In the Laboratory
Thermokinetics: Iodide-Catalyzed Decomposition Kinetics of Hydrogen Peroxide An Initial Rate Approach Frazier Nyasulu* and Rebecca Barlag Department of Chemistry and Biochemistry, Ohio University, Athens, OH 45701; *
[email protected] The iodide-catalyzed H2O2 decomposition reaction is
2H2O2(aq)
I–
2H2O(l) + O2(g)
(1)
Typically, the reaction kinetics is determined by measuring the volume of O2(g) at constant pressure (1–3) or the pressure at constant volume (3–5). In this article, we describe a temperaturebased determination of the kinetics using the method of initial rates. Small volumes of reagents (5 mL total volume) are added to a microcalorimeter and the temperature, T, is measured as a function of time, t, using a datalogger and temperature sensor. A typical measurement takes less than 15 seconds. The datalogger has a built-in linear regression analysis functionality that allows immediate determination of the initial rate.
The initial rate is equal to the slope in the thermogram ΔT initial rate = (2) Δt
However, it is desirable to express the initial rate in terms of the H2O2 concentration,
initial rate = −
( constant input Cp, mic =
energy rate
Cp, mic dT d [ H2 O 2 ] (3) = − 2dt 2 Δ rxn H V d t
where dT/dt is the slope in the thermogram; Cp,mic is the heat capacity of the microcalorimeter; Δrxn H is the enthalpy of reaction per mole H2O2; and V is the volume of solution in the
)
dT dt
=
( voltage ) (current)
(4)
dT dt
With the concentration of I– fixed and the concentration of H2O2 varied from one run to another,
initial rate = −
d [ H2 O 2 ] 2dt
= k [I
Theory
calorimeter. When energy is transferred at a constant rate to a calorimeter using a dc power supply in a well-stirred solution, the thermogram is linear and therefore the calorimeter constant (Cp,mic) can be calculated using
] [ H2 O 2 ]
− i
(5)
= k ′ [ H2 O 2 ]
h
h
where
i k ′ = k [ I− ]
(6)
The order of reaction with respect to [H2O2] is determined via hypothesis testing. The hypotheses are the guessed orders of reaction with respect to [H2O2], namely h = 1, 2, 3, .... The hypothesis that h = 1 is tested by plotting the initial rate versus [H2O2]. This hypothesis is valid if the plot is linear and goes through the origin; the slope is equal to k′. To test the hypothesis that h = 2, a plot of initial rate versus [H2O2]2 is constructed. When the reaction is run with the concentration of H2O2 fixed and the concentration of I– varied,
initial rate = −
d [ H2 O 2 ] 2 dt
= k [I
] [ H2 O 2 ]
− i
h
(7)
i = k ′′ [ I − ]
where
h k ′′ = k [ H2 O 2 ]
(8) [I–]
The order of the reaction with respect to is determined by the same hypothesis testing procedure described earlier for [H2O2]. Having determined the orders of reaction, the rate constant is determined using eqs 6 and 8.
Figure 1. Setup for the determination of the enthalpy of the reaction and the determination of the calorimeter constant.
Experimental Materials and Equipment GLX datalogger (Pasco Scientific), temperature sensor (Pasco Scientific), dc power supply (Extech Instruments, 2 per 24 students), electric calorimeter (home-built; dc power source connected across a heating resistor), microcalorimeters (homebuilt, see Figure 1), digital pipets, 15% H2O2, 30% H2O2, 0.25 M KI, and 1.00 M KI.
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 86 No. 10 October 2009 • Journal of Chemical Education
1231
In the Laboratory
Procedure: Enthalpy of the Decomposition of H2O2 and Determination of the Calorimeter Constant The experimental setup is shown in Figure 1. The enthalpy of the reaction is determined using 25 mL of 1.00 M KI and 0.50 mL of 30% H2O2 in a Styrofoam cup. Immediately after the reaction is complete, a dc power source is connected across a heating resistor, is turned on (preset to ~2.8 V), and the heating is continued until enough data points defining a straight line have been obtained. The current that flows is recorded. The density of the 30% H2O2 solution is determined by measuring the mass of 1.00 mL digital pipet-delivered solutions. Procedure: Rate Law The experimental setup for the determination of the rate law is shown in Figure 2. The composition of the solutions used to determine the orders of reactions are shown in Tables 1 and 2. The slope is determined using an in-built linear regression function. The density of the 15% H2O2 solution is determined by measuring the mass of 1.00 mL digital pipet-delivered solutions.
