edited hv ------,
JAMES P. BIRK Arimna State University
computer series, 161 LlMSport (V): pH Data Acquisition: An Inexpensive Probe and Calibration Software Ed Vitz and Thomas A. Betts Kumown University Kumown. PA 19530
Several articles (14)in this Journal have described designs for homebuilt pH meters, and standard hardware designs can be found in many texts oninstrumental analysis. Running on IBM-compatible computers, LIMSport facilitates a significantly different approach, using software for calibration, so that the pH meter can be constructed from only a pH probe and an operational amplifier ("op amp"). The O D amD draws i t s Dower from the cornouter bus throuih an analog-to-digital (A/D)board, whichis used for data acauisition. Thus. the hardware that is usuallv required f& the slope, offset and temperature calibratibn is eliminated. The power supply and display are supplied by the computer. Since the LIMSport system (6-10) incorporates an inexpensive multifunction board with a 12-bit A/D converter, we can add pH-meter capabilities for less than $40.00. For any laboratory owning computers equipped with multifunction cards, the approach we describe here is clearly the least expensive. We believe that our approach provides performance comparable to most commercial pH meters, but most importantly, that it provides a substantial oedaeoeical advantaee. L1MS~ortcan introduce im, portant concepts in pH measurement that are obscured by "black box" DH meters. without hidine anv thcorctical details in another "black box" of software. Al"though we present macros in this article, their purpose is to present the user with data organized to facilitate understanding. It is not necessaly for students to understand Lotus macros to benefit from this approach. They need only know a few s i m ~ l ecommands to obtain a more com~letepresentation of the data than a commercial pH me& p;ovides. Students need not know mechanical details of how these data are obtained to gain a n understanding of the concepts involved in pH measurement. Althou~hthe comoonents needed to assemble the comp u t e r / p f meter hake been available for some time, we wish to describe the most efficient way to construct the de-
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h he RCA 3240AE operational amplifier is available from Newark Electronics, 4801 N. Ravenswood Ave., Chicago, IL 60640 (Phone: 312-784-5100).Newark Electronics has many regional offices in the United States. 'Olher common op amps, lake the LF353N have lower ompLt impedance. Tnis ieaos to mardeo cnanges In performance w t h cnanges In temperatdre, abe lo me large temperaidre coencenl ol resmance of the pH prooe, and no isolnermai pomt s oblalned. The LF353N does work fa measdrements are made at a smgle temperawe. It is available from Raoio Snack Stores,or DfglKey.701 Brooks Ave. South. P. 0.Box 677.Tn ef Rwer Fal s M N 56701-0677(Pnone: ~
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3~artsrequ/red include the socket (Radio Shack #276-1995),circuit board (Radio Shack #276-159),box (Radio Shack #270-230), and BNC connector (Radio Shack #27S-105).
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Journal of Chemical Education
Tempe, AZ 85287-1604
vice, and to describe software that facilitate its use among educators and their students. pH Meter Construction Our "software DH meter" has essentiallv five comDonents: (1) a combination glass pHreference Llectrode, a high input impedance op amp, (3) a n analog-to-digital (AID)converter, (4) a personal computer, and ( 5 ) Lotus 1-23 and LIMSvort software. including the data acauisition @-functions(9,lO). It is to use an alternative programming language such as BASIC, Visual BASIC, or C to control data acquisition. The use of a spreadsheet, however, greatly simplifies the data acquisition and presentation tasks so that users need not deal with the details of interfacing or involved software routines such as those used for plotting or regression analysis. We consider this device a "soRware pH meter" because calibration and data reduction are controlled by sofiware that is easily written or modified by the user. The components of our system are described in detail below.
