ABSTRACT

The objective of this experiment was to find the rate constants at different temperatures of the inversion of 20% sucrose solution with the use of two methods: The Guggenheim Method and the Kezdy-Swinburne Method. Polarimetry permitted to observe the optical rotations of the acid catalyzed hydrolysis reaction of sucrose to glucose and fructose. Four different runs were performed under different temperatures and acid catalyst concentration: one run at 25˚(4N HCl), a second run at 35˚ with a 4N HCl, a third run at 35˚ with a concentration of 2N HCl and the fourth runs at 45˚ 4N HCl. Firstly 25 mL of the sucrose solution and 25 mL of HCl solution were put into separate flask. They were then put in a hot water bath that was at 25 degrees Celsius. The optical rotation was measured as a function of time at 60 second intervals. This procedure was repeated for 35 and 45 degrees celcius as well as at 35 degrees Celsius but this time with a 2N concentration of hydrochloric acid. The catalyst HCl also has an effect on the rate of the reaction as it lowers the activation energy of the reaction hence the half-life. The k value for the four runs was calculated using two different methods: the Guggenheim method and the Kezdy-Swineburne method. Which were of 0.0007 s-1, 0.0027 s-1, 0.0008 s-1, and 0.0091 s-1 for the Guggenheim method and the Kezdy-Swineburne method gave constant rates of 0.00067 s-1, 0.00267 s-1, 0.0008058 s-1, and 0.0096 s-1. The results yielded by these two methods were slightly different for the k value but the difference in the results only increased when we calculated Activation energy, entropy of activation. The activation energy for the Guggenheim method was found to be 101.064 KJ/mol and the activation energy for the Kezdy-Swinburne method was found to be 104.884 KJ/mol. The entropy of activation for the Guggenheim method were found to be, -478.86 J/K, -386.9448 J/K, -138.2296 J/K, -290.11596 J/K, and the entropy of activation for the Kezdy-Swinburne method were found to be -2151.3061 J/K, -1701.485 J/K, -617.3197 J/K, and -1281.377916 J/K. The experimental angle of rotation was found to be 66.2º, but where the theoretical angle of rotation of sucrose is 66.47o.

RESULTS

STEP # 1. RAW DATA

**STEP # 2. Calculation of rate constant (k) using the two different methods**

T=25ºC 4N HCl

In order to calculate the rate constant three are two possible ways; the Guggenheim Method and the Kezdy-Swinburne method.

A) The Guggenheim Method requires plotting a graph of ln (a-a’) vs. t, and the slope of this graph will be equal to –k. Where a is the angle, anda’ is the next angle point.

A) The Kezdy- Swinburne method requires plotting a graph of a vs. a’, and the slope of this graph will be placed in the equation k = [(1/Δt)ln slope]. Where a is the angle, anda’ is the next angle point.

In order to calculate the rate constant three are two possible ways; the Guggenheim Method and the Kezdy-Swinburne method.

A) The Guggenheim Method requires plotting a graph of ln (a-a’) vs. t, and the slope of this graph will be equal to –k. Where a is the angle, anda’ is the next angle point.

B) The Kezdy- Swinburne method requires plotting a graph of a vs. a’, and the slope of this graph will be placed in the equation k = [(1/Δt)ln slope]. Where a is the angle, anda’ is the next angle point.

In order to calculate the rate constant three are two possible ways; the Guggenheim Method and the Kezdy-Swinburne method.

A) The Guggenheim Method requires plotting a graph of ln (a-a’) vs. t, and the slope of this graph will be equal to –k. Where a is the angle, anda’ is the next angle point.

B) The Kezdy- Swinburne method requires plotting a graph of a vs. a’, and the slope of this graph will be placed in the equation k = [(1/Δt)ln slope]. Where a is the angle, anda’ is the next angle point.

B) The Kezdy- Swinburne method requires plotting a graph of a vs. a’, and the slope of this graph will be placed in the equation k = [(1/Δt)ln slope]. Where a is the angle, anda’ is the next angle point.

