilution of this stock solution was taken as 2.642 X 10-3M. Hypobromite was generated from an anolyte solution containing 10.0 grams of sodium tetraborate decahydrate and 200 grams of sodium bromide in 500 ml of redistilled water. The ~~
p H of this solution was adjusted to 8.6 f 0.1 (Corning Model 7 p H meter) by adding solid sodium hydroxide. In order not to evolve a gas at the cathode in the pressuremetric work, a solution which was 1.OM in ferric chloride hexahydrate dissolved in 2.ON sulfuric acid was used as the cathodic depolarizer. Check Methods. To determine the accuracy of the pressuremetric end-point technique, check analyses were performed using the same samples, titrants, and buffers as used in the pressuremetric procedure, but using a different endpoint detection method. A. HYDRAZINE-IODATE. To a 25-ml Erlenmeyer flask were added 10.00-ml of stock potassium iodate solution, 0.5 gram of potassium iodide, 6 drops of 18N sulfuric acid, and 10.0 ml of phosphate buffer. Hydrazine sulfate titrant was added from a microburet, with starch indicator added only near the end point. B. HYPOBROMITE-AMMON~UM. To a 30-ml beaker, fitted with a rubber stopper containing two platinum wire indicating electrodes, the generating electrode, and the frit-isolated cathode, were added 10.00-ml of stock ammonium sulfate solution and 10.0-ml of anolyte. ‘Hypobromite was generated coulometrically; and the end point was determined amperometrically according to the procedure of Christian, Knoblock, and Purdy (17). Blanks were determined in a similar manner using 10.00-ml of redistilled water instead of the ammonium sulfate sample. Procedure for Pressuremetric End-Point Detection. A. HYDRAZINE-IODATE, Ten milliliters of stock potassium iodate solution, 0.5 gram of potassium iodide, 6 drops of 18N sulfuric acid, and 30.0 ml of phosphate buffer were added to the pressuremetric titration vessel. The two microburets, one containing hydrazine sulfate titrant and the other empty save for a plug of water to ensure pressure tightness, were fitted into their appropriate positions with all joints well sealed with Dow Corning High Vacuum Grease. The reference vessel, similar in appearance to the reactor vessel except holding no microburets, was prepared by filling with the appropriate volume of water. The two cells were mounted on a ring stand; and the submersible magnetic stirring motor was placed in position under the titration vessel. The manometer, which had been filled to the bottom of the electrodes with the manometer fluid, was then connected to the cells and the ball and socket joints secured with clamps. The cells, stirring motor, and manometer were then immersed in the constant temperature bath until only the open stopcocks, the upper sections of the microburets, and the electrical leads t o the manometer electrodes were above water. Electrical connection t o the manometer electrodes was then made, and the amplifiers of the pressure transducer system were balanced. The function switch was then turned to the “on” position, and the frequency and amplitude of the alternating current source were adjusted. The titration vessel stopcock was then closed and stirring was begun. After a few minutes a steady pressure base line was attained, indicating equilibrium. Generally, four increments of titrant were added both before and after the end point. After the addition of each increment of titrant, the volume compression due to this addition was compensated by withdrawing the plunger of the second microburet. The output voltage was continuously monitored using the strip chart recorder. When a steady recorder trace indicated that equilibrium had been reached for a given increment, the output voltage was accurately measured with the potentiometer. End points were obtained from the inverted L-shaped titration curves which result when the transducer output in volts is plotted cs. microliters of titrant added. B. HYPOBROMITE-AMMONIUM. Ten milliliters of stock ammonium sulfate solution and 10.0 ml of anolyte were added
~~~~~
(15) J. A . Page and J. J. Lingane, A m l . Chim. Acta., 16, 175 (1957). (16) I . M. Koltoff and R . Belcher, “Volumetric Analysis,” 1st ed., Interscience?New York, 1957, Vol. 111, p 208.
(17) G. D. Christian, E. C. Knoblock, and W. C. Purdy, ANAL CHEM., 35, 2217 (1963). ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
361
Table 11. Linearity and Reproducibility of Pressure Transducer System H?-N? - - coulometer ____ __- Pluneer source --Pressure range (mm Hg, gauge) NO. of Reproducibility S,,, Reproducibility S,,, % pmoles gas Apparent” Actualb detn of slope, of slope, 2 I
6.30 3.84 1.92 0.630 0.315
144 88 44 14.4 7.2
9 9 9 8 8
0.41 0.26 0.48 0.51
...
0.22 0.30 0.26 0.25
0.29 0.41 0.36 0.28 0.25
...