(i)
Hardware
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We construct a Drobe accordine the circuit diaeram shown schematically in Figure 1, which incorporates an op amo and s(xket costine about $2. three 114-Watt resistors. and a pH probe costingabout $35. Afonr-conductor ribbon cable connects the output and ground to the AID board, and connects the V+ and V-pins to the +/4 V or +/-I2 V supply available on the multifunction board connector. The CA 32401 op amp is readily available and provides superior performance.2It is convenient to build the op amp circuit3 according to the diagram in Figure 2, by mounting the op amp socket on a small printed circuit board enclosed in a plastic project box drilled to accept a chassis-mount female BNC connector. Afour-conductor ribbon cable connects the box to the computer, and the standard pH probe lead can be connected to the BNC jack. An alternative approach is to build the preamplifier as a unit with the electrode, as follows. The coaxial cable from the electrode is cut off close to the electrode body, and these wires and other compo330 kL2
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Output signal
A
Coaxial Cable
pH Electrode
Figure 1.Schematic diagram far the op amp circuit
From AID Board Acqutek CON1 or CON2 ( Pin 16 Pin I9 To Analog-to-DigitalConverter +5 V -5 V
1
Ground
Output signal
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as the basis of the LIMSport pH meter. We used the Acqutek PACP12' for the work reported here. Software LIMSport offers a convenient method to control the multifunction board and import data directly into the Lotus worksheet using simple "@-functions"that can be added to the Lotus command language (9, 10). The "@AD(2,100)"wmmand, for example, returns the average of 100 samplings of the potential, in Volts, of the electrode connected to input terminal two of the multifunction board. This wmmand can be embedded in a macro like the one below to record a pH in the current cell, when the user types "Albp", assuming that the slope "m" and intercept "b" of the response curve are known. The cell opposite PMV serves as a temporary buffer, and the formula in the cell PHVAL wnverts the potential to a pH. PMV
PHVAL \P pH Electrode
u Figure 2. Pictorial diagram forthe op amp circuit. nents are soldered to an eight-pin DIP socket. After the op amp chip is installed, the end of the pH probe with the attached assembly is immersed in a vial of casting resin4 until it sets. This procedure yields a compact and rugged device, with electronic wmponents visible if the clear casting resin is used. If any wmponent fails, however, the entire unit must be discarded. Appropriate combination electrodes that include both the pH-sensitive electrode and an internal reference electrode (usually the silver/silver chloride electrode) are available from many suppliers for prices ranging from less than $40' to over $200 depending on response time and physical configuration. ~lternatively,p&arnplified electo the ones we construct) are available6 trodes (eauivalent . although their cost (without power supply) is approximately twice as high as the homebuilt equivalent. pH preamplifiers are also available. Their cost may be extraordinarily high,? although Vernier SoftwareKbsupplies an inexpensive kit based on the LF356 op ampa that provides performance similar to the CA3240. It was used in a previous article in this Journal (11). Any of the multifunction boards described in previous ~ l ~ ~ particles o r t (9, 10) manufactured by ~ c ~ u t e k , Metrabyte, or Computer Boards Incorporated can be used
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4 ~usee casting resin available from most hobby stores, manufactured by ETI, Fields of Landing, CA 95537 (800-443-9323).An alternative is Bondo auto body plastic, available from most automotive stores. manufactured by DynatronIBondo Corp., Atlanta, GA 30331. 58~ensorex. 11661 Seaboard Circle, Stanton, CA 90680 (Phone: 7141895434) Model St00C. Sb~ernier Software, 2920 S.W. 89th st.. Portland. OR 97225 (Phone: 5031297.5317) Model 71206. 7. CT 06907%mega Engineering, Inc., P. O. ~ 0 x 4 ~Stamford, 0047 (Phone:8001622-2378).Model # PHE-1304. %mega Engineering, Inc., P. O. BOX 4047, Stamford, CT 069070047 (Phone:8001622-2378).Model # PHE-1304-NB.The NB option specifiesa prearnplified electrode with an external power supply. 'Extech lntrurnents Corporation, 335 Bear Hill RD.. Waltharn, MA 02154 (Phone6171890-7440).Model HF40405PA is typical. 'The LF356BJ is available from Newark Electronics (Footnote 1). '~cqutekCorporation, 1549 South 1100 East Northside. Salt Lake City, UT 84105 (Phone 80114854594). The PACPt2 board wsts $125.