The k constant of the graphs for the Guggenheim method 1 and the Kezdy-Swinburn method 2 (k calculated from slope as mentioned earlier)

**STEP # 2. CALCULATION OF ACTUVATION ENERGY (Ea) FOR THE FOUR RUNS, USING THE 2 PREVIOUS METHODS**

In order to calculate Ea, a graph of ln k vs. 1/T was plotted, and the slope was equal to m = -Ea/R

Ea = -(-12156) 8.314 J K^{-1} mol^{-1}

Ea = 101 064.984 J mol^{-1}

The activation energy for the Guggenheim method was found to be 101.064 KJ/mol

The activation energy for the Kezdy-Swinburne method was found to be 104.884 KJ/mol

## Ln(k) for both methods as a function of 1/T in K

**STEP # 4. Calculation of entropy of activation (ΔS) for the runs, using the 2 previous methods**

In order to calculate the entropy of activation (ΔS), ΔS_{a} = R ln k (Ah/e^{2}KT)

Where:

ΔS_{a }: entropy of activation

R : gas constant, 8.314 J K^{-1} mol^{-1}

k : rate constant, s^{-1}

A : exponential factor

h : Planck’s constant, 6.626 x 10^{-34} J s

K : Boltzmann constant, 1.380658 x 10^{-23} J K^{-1}

T : temperature, K

SAMPLE CALCULATIONS

ΔS_{a} = R ln k (Ah/e^{2}KT)

ΔS_{a} = (8.314 J K^{-1} mol^{-1}) ln 0.0007 [(3.6376x10^{14 } x 6.626 x 10^{-34 }J s)/ e^{2 }1.380658x10^{14} J K^{-1} 298K)]

ΔS_{a} = -478.86 J/K

**STEP # 5. CALCULATION OF SPECIFIC ANGLE OF ROTATION**

In order to calculate the specific angle the following equation was used:

[a]^{t}_{λ }= 100 a / LC

Where;

a; is the angle of rotation

L: light path, 1dm

C: concentration of solute, 20g/100ml

[a]^{t}_{λ }= 100 a / LC

[a]^{t}_{λ }= 100 (13.241º) / 1 dm (20/100)

[a]^{t}_{λ }= 66.2º

The experimental angle of rotation was found to be 66.2º, but where the theoretical angle of rotation of sucrose is 66.47^{o}.

Discussion

As mentioned in the abstract, the purpose of this experiment was to determine the rate constants at different temperatures of the inversion of 20% sucrose solution with the use of two methods: The Guggenheim Method and the Kezdy-Swinburne Method. Polarimetry permitted to observe the optical rotations of the acid catalyzed hydrolysis reaction of sucrose to glucose and fructose. Four different runs were performed under different temperatures and acid catalyst concentration: one run at 25˚(4N HCl), a second run at 35˚ with a 4N HCl, a third run at 35˚ with a concentration of 2N HCl and the fourth runs at 45˚ 4N HCl. Firstly 25 mL of the sucrose solution and 25 mL of HCl solution were put into separate flask. They were then put in a hot water bath that was at 25 degrees Celsius. The optical rotation was measured as a function of time at 60 second intervals. This procedure was repeated for 35 and 45 degrees Celsius as well as at 35 degrees Celsius but this time with a 2N concentration of hydrochloric acid. The catalyst HCl also has an effect on the rate of the reaction as it lowers the activation energy of the reaction hence the half-life. The k value for the four runs was calculated using two different methods: the Guggenheim method and the Kezdy-Swineburne method. Which were of 0.0007 s^{-1}, 0.0027 s^{-1}, 0.0008 s^{-1}, and 0.0091 s^{-1} for the Guggenheim method and the Kezdy-Swineburne method gave constant rates of 0.00067 s^{-1}, 0.00267 s^{-1}, 0.0008058 s^{-1}, and 0.0096 s^{-1}. The results yielded by these two methods were slightly different for the k value but the difference in the results only increased when we calculated Activation energy, entropy of activation. The activation energy for the Guggenheim method was found to be 101.064 KJ/mol and the activation energy for the Kezdy-Swinburne method was found to be 104.884 KJ/mol. The entropy of activation for the Guggenheim method were found to be, -478.86 J/K, -386.9448 J/K, -138.2296 J/K, -290.11596 J/K, and the entropy of activation for the Kezdy-Swinburne method were found to be -2151.3061 J/K, -1701.485 J/K, -617.3197 J/K, and -1281.377916 J/K. The experimental angle of rotation was found to be 66.2º, but where the theoretical angle of rotation of sucrose is 66.47^{o}.