0.31 0.24 0.29 0.35 0.27
280 171 85.5 28.0 14.0
Determined from moles of gas evolved and assuming constant volume. * Determined from the height difference between the two arms of the manometer. Table 111. Titration Results with Pressuremetric End Point Detection No. of Re1 std dev, Titrant Taken, mgn Found, mg detn % 14.32 8 0.1 N2H4. HzS04 14.33 f 0.02
Sample 103NH4+ a
1.433 i 0.002 4.737 f 0.007 0.4737 ?C 0.0011
BrO-
1.429 4.742 0.4746
6 7 6
0.2 0.1 0.5
Re1 accuracy,”
z
-0.1 -0.3 +0.1 +0.2
Based on check method.
t o the anode compartment of the titration vessel. To prevent the solution from flowing into the cathode compartment, sufficient catholyte was added so the liquid level of the catholyte was higher than that of the anolyte. All joints were well greased, and the electrodes were fitted into their positions. The procedure from this point was identical to the previous system, except that no compensation was required since the titrant was generated coulometrically. RESULTS AND DISCUSSION
Table I1 summarizes the results obtained in testing the linearity and reproducibility of the pressure transducer system. These data were obtained over a one-month period using both the automatic plunger driven pressure source and the hydrogen-nitrogen coulometer. Dynamic conditions prevailed; that is, the pressure was varied and the output signal was recorded on a strip chart recorder. A least squares computer program (Wang Calculator) was used to obtain the statistical analysis. Sur is the standard error of estimate of y on x defined by: SUZ =
2-ag
zy-al z x y
N
(1 5)
where x and y are the coordinates, a, and al are the intercept and slope, respectively, of the regression line, and N is the number of points. Thus Sv2.is a measure of the scatter about the regression line, and has properties analogous to those of the standard deviation. If lines parallel to the regression line are constructed at vertical distances of 1, 2, and 3 Svr,then these lines will contain 68, 95, and 9 9 . 7 z of the points, respectively. The linearity and reproducibility of the transducer system output is thus within 3 to 5 parts per thousand on all scales. In order to achieve continuous recording of pressure signals, the “free manometer” technique of Goldstein was used (18). In this technique the manometer fluid is not levelled during a reaction, and both pressure and volume are allowed to vary. As a consequence, the volume capacity of the manometer is substantially increased while sensitivity is usually reduced. Thus it becomes possible to measure a total gas change much larger than that by standard manometry; but small quantities (18) A. Goldstein, Proc. Amer. Acad. Arrs Sci., 77, 237 (1949).
362
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
of gas cannot normally be detected. However, a linear function between the voltage output and the moles of gas evolved (or absorbed) is maintained (See Appendix). By electronically monitoring the liquid level in the manometer, small quantities of gas can be detected and measured. Experimental confirmation of the linear function between output voltage and moles of gas evolved is given in Table 11; and the last column of this table shows the quantities of gas measured. It should also be noted that since the volume of the system is allowed to increase, the pressure inside the system is considerably less that expected. Thus the apparent pressure range given in column 1 of Table I1 is the pressure increase expected if the given number of micromoles of gas is evolved in a closed system with no volume change. The second column of this table gives the actual pressure increase in the reactor as determined from the height difference between the arms of the manometer. Full scale output of the transducer system is 33.0 volts dc on the 144 and 14.4 mm Hg scales. The voltage-pressure relationship on these scales is thus 0.229 and 2.29 volts/mm Hg, respectively. On the more sensitive scale, the smallest significant voltage signals that could be distinguished was 5 mV, based on the practical consideration that the mechanical vibration of the water bath stirring motor imparted a ripple to the surface of the manometer fluid causing an uncertainty in voltage readings on this scale of =kZmV. Thus the pressure sensitivity of this instrument is 2.2 X loF3 mm Hg, which corresponds to the evolution of 4.2 nanomoles of gas. Table 111 summarizes the results of volumetric and coulometric titrations utilizing the pressuremetric end-point technique. The theoretical basis of this technique has been presented previously (5, 6). Briefly, it involves monitoring the pressure change in a closed system due to the evolution (or absorption) of a gas by the reaction of analytical interest. The precision and accuracy of the pressuremetric technique using this transducer system is a few parts per thousand. Titration curves for the titration of 4.737- and 0.4737-mg samples of ammonium ion with electrogenerated hyprobromite are shown in Figure 4 as an example of the method. In contrast to the work of Curran and Curley (6), a cathodic depolarizer which did not evolve a gas was used (Fe3+ e- + Fez+). This led to less uncertainty in the intersection of the
+
Table IV. Least Squares Analysis of Titration Curves Hydrazine : Iodate Before end point After end point Titration Slope (Vifil) SYz, mV Slope, Vigl S,,, mV 19.56 -0.ooOI 3.3” 1 0.1624 2 3
4
0.1599 0.1601 0.1576
2.1 29.2 12.2
0.0002 0.0001
O.oo00
4.7
7.8 7.6
2 3
J
+.