(F'MV-b)lm [put PMV,O,O,@AD(2,1OO)l~CALC) ImPHVAL--
The slope and intercept may be determined by the "standard" two-point calibration technique, which is executed by a simple calibration macro. It prompts the user to immerse the probe in one pH buffer, enter the known pH of the buffer, then push the 'Return" key to record the measured potential (which is displayed on the spreadsheet about once per sewnd) when it stabilizes. The routine is repeated foithe sewnd buffer. The slope and intercept are then calculated and stored. and a calibration manh is oresented on the screen. ~ h i s ' ~ r o c e enables ss t h l user &see exactly what is meant by the slope and intercept of the response curve. Using the LIMSport temperature sensing capabilities, we also have constructed a calibration routine that compensates for temperature variations. The temperatures of the buffer solutions are acquired with the thermistor during calibration and averaged to give T,d, the temperature of calibration. Because the slope of the response curve is proportional to RTInF, the slope of the response curve for the temperature at which pH is measured (Tz) is calculated by multiplying the slope of the calibration line by the ratio of absolute temperatures T2/T,,,:
Temperature Dependence of E l e c t r o d e R e s p o n s e 3
Figure 3. Typical electrode caiibratnn curve at two temperatures Volume 71 Number 5 May 1994
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The user is prompted for empirically determined values of the potential and pH a t the isopotential pH, or the default values of 0 mV and 7.0 may be selected. The isopotential pH (or isothermal point)'' is the pH a t which the electrode &ponse is independent of temperature (see Rg. 3,. The values 0 mV and pII = 7 reflect the design criteria for most p11 electrodes (121, although many elertrodes do not behave ideally, especially as they age, so temperature compensation may not be accurate in standard meters. The intercept 'bcn," for the new temperature can then be calculated from the slope and isothermal point:
E f f e c t of S i g n a l Averaging o n Precision 8
b o ) = Vim - ( s h e t n )* P%.) Then we use the new parameters =b(=," and "slope(n," in the usual way to calculate the pH a t Tz.One simply immerses the thermistor along with the DHelectrode into the solutions to be measured and executes the macro Alt-Q. I t is, of course, possible to use much more sophisticated calibration routkes with this instrument, and they are described below. Pedagogical Advantages and Sample Experiments Calibration When students adjust the "slope" and "offset" controls of a typical pH meter, there is no indication of what they are actuallv doing. The situation is much different with the ~ ~ ~ s pp~-meter. b r t Since the calibration curve is automatically d o t t e d , t h e teacher and student can immediateli see what the "slope" and "intercept" are, and what the actual output of the electrode is, in mV, for any pH. We feel that this improvement in pH measurement practice is valuable to students a t any level. More advanced students may be surprised a t the variety of obsewed values for the slope. The Omega electrode6was designed to be used with common pH meters, so the slope of the amplified output is near the 0.059 VIpH expected for the best elass electrodes. The resvonse of an electrode depends o n k a n y factors (12,131, cgef among them being the com~ositionof the elass. Corning 015 elass eives near theo r e t h response, while Pyrex lhas a response close to 0 mV1pH. The Op Amp in our circuit has a gain of around 10, so we expect slopes of about 590 mV1pH. This value allows high precision pH measurements with our 12-bit AAJ board, hut retains some obvious pedagogical meaning. In advanced courses, instructors may want to include a potentiometer in the 330 kn feedback resistance of the op amp, so that the gain of the amplifier is adjustable. One might measure the gain with an oscilloscope or VOM, so that the actual electrode response can be determined. For the first set of experiments for upper level students, we sumest a multivle buffer calibration. This exercise allows students to ch&acterize a n electrode, and can be completed in a short time with LIMSport, which uses Lotus functions to collect, tabulate, and reduce data. The student determines:
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the value of the slope and intercept of a regression line, as well as the eoodness of fit (R2). .the variation from ideal behavior at low pH caused by the increase in activity eallieirnt for hydronium ion resulting from its higher concentration. ''?he term "isothermal point", used in recent editions of reference 12, is misleading because it is the temperature which is changed while the potential remains invariant. We prefer the older term "isopotential pH" used in Bates. R. G. Determination of pH: Theory and Practice; Wiley: New York, 1964; p 366. "Data acquisition rates usually are given as sampling frequencies. in Hz. For example, our ' 5 kHz" board makes a measurement every 0.0002 s.
