In the Laboratory
W
Dissolution Kinetics of Solids: Application with Spherical Candy
3
m = 3 m 0 – kt
(1)
2
m1/3 / g1/3
The main purpose of this experiment is to present a simple and novel kinetics laboratory assignment in the aqueous dissolution of solids. It involves an unusual order with respect to mass, which is due to the influence of surface area on the rate. In a general chemistry course, this experiment may also serve as an introduction to the concepts of solubility and diffusion. The simplicity of the procedure lies in the fact that only mass measurements are taken over time, so dissolution is directly observed and monitored. By calculating the dissolution rate constant at different temperatures, the Arrhenius activation energy is determined. Dissolution of a spherical solid particle in excess water follows the Hixson–Crowell cube-root law (1) characterized by eq 1,
0
3
2 –1 k
3
m0 2
120
240
360
480
600
720
t/s Figure 1. Graph of the cube root of mass of candy versus time.
where m0 is the initial mass of the spherical particle, m the mass of the particle at time t, and k the rate constant. The half-life (t1/2) of the dissolution process can also be derived:
t 1/2 =
1
0
-5.9
-6.1
(2)
Experimental Procedure A 1000-mL beaker containing 900 mL of distilled water at 20 °C is placed on a magnetic stirrer set at maximum speed. A thermometer is suspended in the water and secured to a stand and rod with a clamp. A spherical candy is weighed and dropped into the beaker at time zero (t = 0). At 2-min intervals the stirring and timer are interrupted, the candy is quickly removed with a spoon and dried on absorbent paper, and its mass is recorded. This procedure is repeated until 5 data points have been collected (8 min). The experiment is repeated with other samples at temperatures of 10, 30, and 40 °C. Small pieces of ice (distilled water) can be regularly added to maintain the colder temperature constant, and hot distilled water is added for the warmer temperatures. A student can complete three temperature assays in less than one hour. Hazards There are no significant hazards associated with this experiment. Results and Discussion I repeated the whole experiment 8 times in order to assess reproducibility of measurements. Typical result of the variation of mass of candy as a function of time exhibits a characteristic asymptotic curve because the rate of dissolution (slope) is proportional to the decreasing surface of the candy. Measurement of the candy diameter with a slide caliper as a function of time shows that the radius of the dissolving candy recedes at a
ln (k / (g1/3 s᎑1))
J. Chem. Educ. 2001.78:523. Downloaded from pubs.acs.org by NEW MEXICO STATE UNIV on 07/05/18. For personal use only.
Guy Beauchamp Department of Chemistry, Collège de l’Outaouais, Hull, PQ J8Y 6M5, Canada;
[email protected] -6.3
-6.5
-6.7
-6.9 3.1
3.2
3.3
3.4
3.5
3.6
T ᎑1 / (10᎑3 K ᎑1) Figure 2. Graph of natural logarithm of the rate constant as a function of reciprocal Kelvin temperature.
constant rate (zero order). This assessment, which is optional in the student experiment, illustrates a particular feature in dissolution of spherical particles. In Figure 1, which depicts the cube-root mass of the candy as a function of time, conformity to the Hixson–Crowell law is readily apparent from the linear aspect of curve. Thus a rate constant, expressed in g1/3 s᎑1 units, may be obtained from the slope for each temperature assay. The calculated coefficient of variation for the rate constants was 3%. Finally, the Arrhenius activation energy (E a) of the dissolution process is determined from the slope of the plot of the natural logarithm of the rate constant versus reciprocal absolute temperature (Fig. 2). In this case, the calculated Ea of the dissolution process (23,000 J/mol, SD = 700 J/mol) is not related to classical
JChemEd.chem.wisc.edu • Vol. 78 No. 4 April 2001 • Journal of Chemical Education
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In the Laboratory
collision theory. Rather, it is associated with the energy barriers that must be overcome in order to respectively dissolve and diffuse the solute in the solvent. In the pharmaceutical industry (2), determination of the energy of activation of a drug in its tablet form helps in designing effective therapeutic formulations. Data from a group of 40 students who performed the experiment produced an average Ea value of 23 kJ/mol with a standard deviation of 3 kJ/mol. The purity of the round striped mint candy used was evaluated by melting point determination. The observed temperature interval is 102–104 °C, which most likely corresponds to the melting range of fructose (m.p. 103–105 °C; the melting point of sucrose is 160 °C ). The artificial color and flavor on the surface of the candy (
