Pressure Measurements to Determine the Rate Law of the Magnesium-Hydrochloric Acid Reaction James P. Birk and David L. Walters Arizona State University, Tempe, AZ 85286-1604 The kinetics of reaction of an active metal with an acid have been studied by measuring the time required to completely dissolve the metal (13).We report here another approach to measuring the kinetics of such heterogeneous reactions: the determination of pressure as a function of time. The reaction used in this study is that between magnesium ribbon and aqueous hydrochloric acid. Mg(4 + 2Ht(aq)+ Mgh(aqI + H z ~ ) Theoretical Because the reaction is heterogeneous, the rate law must be written in terms of concentrations of dissolved species, pressures (or concentrations) of gases, and surface area of solids. The rate law for this reaction is expected to have the following form:
Glass c
"IWl
W
rate = k(surface area of M ~ ) = [ H + I ~ The reaction was carried out in a closed vessel, so the progress could be followed by measuring the pressure in the vessel as a function of time, with rate defined in terms of partial pressure.
% Rate = At
The expected rate law can be rewritten as follows.
Experimental Caution: W~ththe amounts used here, minimal quantities
of hydrogen are produced. Nevertheless, it is advisable to
work in a well-ventilated area due ta the explosive properties of hydrogen. As usual, students should be required to wear goggles. Substantial increases in the amounts should be accompanied by appropriate precautions consistent with the quantity of hydrogen produced. We found that pairs of students could readily complete 10-12 experiments in a 2-h lab period using this method. In comparison, each pressure-time experiment requires 15-20 min, most of the additional time being due to the required temperature equilibration. Equipment We used a pressure sensor (4) connected to an Apple IIe game port tomeasure the partial pressure of hydriien gas as it is produced in this reaction. Other methods of measuring pressure could also be used for this experiment if amounts were increased to give greater pressure changes. A special glass container was constructed to act as a reaction vessel (Fig.1).It consisted of two large 50.0-mL test tubes. Ground glass joints were attached to give a gastight fit. Aglass stopcock and a small glass port were fused to the female test tube and a glass ear was attached to each test tube.
HCI Solution
Figure 1. Apparatus used to measure the pressure of hydrogen gas in the magnesium-hydrochloricacid reaction. Procedure To carry out a reaction, 50.0 mL of the appropriate concentration of hydrochloric acid was pipetted into the male test tube. The test tubes were sealed together with silicone grease. Rubber bands were attached to the glass ears to keep the tubes sealed together as hydrogen gas was produced. A strip of magnesium metal (width 3.5 mm) was folded over a piece of copper wire and placed through the opened stopcock onto the glass lip above the solution (Fig. 1). The copper wire acts as a weight, keeping the magnesium submerged in the solution during the reaction. Otherwise, the magnesium reacts a t the surface of the solution, causing random variations in the surface area of the magnesium exposed to the solution. Tygon tubing was used to connect the glass container to the pressure sensor. With all reactants in place, the stopcock was closed to seal the system, which was placed in a water bath and allowed to reach constant temperature. As the system came into equilibrium with the surroundings, the pressure within the system changed. Constant pressure, which was used as the value of the initial pressure (Po),was usually obtained in about 15 min. The magnesium was then added to the hydrochloric acid by tipping the glass container. As the reaction proceeded, the pressure was recorded as a function of time. Once the magnesium strip had worked free of the copper wire, pressure and time changes were no longer measured. After complete reaction of the magnesium, the final pressure (P,) was recorded. Volume 70 Number 7 July 1993
587
The slope of the line was determined by a least-squares analysis using CricketGraph (5). The Rate Law
Experiments camed out under seven different sets of conditions are described in Table 1.Variations were made in the concentration of hydrochloric acid the surface area of magnesium the temperature at which the reaction oecurred Each experiment was repeated between three and six times. The average values of the rate for each experiment and their standard deviations are reported in Table 1. Values for the orders a and b were determined from loglog plots (61, based on a logarithmic form of the rate law. log (rate)=dog (surfacearea of Mg) + blog [H'] + log k
0 0
10
The first three experiments in Table 1vary only in the acid concentration, while the temperature and initial surface area of magnesium are constant. For these experiments, the logarithmic form of the rate law can be simplified to the following form. log (rate)= blog [H'I + C1
20
time (s)
Figure 2. Plot of the pressure of hydrogen versus time for the reaction between magnesium and hydrochloric acid.