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Journal of Chemical Education
Figure 4. Effect of increasing the number of samples, N, which wnstitutes a measurement, on the standard deviation of 1000 measurements. the variation from ideal behavior, which increases as pH increases, caused chiefly by interferences from other cations when [Ht1 is low. Calibrations for high ionic strength solutions are typically quite different from those at low ionic strength. the true isopotential pH, if full calibrations are run at different temperatures, as shown in Figure 3. Our Lotus template contains tabulated values for the NIST Reference pH Buffer Solutions (12)at various temperatures to facilitate calibration. It may be most interesting for a student to plot the slope of each calibration versus the Kelvin temperature, and determine the slope of this new plot by Lotus regression analysis. It, of course, should have the value RInF = 8.6 x 10" with a unity gain amplifier. Precision Analysis of error in pH measurements is complex, and the reader is referred to standard texts (12.13) for much of the detail. However. i t is easv to demonstrate the imnrovement in precision that is 06tained by multiple measurements usinc LIMSoort. Our twical ~Hmeasurementis exY , returns an ecuted by ;he function - ~ A D ( P , ~ ~ owhich average of 100 samplings of the potential applied to port "p". I t is easy to demonstrate that the standard deviation (01 will decrease for m u l t i ~ l emeasurements. as the number of samples "n" that coktitutes each measurement is increased. A plot of o versus n m is shown in Figure 4. For precise work, we may use a macro that reports 10 of these measurements, so an average and standard deviation of 10 measurements (each an &;age of 100 samplmgs, may be calculated. The standard deviation is typically 1 mV with the 10-fold amplifier, indicating excellent noise reduction. A student mav be surmised a t the noise levels that can arise in measurements a s the measurement time decreases. Because even inexpensive multifunction boards may take several thousand samples per second," even a s easilv be remeasurement composed of 100 s a m ~ l e mav turned in less th& 0.1 s. If the pH klectroie is used on a heater or magnetic stirrer, the standard deviation of 10 measurements (each the average of 100 samples) can easily exceed the mean(!), because a measurement may be completed during the closure of the heater relay (or swing of a magnet) which generates large noise levels. This noise is eliminated by taking samples over a longer period of
time, or by placing a grounded piece of aluminum foil between the stirrerhotplate and the sample vessel. Commercial instruments escape the noise problem by increasing integration times to around one second, but the user typically has no control over the signal conditioning algorithm. There are. of course. limits to the advantaee of increasing precisiok by multiple sampling: The AID goard has 12bit orecision over a ranee of +/-5 V. which leads to a auantization error of about 2 mY If we obtain a sensitivity of 590 mV/pH with the amplified pH probe, an error of
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(2 mV) K590 mV/pH)= .0033p H unit
is expected due to digitization. The AiD board may contribute other (random) errors that are beyond the scope of this oaoer. but no source of error exceeds the 0.005 DH unit error usually ascribed to the NIST Standard ~;ffers,or other practical limits to accurate and orecise oH determi.
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Easy Combination ofpH Measurements with Measurements of Temperature, Conductivity, or Other Parameters for Data Reduction
The LIMSoort svstem allows acouisition of temperature data to a reshution of 0.01 'C, as well as conducti6ty data, For with simple commands (Alt-T and Alt-C.. res~ectivelv). . users wgo are inclined to learn the Lotus macro language, the process can be automated by writing a Lotus macm thaGeads both the temperature and pH probe (or conductivity cell) output and records results in the spreadsheet. Very interesting plots for acid-base titrations are obtained when thermotitrimetric (and conductometric, etc.) curves are added to the usual pH curves for a titration. The spreadsheet environment facilitates the construction of Gran plots (14, 15)because the calculation of the concentration from the pH is entered easily and copied down the column adjacent to that containing the pH values, and the necessary regression analysis is facilitated. Similarly, the volume correction (V + ulN needed for a Gran plot with "known additions" is added easily in a third colukn. A recent article in this Journal (16) has described spreadsheet error analysis applied to titration curves u s k g Gran's plots and spreadsheets. Performance Advantages
All of the advantages described in the previous section could be classified as performance advantages, . but several may be added in thiseategory Expense
In our system, a pH meter costing $500-$1500 is replaced by a computer that requires a similar initial investment, but which has much broader utility for not only electrochemical measurements, but many other Dumoses as well. We find it odd that expensive digital meters are still sold. because thev could be viewed as reasonably expensive computers laEking disk drives, keyboards, monitors, standard VO, and RAM. The fact that designs incorporating hardware calibration still predominate suggests that the option we present here is underappreciated. Furthermore; the addkion of RS232 outputs to pH meters seems addlepated: Why not eliminate the pH meter altoaether? We have found that usine a commercial oH meter as a display and amplifier, (as others have done, by connectine the AID board to the recorder outout). offers no improvement over our simple preamplifier. It may, however, increase the noise level by at least an order of magnitude.
