The Inversion of Sucrose A Determination of the Rate of Reaction and Activation Energy Andrew Kline, Department of Chemistry, University of North Florida With assistance from Chad McDaniel, and Joe Henthorn 2-8-2011
Abstract: In this experiment the inversion of sucrose was determined by an acid catalyzed reaction and from plotted data taken from a polarimeter, the activation energy, rate of reaction, the rate constant, and order was calculated. It was found that the best fit linear plot was that of the ln ( α) (found to be -0.107 for the 30°C HCl run, -0.1532 for the 40°C HCl run, -0.0148 for the 50°C MCAA run, and -0.0389 for the 60°C MCAA run) and the activation energy was found to be 263.5 kJ/mol for HCl and 2322.2 kJ/mol for the MCAA.
Introduction: The inversion of sucrose has several benefits both in the food industry and in the medical field. The conversion of sucrose into its single sugars, glucose and fructose, happens in the body with the use of the invertase enzyme which is found in saliva. There are several other enzyme catalyzed reactions which can be carried out under non-biological conditions by using an acid catalyst (H +). The rate of reaction is of the form: (1)
The purpose of this experiment is to determine the rate of the reaction and the activation energy of the inversion of sucrose by measuring the angle of polarized light being shown through a sample and graphing the data of the observed angles of rotation vs. time. Once the experimental data reaches a negative value stop taking data and allow the solution to sit for one week, this is to obtain a α∞ value, which you subtract from the experimental values. The activation energy is determined using the Arrhenius equation: [1] (2)
Where k is the rate constant, A is the frequency factor, E a is the activation energy, R is the gas constant, and T is temperature in K. Sucrose is dextrorotary however the combination of glucose and fructose is levorotary. As the degradation of sucrose continues the angle changes from right to left (or (+) to (-)).[2] This reaction will occur on its own but an acid catalyzed reaction is much more efficient.
Sucrose
Glucose
Fructose
[3]
Materials: A 4M HCl (EMD Chemicals, Gibbstown, NJ) solution was made, along with a 4M MCAA (Aldrich, St. Louis, MO) and a 0.58M sucrose (Mallinckrodt, Phillipsburg, NJ) solution, and a Linos photonics SR6 polarimeter.
Procedures: The stock solutions were equilibrated to their respective temperatures; the HCl was heated to 30 and then 40°C, while the MCAA was heated to 50 and then 60°C, using a circulating hot water bath. Once the solutions reached temperature they were mixed in equal amounts (25 mL ea.), and immediately added to one of three polarimetery tubes and an initial reading was taken. The tubes were placed into a re-closable plastic bag and returned to their respective hot water baths, and then every two minutes another reading was taken (the time spacing of two minutes may be adjusted as needed either up or down in order to obtain more accurate data.). The time interval for the MCAA runs was ten minutes due to the fact that MCAA is weaker acid than HCl so it takes a longer time to overcome the activation energy in order for the reaction to proceed. Readings are taken on the polarimeter until a negative reading is taken; this reading indicates that the sucrose has been inverted.
Results: The results of the inversion of sucrose show that the activation energy of the acid catalyzed reaction is negative. This negative trend is due to the activation energy being lowered. The slope of the equations of the lines results in a –k value for the activation energy.
ln(Alpha) vs. Time of 30 C HCl Runs
3.0 2.5
30 C Run 1 30 C Run 2
2.0
30 C Run 3 Linear (30 C Run 1)
1/α Cor 1.5
Linear (30 C Run 2) Linear (30 C Run 3) y = -0.157x + 2.7502 R² = 0.8896 y = -0.1334x + 2.6979 R² = 0.9382
1.0 0.5 0.0 0
5
10
Time15 (min)
20
Figure 1: All equations are in order of run and the average slope is -0.107
25
30
y = -0.0306x + 2.6479 R² = 0.9846
ln(Alpha) vs. Time 40 C HCl Runs 40 C Run 1
3.0
40 C Run 2
2.5
40 C Run 3 2.0
Linear (40 C Run 2) Linear (40 C Run 3)
1/α Cor 1.5 1.0
y = -0.1495x + 2.7573 R² = 0.9945
0.5 0.0 0
2
4
6
8
10
12
y = -0.1606x + 2.6751 R² = 0.9925
Time (min) Figure 2: All equations are in order of run (run1 and 2 were exactly the s ame therefore there is only two equations) the average slope is -0.1532.
ln(Alpha) vs. Time 50 C MCAA Runs 50 C Run 1
3.5
50 C Run 2
3.0
50 C Run 3 2.5
Linear (50 C Run 1) Linear (50 C Run 2) Linear (50 C Run 3) y = -0.0159x + 3.0289 R² = 0.9829
2.0
1/αCor 1.5 1.0 0.5
y = -0.0138x + 2.9127 R² = 0.9782
0.0
y = -0.0146x + 2.8526 R² = 0.9623
0
20
40
60
80
Time (min) Figure 3: All equations are in order of run and the average slope is -0.0148.