2100r
a 80-
Hypobromite : Ammonium 1
140-
r 1209 w
0.0189b 0.0190 0.0186
17.8c 28,5 28.5
0.0001 0.0002 o.oO01
12.2c 10.5
9.7
Total output 18.1 volts. b Slopes for coulometric titrations in V/peq. c Total output S 14.3 volts.
2 2 60f
40-
4
/ ,A0 *A0 A 0
4&
5;0
6bC
7b3
E&
3b3
.Ck
’23
GENEiiATlON T WE SEC
two titration curve segments and improved accuracy and precision. Normally, four increments of titrant are added both before and after the end point. However, to permit a least squares analysis of the titration curves obtained with this transducer system, some titrations were performed with the addition of eight increments of titrant both before and after the end point. Table IV shows the results of this analysis. Of particular interest is the stability after the end point where a gas is no longer evolved. These lines are virtually horizontal; and the Syzranges from 3 to 12 mV out of approximately 18 volts total output. At high transducer sensitivities, fluctuations in ambient pressure and temperature had an effect on the stability of the signals measured. Particularly bothersome were gross pressure fluctuations produced by opening and closing the laboratory door. A reference volume was attached to the manometer; and pressure signals in these titrations were recorded os. this closed reference rather than os. ambient conditions. Since the volumetric displacement of the manometer was limited by the fixed reference volume, the resulting output signals were lower. However, it was found that if the reference volume is large enough (approximately 50-100 cma), the linear function between voltage output and moles of gas evolved is maintained. CONCLUSIONS
In this paper we have presented a simple and inexpensive pressure transducer system for use in chemical analysis. Although the pressures measured must be corrected for the volume of manometer fluid displaced, the instrument does produce a high level dc output which is a linear function of the moles of gas evolved or absorbed in a closed reactor system. Therefore it is suitable for use in reaction kinetics, analytical hydrogenations, and pressuremetric titrations. If information is desired on the total number of pmoles of gas evolved, a simple calibration with a hydrogen-nitrogen coulometer is required. We have demonstrated the applicability of this instrument as an end-point detection device in pressuremetric titrations of milligram samples of iodate and ammonium ion. Excellent precision and accuracy is obtained, even at the concentration level where only 12 pmoles of gas are evolved. It has been observed by Smith (10) and confirmed in this laboratory that the conductivity electrode technique is capable of detecting a change of 30 pinches in the liquid level in the manometer. Thus the construction of a suitable capillary manometer of dimensions outlined in the Appendix should
Figure 4. Pressuremetric titration curves of ammonium ion with electrogenerated hypobromite 10.00 ml of 2.642 X 10-2MNH, + Left ordinate Generation time X 0.1 = Mquiv B. 10.00 ml of 2.642 X 10-aM NH4+ Right ordinate Generation time X 0.01 = pequiv A.
increase the sensitivity of the instrument to 6 X 10-6 mm Hg. However, even without modification this instrument fills the need for a multirange, dc output pressure transducer system which is simple in principle and construction and low in cost. ACKNOWLEDGMENT
S.J.S. is grateful to L. B. Jaycox for meaningful discussions on the electronic circuitry. APPENDIX
Recording of the liquid level in a manometer is facilitated if the fluid is not levelled during a reaction. Furthermore, the errors introduced by the levelling procedure are avoided. Goldstein has called this procedure the “free manometer” technique (18), and he has derived the appropriate equations for a Warburg apparatus in which both pressure and volume are allowed to vary. The following derivation is more general, applying to all manometric readings. However, for simplicity it is assumed that the solution and gas phases are ideal and that the manometer fluid is saturated with the gas of interest. Initially,
PiVi= niRT
(1)
where the subscript i refers to initial conditions and the symbols have their usual significance. If a gas is generated or absorbed,
P,Vf = nfRT
(2)
where the subscript frefers to final conditions and n = ni =k An. In the case where a gas is evolved in a closed reactor to which a fluid manometer is attached, the pressure in the system increases by an amount dependent on p, the density of the manometer fluid; g, the acceleration due to gravity; and h, the total height difference between the two arms of the manometer (Figure l). Thus, Pf = PI ANALYTICAL CHEMISTRY, VOL. 43,
+ pgh NO. 3, MARCH 1971
(3)
363
However, the volume of the closed system also increases by an amount deDendent on w * , the cross-sectional area of the manometer and / I , the length of the column of water displaced. Thus,
V , = Vi
+
It has been previously shown that h substituting in Equation 2
,., [P,arz + k‘V,pg /I
(4)
d I l ’
=
kl, so h
+ pgnrZh]
=
=
k‘l‘ and