The results for this experiment were obtained using a polarimeter. The polarimeter is an instrument that can measure the optical rotation of a substance and report it on a dial in front. Its function consists of polarizing light by making it pass through an anisotropic crystal. The purpose of this step is to make light do in only one direction rather than in every direction. The light produced in the instrument is made by a sodium vapor lamp. This crystal is divided into two parts. The division is filled with Canada balsam that is a substance with a high refractive index. (This first crystal is called the polarizer) This reflects the light to the solution. Once it passes through the solution, the light might be rotated. This is picked up by another crystal of similar structure than the first one. (This one is called the analyzer) This crystal can move and one can find the actual angle of rotation by turning it until what you see is completely gray. Of course in this experiment a computerized machine did this automatically. Since sucrose is dextrotatory and the products of the reaction are levrotatory we can use optical activity to monitor the extent of the reaction and thus the rate. Optical activity here is a good choice since it can be measure throughout the reaction. Another way maybe to have done this might be through NMR spectrometry but this method poses a problem, we cannot maintain a constant temperature in that machine unless we have one that supports this feature.

The two methods used to calculate k yield almost the same values of k except for the last run at 45 degrees Celsius where the reaction happened too fast so we did not have enough data to treat this temperature accordingly. Nevertheless the two methods give corresponding values. The divergence of these two methods arises when we start to calculate the activation energies for the reactions. This tells us then that the precision of the methods decreases as we use the values of k in calculations. So to decide which method was more precise, literary data of previous experiments were found. Activation energy was of 107403.28J. The activation energy for the Guggenheim method was found to be 101.064 KJ/mol and the activation energy for the Kezdy-Swinburne method was found to be 104.884 KJ/mol so I therefore conclude that the Kezdy-Swinburne method is more precise.

A lower concentration of the catalyst HCl yields a slower reaction rate. The catalyst here helps lower the half-life of the reaction. It lowers the activation energy so that the reaction can manage to get over the energy barrier (see graph 11).

The hydrolysis of sucrose was catalyzed by hydrochloric acid. In this reaction the chlorine ions were spectator ions. We considered this reaction a first order reaction because it is truly a pseudo first order reaction. Water was present in large excess so its concentration could be considered constant. (We must remember here that the solvent water is a reactant) Hence the pseudo first order.

Possible experimental error might be the starting of the timer. We might have either started the time slightly earlier or after the reagents were mixed. Another error might be in maintaining the right temperature for the reaction vessel. The water that was passed through tubes might have had time to decrease it temperature before reaching the reaction.

**CONCLUSION**

The objective of this experiment was to find the rate constants at different temperatures of the inversion of 20% sucrose solution with the use of two methods: The Guggenheim Method and the Kezdy-Swinburne Method. Polarimetry permitted to observe the optical rotations of the acid catalyzed hydrolysis reaction of sucrose to glucose and fructose. Four different runs were performed under different temperatures and acid catalyst concentration: one run at 25˚(4N HCl), a second run at 35˚ with a 4N HCl, a third run at 35˚ with a concentration of 2N HCl and the fourth runs at 45˚ 4N HCl. The optical rotation was measured as a function of time at 60 second intervals. The catalyst HCl also has an effect on the rate of the reaction as it lowers the activation energy of the reaction hence the half-life. The k value for the four runs was calculated using two different methods: the Guggenheim method and the Kezdy-Swineburne method. Which were of 0.0007 s^{-1}, 0.0027 s^{-1}, 0.0008 s^{-1}, and 0.0091 s^{-1} for the Guggenheim method and the Kezdy-Swineburne method gave constant rates of 0.00067 s^{-1}, 0.00267 s^{-1}, 0.0008058 s^{-1}, and 0.0096 s^{-1}. The results yielded by these two methods were slightly different for the k value but the difference in the results only increased when we calculated Activation energy, entropy of activation.

The activation energy for the Guggenheim method was found to be 101.064 KJ/mol and the activation energy for the Kezdy-Swinburne method was found to be 104.884 KJ/mol. The entropy of activation for the Guggenheim method were found to be, -478.86 J/K, -386.9448 J/K, -138.2296 J/K, -290.11596 J/K, and the entropy of activation for the Kezdy-Swinburne method were found to be -2151.3061 J/K, -1701.485 J/K, -617.3197 J/K, and -1281.377916 J/K. The experimental angle of rotation was found to be 66.2º, but where the theoretical angle of rotation of sucrose is 66.47^{o}.

The hydrolysis of sucrose was catalyzed by hydrochloric acid. In this reaction the chlorine ions were spectator ions. We considered this reaction a first order reaction because it is truly a pseudo first order reaction. Water was present in large excess so its concentration could be considered constant. (We must remember here that the solvent water is a reactant) Hence the pseudo first order.

Possible experimental error might be the starting of the timer. We might have either started the time slightly earlier or after the reagents were mixed. Another error might be in maintaining the right temperature for the reaction vessel. The water that was passed through tubes might have had time to decrease it temperature before reaching the reaction.