Figure 2. Setup for the determination of the rate law. Table 1. Volumes Used To Investigate the Effect of KI Concentration on the Rate of the Reaction Run Number 1
Hazards The H2O2 solutions are oxidizers and should be handled with care. Potassium iodide may cause irritation to skin, eyes, and respiratory tract. Results and Discussion Enthalpy of Decomposition of H2O2 The thermogram for the enthalpy of H2O2 decomposition and the determination of the calorimeter constant is shown in Figure 3. Adding 8.7 J∙s (3.0 V and 2.90 A) after the decomposition reaction is complete, yields a slope of 0.0762 °C∙s. Using eq 4 the calorimeter constant is calculated to be 114 J∙°C. Using the definition of the reaction enthalpy at constant pressure and the measured density of the 30% H2O2 solution (~1.12 g∙mL), the enthalpy of H 2O 2 decomposition is calculated to be ‒91.7 kJ∙mol H2O2.
R 2 = 0. 9994
(9)
Equation 9 verifies that the order of the reaction is first order with respect to [KI]. Clearly the reaction is not second order in [I–] as implied by the lack of linearity in the plot of initial rate versus [I–]2 (see Figure 5). 1232
0.00
4.00
2
1.00
1.00
3.00
3
1.00
2.00
2.00
4
1.00
3.00
1.00
5
1.00
4.00
0.00
Run Number
V(15% H2O2)/ V(0.25 M KI)/ mL mL
V(H2O)/ mL
6
0.00
3.00
2.00
7
0.25
3.00
1.75
8
0.50
3.00
1.50
9
0.75
3.00
1.25
10
1.00
3.00
1.00
Table 3. The Effect of [KI] on the Initial Rate of Reaction
In the runs in Table 3, which correspond to the runs in Table 1, the concentration of H2O2 is fixed at 0.948 M and the concentration of I– is varied from 0 to 0.20 M. Because we do not have enough dc power units and appropriately sized heating resistors, the heat capacity of the microcalorimeter is taken to be that of 5.00 g of water (20.9 J∙°C). The initial rates (dT∙dt and –d[H2O2]∙2dt) as reported by a student are shown in Table 3 and an example of a thermogram is shown in Figure 4. To test the hypothesis that the order of reaction with respect to [I–] is 1 (i = 1), a plot of initial rate (d[H2O2]∙2dt) versus KI concentration is constructed (Figure 5). This plot is linear and passes through the origin as described by eq 9 y = 0. 009 589 x − 0. 000013
1.00
V(H2O)/ mL
Table 2. Volumes Used To Investigate the Effect of H2O2 Concentration on the Rate of the Reaction
Reaction Order with Respect to I¯
V(15% H2O2)/ V(0.25 M KI)/ mL mL
Run Number
[KI]/ (mol L–1)
[KI]2/ (mol2 L–2)
(dT/dt)/ (˚C s–1)
(–d[H2O2]/2dt)/ (mol L–1 s–1)
1
0.000
0.0000
0.0000
0.00000
2
0.050
0.0025
0.0199
0.00045
3
0.100
0.0100
0.0416
0.00095
4
0.150
0.0225
0.0613
0.00140
5
0.200
0.0400
0.0844
0.00193
Table 4. The Effect of [H2O2] on the Initial Rate of Reaction Run Number
[H2O2]/ (mol L–1)
[H2O2]2/ (mol 2 L–2)
(dT/dt)/ (˚C s–1)
(–d[H2O2]/2dt)/ (mol L–1 s–1)
6
0.000
0.000
0.0000
0.000000
7
0.235
0.055
0.0142
0.000324
8
0.470
0.221
0.0288
0.000657
9
0.705
0.497
0.0449
0.001024
10
0.940
0.883
0.0652
0.001487
Journal of Chemical Education • Vol. 86 No. 10 October 2009 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory 29
Reaction Order with Respect to H2O2 Using the same approach as described above, the order of reaction with respect to [H2O2] is 1; see Table 4 for typical results. The equation of the line for the initial rate versus [H2O2] plot is y = 0. 001564 x − 0. 000036 (10) R 2 = 0. 9900
28
Temperature / °C
27 26 25 24 23 22 21 0
50
100
150
200
250
Time / s Figure 3. Thermogram when 0.50 mL 30% H2O2 is added to 25 mL of 1.00 M KI. Last linear region (180–220 s) corresponds to the addition of 8.7 J/s.