AnRT
Substituting the following constants: p = 1.00 g/cm3,g = 980 cm/sec2, = 3.14, and Pt = 1.01 X l o Gdynes/cm2 (760 mm
Ha) /7//i‘
x
103[3171r 2
+ 0.980 k’Vi + 3.080 r2h]= AnRT
(7)
The relationship between / I and An will be linear if the third term in the brackets is negligible compared with the sum of the
other two. For the manometer system used in this work, r = 0.75 cm, Vi = 50 cm3, and k’ = 2.22 h/2.22 X 1O5[1784
+ 109 + 1.73
/I] =
AnRT
(8)
and the third term is less than 0,9% of the sum of the other two if h is less than 10 cm. Thus this term can be dropped and the height difference between the two arms of the manometer is linearly related to the moles of gas evolved. From Equation 4 it is seen that if r is small enough, the volume change caused by the movement of manometer fluid is negligible. Then V I V , and the pressure changc. measured in the manometer is a true differential pressure, i.c. it docs not have to be corrected for the voltinic change. A simplc calculation shows that if Vi is approximately 50 cm3, r would have to be 0.10 cni or less. But the placement of conductivity electrodes in a manometer of this size would be quite difficult. However, a suitable compromise between V # ,r , and sensitivity should be possible. RECEIVED for review September 8, 1970. Accepted December 1, 1970. Thanks are due to the Analytical Chemistry Division of the American Chemical Society for the Anacon Summer Fellowship awarded to S.J.S.
Near Optimum Computer Searching of Information Files Using Hash Coding Peter C.Jurs Department
of
Clieniistry, The Penns) loania State Unicersity, Unicersity Pork, Pa. 16802
The technique of hash coding has been applied to searching information files similar to those used in spectrometry laboratories. A discussion of several searching strategies, including the optimum one, is presented, and it is shown that hash coding yields nearly optimum matching algorithms for which search times are independent of file size. Two algorithms using hash coding have been implemented; the results of experiments with these algorithms are presented, The first algorithm matches blocks of unknown 16-bit spectra to a file of known spectra at the rate of approximately 20,000 spectra per second, independent of the number of unknown spectra being matched. The second system employs a double hashing procedure to search a data file of 20,000 spectra for one unknown at a time and verify its presence or absence in 40 milliseconds, on the average.
EXPERIMENTAL SITUATIONS routinely arise in which it is necessary to match an unknown spectrum to a file of known spectra. Several investigations which deal with the problem of computer searching of infrared spectrometry files have been reported. Anderson and Covert (I) reported a system using an IBM 7080 computer with magnetic tape input which could search 167 spectra per second. Erley ( 2 ) packed the words within the computer’s memory and used logical operations to make the necessary comparisons. His system was developed with an IBM 1130 using a disk input, and it could process 1000 spectra per second. Lytle (3) used an inverted file of IR ( 1 ) D. H.
Anderson and G . L. Covert. ANAL. CHEM., 39, 1288
(1967). (2) D. S . Erley, ibid., 40,894 (1968). (3) F. E. Lytle, ibid., 42, 355 (1970). 364
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
spectra and developed a system which could search 1000 spectra per second using a 500 card per minute card reader for input. This inverted file system suffers from the disadvantages that new spectra cannot be added to the file as conveniently as with the other systems and that only one search can be performed at a time. It can, however, find near matches relatively easily. Lytle and Brazie ( 4 ) have more recently reported a system which uses compressed IR spectra to obtain search rates of 333 spectra per second with 45-bit spectra on a small laboratory computer. They also use statistical data compression to develop a system on a XDS Sigma 5 computer using disk input which can process 18000 16-bit spectra per second. These 16-bit spectra do not contain all the information present in the original spectra, however. A major drawback of most searching systems is that the search time is proportional to the number of members in the file being searched. This paper discusses a method, both in theoretical and experimental terms, for which this limitation is not present. A nearly optimal searching strategy can be developed by using hash coding to drastically reduce the time necessary to search files of data, such as IR spectra. The problem of exactly matching an unknown query word to one of the members of a dictionary of words arises repeatedly in information handling applications. The problem of retrieving infrared spectra from a file of standard spectra is only one example of such an application. The terminology “word” for the query is used because the information, whether it is an actual English word or a number or a spectrum, is (4) F. E. Lytle and T. L. Brazie, ANAL.CHEM., 1532 (1970).
