edited by ROBERT REEVE;
Marlborough School 250 S. Rossmore Avenue Los Angeles, CA 90004
An Example of a Constant-Rate Reaction Khalid M. Tawarah Yarmouk University, Irbid, Jordan At constant temnerature and nressure the rate exnression for a chemical reaction can be expressed in the form: rate = k f(cl,cz,. . .),where k is the rate coefficient and f(c1,cz.. . .) is a functionof concentration of reactantsor products. When the order of a reaction is zero with respect to each reactant and product (a very rare case), the function f(cl,cz,. . .) is identical to 1. In this case the reaction oroceeds at constant rate (rate = k). On the other hand, a reaction can proceed at a constant rate (rate = k') when the function f(cl,cz,. . .) is constant but $1. This case can be illustrated by (1) a reaction that is zero order with respect to a reactant, such as iodation or bromination of acetone (11, (2) a surface reaction occurring on a saturated surface such as the decomposition of ammonia on a point ( 2 ) ,(3) the maximum-rate limit of an enzyme-catalyzed reaction (3),or (4) a steady-state rate in a continuous flow annaratus. The purpose of'& article is to describe a simple experiment whose rate of reaction proceeds a t constant conditions. The experiment chosen is the burning of a candle. Although the burning of acandle has been the subject of several educational accounts (4-7),the experiment described here can be adapted as an introductory experiment in the teaching of chemical kinetics with emphasis on data collection, computations, and graphical presentation. Once a candle is lit, the heat energy released during the burning of the candle wax causes melting of the top part of the candle. A surplus of melted wax can always he seen underneath the burning wick. Before being burned, the melted wax has to ascend to the tip of the wick, most likely by a capillary action. Vaporization and combustion of wax
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molecules then takes place. Consequently, the mass and the height of a candle both decrease as time goes on. Changes in mass, height and shrinkage of the shadow cast by a candle were studied, each in a separate set of experiments. Materials The candles used in the present study were purchased from a local store. Each candle weighs about 10.5 g, has a height of about 110 mm and an average diameter of about 12 mm. The candle wick consists of five strands twisted together. The wick has an average diameter of about 1.5 mm.
Results Changes In Candle Mass In order to follow the change in mass during burning, the candleunder study was stuck vertically on a pan of a doublebeam balance, which has an accuracy of 0.01 g. After some trials, the balance was set to indicate 0.40 g less than the actual mass. The time required for the balance to indicate the actual mass was then recorded. This process was repeated several times without extinguishing the candle until about 90%of the candle was burned. Typical data are shown in Table 1. The mass w a t time t was found to obey the relation and the mass burned after time t is given as
Table 1.
Data on Candle Mass wand Cumulative Mass Loss Aw
Time (min)
w(g)
Aw(g)
Time (minl
w(g)
Aw(g)
0 5.5 11.0 17.7 22.7 27.6 32.6 37.5 42.2 47.5 52.3 57.3 62.0
10.90 10.50 10.10 9.70 9.30 8.90 8.50 8.10 7.70 7.30 6.90 6.50 6.10
0 0.40 0.60 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80
67.0 71.6 76.2 80.8 85.8 90.6 95.6 100.5 105.0 109.8 114.4 119.2
5.70 5.30 4.90 4.50 4.10 3.70 3.30 2.90 2.50 2.10 1.70 1.30
5.20 5.60 6.00 6.40 6.80 7.20 7.60 8.00 8.40 8.80 9.20 9.60
-
-
Table 2.
Data on Candle Height hand Cumulative Helght Decrease Ah
Time (min)
h (mm)
Ah (mm)
-
Figure 2. Plot of candle height hand the cumulative height decreases Ah vs time. Closed circles represent h, open circles represent Ah, and the line represents least-squares fit.
Figure 1. Plat of a candle mass wand the cumulative mass lass Aw vs time. Closed circles represent w, open circles represent Aw, and the line reprc sen% l e a s t - ~ q ~ fit. ~~es
A plot of h, and Ah, versus time is shown in Figure 2. The value of k h is obtainable from the slope of either line in the figure. The constant kh and till have the values 0.8 mmlmin and 68 min, respectively. Changes in Candle Shadow
A plot of w, and Aw versus time t is shown in Figure 1.The slope of either line in Figure 1gives a value of 0.08 glmin for k,. The same value was obtained for two other candles with masses 10.38 and 10.60 g. The time corresponding to 50% mass loss, tIlz,for data in Table 1is 68 min. Changes in Candle Height
A second series of experiments was conducted in order to follow the change in the eight of a candle during the burning process. By the use of a ruler, the average height of a candle was recorded everv 5 to 10 min. In each case the candle was extinguished in eider to get a reasonable height measurement. The process of lighting and extinguishing the candle was repeated several times until about half of the original heieht was burned. Average data on three identical candles areshown in Table 2. I t was concluded that the height h a t time t can be given by the relation
The last set of experiments was concerned with the shrinkage in the shadow of a candle. The shrinkage in the shadow was studied by placing the candle vertically over a ruled sheet of paper. The lines on the ruled sheet were parallel to each other and have a uniform spacing. Each experiment was done in the night under the illumination of a hanging lamp. The position of the lined paper was adjusted so that the shadow of the candle was perpendicular to each line on the ruled sheet. In this case the shadow of the candle was equal to its height. Consequently, a measurement of the length of the shadow 1 is an indirect measurement of the height h. Without extinguishing the candle, the length of the shadow of the candle was measured a t several time intervals. A typical result is shown in Table 3. I t was found that the length of the shadow can be related to time by the relation,
and the total shrinkage is and the height burned after time t is
A1 = lo - lt= k,t ,'...