Conclusion
25
This lab is instructive for the following reasons: (i) Compared to the volume and pressure methods, thermokinetics is not only easier to implement (1.5 h compared to 3 h), it also yields superior results. (ii) It combines thermochemistry and kinetics. (iii) It provides an opportunity for students to experience electrical determination of the calorimeter constant in a manner that accentuates the datalogger system. (iv) It incorporates hypothesis testing. (v) It requires students to perform considerable data analysis in an Excel spreadsheet. With a sensitivity of 0.0025 °C, the temperature sensor can be used to determine the kinetics of many reactions even if they are only slightly exothermic or endothermic. The thermokinetic approach may well be the most universal way to determine kinetics of reactions.
Temperature / °C
24
23
22
21 30
40
50
60
70
80
90
100
Time / s
[KI]2 [KI]
2
1
y = 9.6x ∙ 0.0
d[H2O2] 2 dt
Literature Cited 1. Nelson, J. H.; Kemp, K. C. Laboratory Experiments, Chemistry, The Central Science, 9th ed.; Prentice Hall: Upper Saddle River, NJ, 2003; pp 325–338. 2. Peck, L.; Irgolic, K. J. Measurement and Synthesis in Chemistry Laboratory, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, 1992; pp 257–270. 3. Vetter, T. A.; Colombo, D. P. J. Chem. Educ. 2003, 80, 788–789. 4. Abramovitch, D. A.; Cunningham, L. K.; Litwer, M. R. J. Chem. Educ. 2003, 80, 790–792. 5. Hansen, J. C. J. Chem. Educ. 1996, 73, 728–732. 6. Liebhafsky, H. A. J. Am. Chem. Soc. 1932, 54, 1792–1805.
Figure 4. Thermogram for run 4 (see data in Table 3).
(10∙3 mol L∙1 s∙1)
Determination of the Rate Constant Having determined the orders of reaction with respect to [H2O2] and [I–] both as 1, the rate constant is determined from eqs 6 and 8. The slope in eq 9 (0.00959 s‒1) is equal to k[H2O2] where H2O2 is 0.948 M. The slope in eq 10 (0.001564 s‒1) is equal to k[KI] where [KI] is 0.15 M. The rate constants are 0.0101 L mol–1 s–1 and 0.0104 L mol–1 s–1, respectively. The average reported by students is 0.0108 ± 0.0003 L mol–1 s–1 (N = 17) at ~20 °C. The literature values are in the range 0.0100 to 0.0115 L mol–1 s–1 (5, 6).
Supporting JCE Online Material
R2 = 0.9994
http://www.jce.divched.org/Journal/Issues/2009/Oct/abs1231.html Abstract and keywords
0 0.00
0.05
0.10
0.15
0.20
0.25
∙1
[KI] / (mol L ) or [KI]2 / (mol2 L∙2) Figure 5. The effect of the KI concentration on the initial reaction rate.
Full text (PDF) with links to cited JCE articles Supplement Instructions for the students
Notes for the instructor
Postlab Excel spreadsheet with sample data
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 86 No. 10 October 2009 • Journal of Chemical Education
1233