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Automation and Multiple Measurements
The ability to make many measurements automatically allows control of measurement statistics and allows timed measurements for kinetics studies or process control. We have shown previously how LIMSport demonstrates signal-to-noise enhancement by averaging. While the "soRwarenpH meter does provide noise reduction comparable to commercial pH meters, the true advantage is that the software provides complete control over it. We can average thousands of measurements for maximum precision when time is not critical. Alternatively, if high sampling rates are required but precision can be sacrificed, we can record measurements consistine of 100 samples (or fewer) in hundredths of a second, depending on the computer. This flexibility, of course, is not a common feature of hardware pH meters. For kinetics studies and quality control, timed measurements are easily effected by use of a macro like the following, which makes a pH measurement every 60 s for one day bv re~eatedlvcalline the macro eiven earlier. The OHvalues are listei in a c o h n of the spreadsheet startihg with the cell where the cursor resided when the command was executed. "
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A
\R MEASURE
{FORCTR,O,~~~O,~,MEASUREI I\PIIWAIT@NOW+@TIME(O.O.GO)I
In quality control applications, an alarm can he sounded when a control limit is exceeded, by including our "@DOm digital output command (8, 10) or the "@HCI" 120V controller command (9, 10) in macros like those described in the cited articles. Complete Freedom of Choice of CalibrationAlgorithm
While the standard two-point calibration used in pH meters can be replicated easily, it is almost as easy to carry out rnu~ti~oinicalibrations and use regression o;curve fiiting methods for the ultimate accuracy. For even inexpensive eel-filled combination electrodes., we aet K2 = 0.999 over ;he pH range 2-11, so methods other than linear reeression are unnecessarv. But this is ~rohablvnot so for many ion-selective electrodes (ISE's), and theavailability of higher-order regression analysis in Lotus may be useful in these cases. Of course, our method allows visualization of calibration curves for suspect electrodes, or electrodes used under unusual conditions (higher temperatures, high ionic strength solutions, etc). Furthermore. ISE's for a variety of ions can be com&etely characterized over a variety of calibration ranees and temperatures. If pH must freGuently bemeasured a t temperatures other than the calibration temperature. it is advisable to determine experimentally the fsopotential pH of the electrode, and tailor temperature compensation to the electrode in use. Many electrodes do not kxhibit an isopotential pH a t the "ideal" 0 mY If calibration is camed out in so% ware, it can be tailored to the requirements of the particular determination a t hand.
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Conclusions
We have learned many things about pH measurement by using the LIMSport system that we have not learned throGhout years-of p ~ - m e t euse, r yet we realize that we have hardly begun to exploit the potential (an obviously appropriate phrase) of this new approach. We never will buy an expensive pH meter again. A spreadsheet containine the calibration macros. data tables, and graphs describe; here is available free f m k the first author. Please send a stamped, self-addressed disk mailer. Libraries of Lotus @-functions for controlling multifunction boards, the X-10 Home Control Interface Volume 71
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(mentioned here and described in previous articles) are available for $25 each from the first author. Literature Cited
Energy
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1. Warner, B.D.: Baehme,G.;Pool, K H . J. Chem. Edue. 198% 69,66. 2. Edsbom. R. D . J Chem Educ. 19TS,56.A169. 3. Caeeei,M. S. J Cham.Edur 1084,61,935. 4. Paris, M.R.;Aymes,D. J.; Poupon,R.;Gareaao, R. J. C h . E d u . 19W,67,507. 5. Seiuer8.D. J. Chom.Educ. 1981,68,281. 6. Wfz, E. J. Cham. Edue 1982.69.744 7. WU, E. J.Cham. Educ 1988,70,63. 8. Wtz,E.;Reinhard,S.J. Chom. Edue. 19B. 70,2&&248. 9. vifz, E.;Reinhard,S. J Chom. Educ 19BS,70,758-761. lo. Vitz, E.Sc&fJic ComputingondAuromntion 1993,9,29. 11. Fox, J. N.;Shaner, R.A. J. Cham. E d u . 1990,67,163. 12. W,llard, H.H.;Merritt, L. L.; D-, J. A,;Settle, F A Inatruwntd Methods of Andyais, 6th 4.;Wadawn&: BeLmont,CA,1981;pp 640-663. 13. Skoog,D.A.;Weat,D.M.Fu'undomntolsafAndytiml Chemistry;Holt,Rineha?tand Winston: NY,1976; pp 37-07, 14. Chnatian,G.D. Andytiml Chamistry, 3rd ed.: W i k y New Ymh,198(1:p323. 16. Gran, &Art= Chim. Smnd. 1850.4.659. 16. Sehwarte, L.M.J. Chem E d u . ISSS,E?819. ,