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A plot of lt and A1 versus time is depicted in Figure 3. The slope of either line in Figure 3 gives kl. The constant kl and t11z have the values 0.8 mmlmin and 68 min, respectively.
Table 3.
Data on Candle Shadow land Cumulative Shrinkage In Shadow A1
Time (min) 0 16 28 38 49 80 71
As judged from the values of kh, kl, and tlla, Figures 2 and 3 correlate very well. The correlation of these figures points to the fact that both the reduction in height and the shrinkage in the candle shadow are eauivalent variables. The data of Figures 1, 2, and 3 gave the-same tllz This is an indication that the candles used in this study have a uniform density and diameter. Consequently, the time needed to burn half of the original height of the candle should be the same as the time needed to burn half of its original mass. The ratio k,lkh, as obtained from Figures 1and 2 is 0.1 gl mm. Making use of the conclusion of uniform density and diameter, a check on this ratio can be carried out as follows: mass = rrZdh= w . . . Aw = rr2dAh. . .
RR
~(mm) 108 99 90 81 72 63 54 A5
A1(mm) 0 9 18 27 36 45 54 RR
(7)
(8)
The radius r and the density d of a candle were estimated as 6 mm and 8.8 X e/mm3.resoectivelv. Makine use oieas 2 and 4, then substituting the values of; and d, 8 leads to the result (k,/kh),l, = 0.10 glmm. This result is in excellent agreement with the experimental ratio. In the modern classification of flames, a candle flame is a diffusion flame. The most distinctive character of diffusion flames is that the burning rate is not controlled by chemical reactions as in premixed flames, but is controlled by the rate at which the fuel and oxidizer are brought together in the proper proportions for reaction (8). The rate of wax combustion can be expressed in the form
4
rate = k(POJ"(P,,)"'
wherepstands for pressure and n and m stand for the order of reaction with respect tooxygen and wax vapor, respectively. The observation that the candle mass or height changes with time a t constant rate implies that
Figure 3. Plot of candle shadow landthe cumulative shrinkage in shadow Alvs time. Closed circles represent I, open circles represent AI, and the line represents least-squares fit.
(1) W a x is supplied to the candle flame at constant rate; that is,P,,
is constant during candle burning. diffusesat a constant rate in the flame; that is, Po, is constant. (3) Heat flux from the candle flame to the candle top is constant.
be exploited to indicate time intervals, although the observation had been perceived a long time ago (91, or added by the manufacturer as a characteristic property of a candle.
Under these conditions, the combustion rate is constant (rate = k') and the total order of reaction (n m) cannot be deduced.
Acknowledgments My sincere thanks are due to the referees of the first draft for their thoughtful comments, to Yarmouk University for supporting the publication of this article, and to Tina Nicklin for typing the manuscript.
(2) Oxygen
+
Conclusions (1) The burning of a candle illustrates a case in chemical kinetics where the constancy in the reaction rate does not imolv . - true zero-order kinetics. (2) The measurement of a candleshadow illustratesa gituation in chemical kinetics where an indirect measurement of a oroDertv is beine soueht. (3) The experiment can be utilized t o check for candle uniformity with respect t o diameter and density. (4) The observation of constant height decrease can either .
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Literature Cited 1. Lathsm, J. L.: Burgns, A. E. Elemontory Reaction Kinrfics; 3rd ed.; Butterworth%: London. 1980; p 76. 2. Benron. S. W. Foundation8 o/ChemicolKinafica;McGrsw-Hill:New York, 1980.p 14. 3. Berry R. S.; Rice, S. A,: Rms. J.Physiro1Chemistry; Wile?: New York. 1980,p 1235. 4.
5. 6. 7. 8. 9.
Wikim. H. Foradoy'a Chemical History oflr Candle; Crowell: New York, 1957. Videen. T. Chemistry 1968.39.26. Wdker, J.Sei.Am. 1978,288,154. Oemuth, R.Nolunuiss. Untfer, PhysIChem. 1979.27.334. Miieheli, R. E., PhD diaaertation, MIT, 1975; p 53. Thornley. G. C. Ways offhe World: Longman: London, 1968: p 4.
