Herber! k s s o w
with Doug Hamilton,' Ben Schneeberg,' and Ben Stad'
Germantown Friends school Philadelphia, Pennsylvania 19144
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A Study of the Physical and Chemical Rates of Cac03 Dissolution in HcI
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Kinetics studies of the CaCOrHCl system have been found to provide ideal researchoriented experience for interested high school chemistry students. Materials needed are safe, readily available, easy to handle. The limited amount of previously reported work means that consistent student data can become an important contribution to the chemical literature. Beginning students may therefore experience the excitement of working a t the frontier of scientific knowledge, of knowing that their study of a safe, familiar reaction-the evolution of COp(g) by the action of acid on a carbonate-may provide data that has never been collected, and raise questions that have never been faced by man. Examination of the literature does indeed raise interesting questions, as well as suggest fruitful areas of further study. Both Gortikov and Nanteleeva (I), and Tominaga and his co-workers (8), report firstorder rate dependence on HC1 concentration for the CaC03-HCl reaction. Ferrari and Sessa (5) find that 10" rises in temperature of a well-stirred mixture of calcite in 8% HCI solution approximately doubles the rate of calcite dissolution. Centnerszwer and Heller (4) show this type of temperature-rate dependence for a presumably purely chemical dissolving of Sn in a SnCla aqueous solution. Analysis of the Ferrari and Sessa (5) data reveals, however, an abrupt slope change at 2072, when CaC03dissolution rate is plotted against temperat,ure. To compound the mystery, the nearunanimous findings of all workers studying the CaC03HC1 system show a marked dependence of CaCOa Cissolution rate on stirring speed (1, 5, 5) and viscosity ($1, and the diffusion controlled nature of the reaction that such findings suggest. It appears that whatever inconsistencies do appear in the literature arise from an incomplete recognition of the significant differences between chemical and physical rate processes: the former showing marked dependence on temperature and composition effects; the latter exhibiting special sensitivity to stirring, viscosity, and mass transfer limitations.
Figure 1. Diagram of opparotur w e d to measure CaCOa-HCI reaction m t e d a t a Reoctont~A, consi3ting d 800 rnl HCI (oql and 5 g of 20 me3h CoCOab). are held in 3-neck 1000-ml dirtiliotion Rork, 8, lmmerred in a conrtont temperature both (not rhownl. Thermometer, C, records ternperdure of reoclontr ar they ore ogitoted b y gar-tight closed system stirrer, D, driven b y motor, E. Strobe mork, F, on rsrrer h o f b ir illuminated b y spotlight, G. When mark 1% viewed through homemode stroboscope disc, H, driven b y a 60rpm synchronous motor, I, the rpm of the stirrer rhoft can b e calculated. The COnlg) evolved during the reaction escaper through tube, J, which is anached to a 100 ml gar buret (not shown). The rote of COdg) collection in this buret is determined b y d top watch or sweep second hand wall clack.
is given in the table. Reaction rates are taken as the slopes of volume COz versus time graphs (as read from Fig. 2), and may be expressed in moles COz/sec by use of the room t,emperature conversion factor, 1 mole C0z (g) = 24.6 X lo3ml. Practical considerations dictated conditions chosen. The 960 rpm stirring speed was easy to monitor and control, gave reproducible resultasand fast enough reaction to permit several trials during each 45-min. high
Experimental
Assuming rate of C02(g) evolution to be an accurate measure of CaC03(s) dissolution rate in HC1, the apparatus shown in Figure 1 was used to determine COz rate for a variety of experimental conditions. The several trials run a t each set of conditions indicated reproducibility of 5% or better. Typical data plots are shown in Figures 3 and 4, and a summary of findings
' Students in
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the Class of 1989. This work was completed in June of their senior year.
Figure 2. Doto plats of ml COdg) colleded per second, for 20 me,h CoC03 in 0.037M HCI a t the indicated temperaturn, ot 960 rprn stirring speed. Each point represents the average of several trials ot that temperature. The dope d each line i g the rote of COdg) collection, in mlfrec, a t the indicated temperature.