100
120
ln(Alpha) vs. Time 60 C MCAA Runs 3.5
60 C Run 1
3.0
60 C run 2
2.5
60 C Run 3 Linear (60 C Run 1) Linear (60 C run 2) Linear (60 C Run 3)
2.0
αCor 1.5 1.0 0.5 0.0 0
10
20
30
40
50
Time (min)
Figure 4: All equations are in order of run and the average slope is -0.0389.
HCl Activation E -1.85 -1.9
0
0.01
0.02
0.03
0.04
-1.95 -2 -2.05 ln(K)
HCl Activation E
-2.1
Linear (HCl Activation E)
-2.15 -2.2
y = -31.695x - 1.103 R² = 1
-2.25 -2.3
1/Temp
Figure 5: Graph of the activation energy of HCl
y = -0.0443x + 2.9338 R² = 0.9609 y = -0.0358x + 2.7861 R² = 0.976 y = -0.0357x + 2.7955 R² = 0.984
MCAA Activation E 0 -0.5 0
0.005
0.01
0.015
0.02
0.025
-1 -1.5 ln(K)
MCAA Activation E
-2 -2.5
Linear (MCAA Activation E)
-3 -3.5
y = -279.3x + 1.3707 R² = 1
-4 -4.5
1/Temp
Figure 6: Graph of the activation energy of MCAA.
The activation energy was determined by taking the -(slope *the ideal gas constant(R)) therefore the activation energy of HCl is 263.5 kJ/mol and the activation energy of MCAA is 2322.2 kJ/mol. The rate of reaction was found to be: K for MCAA
K for HCl Actual Temp (°C)
Avg K
Rate
Actual Temp (°C)
Avg K
Rate
28
-0.107
-0.06206
50
-0.015
-0.00856
41
-0.1532
-0.08886
60.5
-0.03893
-0.02258
This rate is determined by multiplying the Average K by the concentration of the sucrose solution used (0.58 M).
Bibliography Garland, C. W., Nibler, J. W., & Shoemaker, D. P. (2009). Experiments in Physical Chemistry 8th edition. New York: McGraw-Hill. Colby College. (2009, September 23). Retrieved January 18, 2011, from Inversion of sucrose:
http://www.colby.edu/chemistry/PChem/lab/InversionSucrose.pdf Grossie, D. (2007, October 23). Wright State University Department of Chemistry . Retrieved January 19, 2011, from Invertion of Sucrose; Kenetics of a pseudo-first order reaction determined by polarimetry: http://www.chm.wright.edu/grossie/chm457/Inversion%20of%20Sucrose.pdf
Appendix A:
Inversion of Sucrose (Actual Temp: 28 C) HCl @ 30°C
Inversion of Sucrose (Actual Temp: 41 C)
° of Rotation
HCl @ 40°C
° of Rotation
Time (min.)
Run 1
Run 2
Run 3
Time (min.)
Run 1
Run 2
Run 3
0.00
11.6
11.5
9.4
0.00
11.2
11.2
10.5
2.00 4.00
6.1 4.0
5.8 4.5
9.0 8.8
2.00
8.4
8.4
7.3
6.00
2.5
2.8
8.0
4.00 6.00
4.3 2.7
4.3 2.7
3.2 1.2
8.00
1.0
2.2
7.4
8.00
0.7
0.7
0.1
10.00
0.8
0.5
6.2
10.00
-0.5
-0.5
-1.0
12.00
-2.4
-1.6
5.9
14.00
5.7
16.00
4.7
18.00
3.7
20.00
3.8
22.00
3.4
24.00
3.0
26.00
2.3
28.00
1.7
HCl ∞
MCAA ∞
-4.0
-4.0
Inversion of Sucrose (Actual Temp: 50 C) MCAA @ 50°C
° of Rotation
Inversion of Sucrose (Actual Temp: 60.5 C) MCAA @ 60°C
° of Rotation
Time (min.)
Run 1
Run 2
Run 3
Time (min.)
Run 1
Run 2
Run 3
0.00
15.6
15.0
14.0
0.00
13.3
13.3
13.4
10.00
13.0
10.6
9.4
5.00
10.4
10.4
10.0
20.00
11.0
9.3
8.9
10.00
8.3
8.0
8.0
30.00
8.7
8.9
7.0
15.00
6.8
5.2
5.2
40.00
6.7
6.8
5.8
20.00
4.4
2.9
3.8
50.00
6.3
5.0
4.5
25.00
3.1
1.9
1.9
60.00
3.9
3.9
3.3
30.00
0.1
1.4
1.4
70.00
3.6
3.4
2.7
35.00
-0.1
0.5
0.5
80.00
2.0
3.0
2.0
40.00
0
0
90.00
1.0
1.7
1.1
45.00
-0.3
-0.3
100.00
0.4
0.2
-0.8
110.00
-1.0
-0.3