Results and Discussion A plot of log (rate) versus log [H+l gives a straight line, as In all experiments, magnesium was the limitingreagent, shown in Figure 3. The slope is 2.06, so we obtain a value and the concentration of hvdrochloric acid was laree of 2 for the order b. enough to remain nearly cons&. The surface area of the magnesium remained constant near the end Table 1. Experimentsfor Measuring the Rate of the Reaction of the reaction. As indicated by the expected form of between Magnesium and Hydrochloric Acid the rate law, as long as the concentration of hydrochloric acid and the surface area of the magnesium remain Rate AmAt Rate Surface Temperature approximately constant, the rate of the reaction Reaction No. M Area of 'C (torrlsec) Constant should he constant. Mg (mm2) (mm-' M-' torrs-') The Rate of Reaction 70 32.0 2.07i0.11 0.0296 I.o If the reaction proceeds at a constant rate, a plot of 70 32.0 0.0749i 0.0013 0.0268 the partial pressure of hydrogen gas (P - Po)versus 2 0.20 time should yield a straight line. The rate of reaction, 3 0.50 0.0255 70 32.0 0.446f 0.063
6
1.0
70
42.0
3.67i 0.13
0.0524
is equal to the slope of this straight line. 7 1.0 70 22.0 1.53 i 0.09 0.0218 Such a plot is shown in Figure 2 for an experiment k _ forexoenments15 = 0,0272f0,00,2 in which a 1.0-cm strip of magnesium reacted with 1.0 M HCl. The d o t is linear over most of the course of the reaction, with deviations occuming once the surface For experiments 3-5 in Table 1,the logarithmic fonn of area of the magnesium begins to decrease significantly. the rate law can be simplified to the following form. log (rate)= alog (surfacearea of Mg) + Cz A plot of log (rate) versus log (surface area of Mg), shown in Figure 4, is linear with a slope of 0.965, giving a value of 1for the order a. The rate law can now be cast into its final form, which agrees with previous determinations (7). rate = k(surface area of M ~ ) [ H ? The rate constant was calculated from this rate law for the seven different experiments. Results appear in Table 1. The average value of the rate constant a t 32 Y! is 0.0272 0.0012 mm-2 M-' tom s?. This compares favorably with the average value obtained by six sections of students (71, which was determined from the time for complete dissolution: 0.033 f 0.011 m d M-' tom 8'.
+
The Activation Energy
Figure 3.A lowlog plot used to find the order (b) in hydrogen ion concentration.
588
Journal of Chemical Education
Data were obtained at three different temperatures, so the activation energy could be calculated from the Amhenius equation.
Table 2. Stoichiometric Data for the Reaction between Magnesium and Hydrochloric Acid Final Pressure of H2(g) Mass of Mg (9)
Calculated (torr)
Measured (torr)
%Error
The volume was obtained by measuring the volume of water required to fill the apparatus (119.5 mL) and subtracting the volume of the acid in the container (50.0 mL). The measured pressure of hydrogen gas is obtained as
-..
P_ - P o
.
1.4
1.6
1.8
log(surface area)
2.0
2.2
Figure 4. A lowlog plot used to find the order (a) in surfacearea of magnesium ribbon.
\
,
where E, is the activation energy; and A is the frequency factor. A fit of this equation to a straight line using data from experiments 1,6, and 7 gives an activation energy of 33.8 kJImol, which is close to the value of 28.5 kJImol obtained previously (7). Confirming the Stoichiometry Finally, data from these experiments can be used to confirm the stoichiometry of the reaction. The Ideal Gas Law and the assumed stoichiometry of the reaction can be used to calculate the expected pressure of hydrogen gas from the mass of magnesium used and the volume of gas.
As can be seen in Table 2, the calculated and measured hydrogen pressures agree well, confirming the stoichiometry of the reaction. Summary The reaction of magnesium with hydrochloric acid pmvides a straightforward system in which students can carry out a complete kinetic study of a reaction, involving determination of the stoichiometry conversion of a system property to the extent of reaction determination of rates development of the rate law measurement of the activation energy Literature Cited: 1. Breacis, F;Arenk, J.;MeisPch,H.; Turk,A.Fun&m~nlolsofChemisfry Lobomtory Studks;AcademicPre% NY,1966:pp 2W-210.
2. Eblin, L. P. Chemistry:A Suroey ofhbomtary Techniquesand PmePdume; Harmurt, Brace and World: NY,1968; pp 141-144 3. irk, J. P . & ~ m lChomislry Lobomtory Monuol; B-ss: -eaplis, 1975,1980. 4. Birk, J.P.;Walters, D. L.; Fruitman, E. J. C k m Educ 1981,68,1\2261\226. 5. CtiekrGmph 13.2, 1990, Cricket Software, Great Valley Corporate Center, 400Valley StreamParkway, Malvern, PA19355. 6. Birk, J. P J. Chem.Educ. 1976,53,704-707. I. Birk, J. P Unpublished results of CHM-113 students st Arizona State University
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