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Figure 3. Plob of COdg1 collestion rates in oqueour HCI, far 2 0 mesh Cocoa, at 9 6 0 rpm stirring speed. Each "doto" point is the dope d o corresponding volume of CO&) collected, versus HCI concentrotion (not shown), or HCI temperotvre (Fig. 2), or reported in the table. Note .abrupt ,lope changer ot 0.1 i 5 M HCI ltop plot, using upper horizontal scale), and 36OC (lower plot, wing bottom horizontal rcole).
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Volume of Coda) -. Collected versus Time ~
HCl conc. HCI temperature Rate COI collection +50/0 (malell) ('C) (OK) A(mllseo) D(mo1elsec)o
960 rpm stirringspeed and 20 mesh CaCOs (s), ur~lessatherwise indicated. a B = A/0.245 X -0 mesh CaCOa. 60 mesh CaCOs. d 80 mesh CaCOa,
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way in which the straightforward simplicity of the CaCO8-HCI system allows the students themselves to plan experimental details. One need only find the number of moles of HCI initially present, reacting, and remaining, to arrive at the 3y0 figure. Diffusion Barrier
school work period. Mesh size seemed the simplest way to standardize the CaCOa(s) surface area, and represented a technique not previously reported in the literahre. HC1 molarity ranges were those that mould keep the reaction rate measurably slow. Finally, assuming the net reaction equation, 1 CaCOa(s) 2 HCl(aq) = 1 CaClz(aq) 1 H20(1) 1 COy(g), it can be shown that the maximum possible HC1 concentration change, using 800 ml of 0.037M acid, is about 3Yo during evolution of 100 ml of COn(g). This figure is well within the above-reported reproducibility, and its calculation provides a striking example of the
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HCI CONCENTRATION(MX~O') Figure 4. Rate of C o d g ) collection (moles/l) versus HCI concentration for 2 0 mesh CaCOa in HCI wlutions ot the indicated temperatures ond 9 6 0 rpm stirring speed. These "data" points are the doper of Figure 2 plots ml). The doper of there multiplied by the factor 1 mole/(0.245 X lines ore the so-called rate sonrtonts, k, at each temperature.
40 60 80 HCI TEMPERATURECC)
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Search
Assuming changes from chemical to diffusion control of reaction rate to be detectable by abrupt slope changes of the type shown in Figure 3, a search for such changes was undertaken by plotting COz(g) collection rates (table) against HC1 concentration (Figure 3 upper curve), KC1 temperature (Figure 3 lower curve), and CaCO8 mesh size. This latter work involved grinding up marble chips and sifting them through standard mesh sieves. Analysis of the Figure 3 graphs show abrupt slope changes at 0.115M HC1 concentration, and 36OC. Chemical control of rate is likely a t low concentration and temperature, small CaC03 particle size, high stirring speeds. Diffusion control is favored by high HC1 concentration and temperature, large CaC03 particle size, low stirring speeds. The above analysis thus suggests change from chemical to diffusion control of rate at 0.115M HC1 and 36"C, using 20 mesh CaCOa(s)and a 960-rpm stirring speed. The absence of any slope change when rate is plotted against CaC03 mesh size may indicate the 960 rpm stirring speed is simply too high to allow other than chemical control, a t 30°C and 0.037M HC1 concentration. If this is true, slope change can be expected if mesh size variations are run at considerably slower stirring speeds. It also seems likely that plots of rate versus stirring speed will show the abrupt slope changes we assume indicative of change from chemical to physical control of rate, providing the experimental conditions chosen allow such control to be determined solely by stirring speed variation. Rate Law
The data show that the rate law can be expressed by the equation Rate = k [HCI]. This is illustrated in
plot of in k versus 1/T has a slope equal to -bE./R. Hence the Arrhenius activation energy, AE,, equals the numerical value of this slope times R. Our data gave a slope of -3.24 X lo3"K (Fig. 5) for the in k versus 1/T plot. Thus Ah'. = 1.99 cal/mole OK X 3.24 X loa OK A 6.4 X loa cal/mole. Smce the data is reproducible within 5%, we can report a Ah', value of 6.4 0.3 kcal/mole of COz, in good agreement with Moelwyn-Hughes' (9) value of 6.3 kcal/mole. Both Moelwyn-Hughes and we neglected viscosity effects. Tominaga and his co-workers (8) corrected for such effects, and reported a AE. value of 5.4 kcal/mole. Results such as these give students confidence in their ability to do independent investigations. This type of activity engenders increased awareness of, and insight into the nature of scientific research; indeed, it may encourage some students to enter the field.