Reaction Coordinate
Deprotonation of Nitroalkanes
Figure 1. Energy profile for a transition structure
Semiempirical Determination of Solvation Effects on a Simple Reaction Cwrdinate William J. Pietro
York University North York, Ontario, Canada Computational chemistry is one of the most rapidly mowing areas of study in the undergraduate chemistry iurricuium. The recent advent of l'w-cost, high-speed workstations and *student-friendly" electronic structure programs have now brought quantum chemical calculations into the classroom for good! Practicing chemists no longer need a detailed knowledge of the underlying mathematical principles of quantum mechanics to explain and predict interesting and potentially useful chemical phenomena by computational methods. Moreover, researchers now may perform their calculations on "realn molecules, rather than the heavily abridged model systems necessary for the slower, smaller, and more expensive computers of just a few years ago. ,Accordingly,computational chemistry soon must become an integral part of the chemistry core curriculum (1). Amone the most i m ~ o r t a n at ~ ~ l i c a t i o n ofs computational methods is the d&rmination of optimum moleklar geometries. Most students involved in computational chemistry have likely calculated optimized equilibrium geometries of some molecules using molecular mechanics, semiempirical, or ab initio methods. An equilibrium geometry corresponds to a local minimum on the energy surface and represents one (but not necessarily the only) thermodynamically stable structure for the molecular system. The overall thermocbemistrv for a reaction. for exam~le. . can be derived using the energies of the reactants and products at their equilibrium geometries. Of course, this kind of analysis tells us nothing about a reaction's mechanism or rate. The use of com~utationalchemistrv to arrive a t mechanistic or kinetic ikormation requires a fundamentallv different kind of -eeometrv . optimization-the determination of a transition structure. A transition structure does not corres~ondto either an absolute minimum or maximum on the eAergy surface, but rather to a saddle point. A saddle point is a geometry for which the energy is minimized with respect to all normal coordinates except one, to which it is maximized. This special coordinate is called the reaction coordinate, and wrresponds to the translation from reactants to products. The lowest energy path connecting reactants with products is shown in Figure 1. The curve is a two-dimensional "slice"
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Journal of Chemical Education
through a multidimensional surface. The peak in the curve is the saddle point. All chemists are familiar with the concept of a reaction coordinate: however, few have actually visualized motion along one. The real-time computer an~mationof a complex reaction coordinate is the subiect of a future paper in this Journal. In the present paper we use semiemp&cal electronic structure theory to generate the energy versus reaction coordinate profile for a simple chemical event, the depmtonation of nitromethane in aqueous solution. Nitmmethane and its DeprotonatedAnion
It is well known to organic chemists that hydrogens a to a nitro group are acidie and dissociate in basic aqueous solution. For nitroalkanes the proton transfer is slow as mmpared to most acid-base reactions, indicating a considerable activation barrier to depmtonation. The depGtonation kinetics of nitroakanes pronde a pedagogically beautiful demonstration of the au&tum meihani-d modeline of transition states and the Lffects of solvation on their el&ronic structures. The calculations described herein require an electmnic structure program capable of semiempirical calculations at the AM1 level (2).constrained seometrv o~timizations.and the ability to display graphicali; molec;lb electrostat;~pocenhals. Combinations of several commerciallv ava~lableorograms enable this; however, one program,- SPAR TAP^, is available that integrates molecular mechanics, semiempirical, and ab initio methods, a Cartesian optimizer capable of fullor constrained equilibrium or transition structure opti-
Figure 2. AM1 calculated geometries for nitromethane and its conjugate base.