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Plot of natural log of k venw 111, where k is the rate mnrtont as calculated from the slopes d Figure 8 plots, and T is the obrdute temperature ( O K ) . Tho slope of this line har a value equal to -AE./R, and hence may be used to cdculote the Arrhenius odivolion energy, AE., for the CoCOrHCI reaction. Figure 5.
Figure 4, where the rate constants are taken as the slopes of rate Cop collection versus HC1 concentration plots at various temperatures, with the Con rates expressed in moles per second. Activation Energy Determination
Acknowledgment
Thanks are due Professor Daniel Perlmutter, School of Chemical Engineering, and Professor Geoffrey Belton, School of Metallurgy and Materials Science, both of the University of Pennsylvania, who served as research advisors, for their help and encouragement. We gratefully acknowledge the support of the Phiiadelphia Section of the American Chemical Society, and its Chemical Education at the High School Level subcommittee chairman, Dr. Harold L. Greenwald. Without this support, in the form of a Chemical Education Projects Award, our work could never have been undertaken. Thanks are also due to Jospeh and Fira Vieland for their help in translating the Gortikov and Nanteleeva (1) article from the Russian.
Eyring (6, 7) and King (8) have shown how a modified form of the Arrhenius equation may be used to calculate the activation energy of a chemical reaction from its kinetics. Assuming this approach applicable to our work, rate constants were found for HC1 concentrations up to 0.112M, and temperatures up to 30°C. These upper limits were suggested by the diffusion barriers found and reported above. The rate constants were found as indicated in the ~ r e c e e d i n ~ Literature Cited paragraph. (1) Gon~zxova m Nanmr.r;~v~. J . @an, c u m . (USSR) 7 , 5 8 (1937). The empirical equation proposed by Arrhenius -(21 T O ~ N A Q AA ~m , m rANDIBOBE. , B d . Cham. SOC.Japan. 14,348 (1939). (3) P ~ n ~ m ANDSEBB*. r GYP&Chim.Itd., 67,501 (1937). states that k = A eCAE"IRT, where k is the rate con(4) CENTNERBZWEBAND HELLER, J . c b m h ~ h y s i q u e 34,217 , (1037). A, a (sometimes the Arrhenius (51 KLEIN, Z.Anova. AUaem. Chem.. 137,SB (1924). (8) E T R I N A,. ~ . J. Chem.Phrrs.. 3,107 (1935). (7) EYAIND. H., GLABBTONE. S., A N D LAID'ER, K., "The Theom of Rate factor); AE,, the activation energy; R, the universal Proouses." MaGraw-HillBook Co., New York. 1941. gas constant; and T, the absolute temperature. (8) KIN~.-HOW chemical TIO ti^^^ O ~ C U ~ , . W. . A. ~ ~ ~I~c..iN ~ W ~ York, 1963, pp. 49. Taking the logs Of both sides Of this equation (0) M o e ~ w r s . H u e ~ ~ s''The , Kinetics of Reactions in Solution," Oxford gives: In k = -AE./RT ln A, which means that a University Presa. Oxford. 1933, P. 284.
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