Inversion of Sucrose - lab report PDF

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Inversion of Sucrose Massimo Ruscitti Partner: Jaci SilvaSa November 28, 2018

Ruscitti 1 Abstract: In this experiment, the extent of sucrose hydrolysis in the presence of a strong acid was followed through polarimetry. As the reaction reached completion, the angle of rotation for plane polarized light slowly inverted from 6.43° to -2.33°. Treatment of this data generated two distinct plots, with slope values equal in magnitude to the rate constant of the pseudo-first order reaction rate. Through the traditional method of data analysis, the rate was found to use a rate constant of 0.0282 s-1. After using the Guggenheim method of data analysis, the rate was found to possess a rate constant of 0.0305 s-1. Comparison of the two rate constants showed that the constants were only different by 8.1%, proving that the two treatments of the data were consistent. Introduction: The purpose of this experiment is to gain an understanding of the kinetics at play in the acid-catalyzed hydrolysis of sucrose. Under these acidic conditions, sucrose will break down into glucose and fructose, as shown in the reaction below:

In tracking the progress of the reaction, a sample solution can be analyzed by polarimetry. Polarimetry involves measuring the specific rotation of plane-polarized light as it travels through a solution containing chiral molecules1. By convention, sucrose is considered a dextrorotatory molecule, whereas the mixture of glucose and fructose is levorotatory. This means that as the

Ruscitti 2 sucrose is consumed in the reaction, the rotation of plane-polarized light will decrease and slowly favor a levorotatory angle of rotation2. Thus, it can be said that the angle of rotation is directly related to the concentration of sucrose in solution, as described in Eqs. (1) and (2) below, where Ct is the sucrose concentration at any time t, Co is the original concentration of sucrose, αt is the angle of rotation at any time t, αo is the angle of rotation at the start of the reaction, α∞ is the angle of rotation at the end of the reaction, and k is the rate constant:

ln

( )

(

)

Ct α −α ∞ =−kt ; ln t =−kt Co αo −α ∞

(1), (2)

Ordinarily, this reaction would be considered second-order, as it is dependent on the concentration of both the sucrose and the water. However, due to the excess of water and the acid catalyst, the reaction is said to be pseudo first-order and will follow first order kinetics. For this reason, making a plot of the experimental data following the relationship set forward in Eq. (2) will yield a slope possessing the same magnitude as the rate constant for the reaction. In an alternate approach to finding the rate constant, one can integrate the differential equation shown in Eq. (1), and through careful manipulation of this equation, the following relationship can be achieved relating two values for the angle of rotation, α1 and α2, which were measured at a difference in time Δt: ln ( α 1 −α 2 )=−kt+ ln [ a C o ( 1−e−k ∆ t ) ] ( 3 ) This approach is known as the Guggenheim method, and while it should yield the same value for the first order rate constant as the traditional method, the benefit of using the Guggenheim method is that it avoids using a measurement at “infinite” time, which is a value taken largely based on the assumption that the reaction reaches completion in the span of a few days. In turn,

Ruscitti 3 this prevents the plotted points from depending on a single observation, thereby eliminating some of the inaccuracies present in the traditional method. Experimental Method: To begin, the polarimeter tube was filled with distilled water, and the polarimeter was zeroed properly. Next, a 25 mL sample of sucrose solution was mixed with a 25 mL sample of distilled water, and the angle of rotation for this solution was recorded as the “zero” time reading for the reaction. After emptying out the sucrose solution from the polarimeter tube, a second mixture was created using a second 25 mL aliquot of sucrose solution and a 25 mL volume of 4N hydrochloric acid. Just as the two solutions started to mix, a timer was started, and a portion of the reaction mixture was used to fill the polarimeter tube. For the following two hours, a polarimeter reading was recorded every ten minutes. Upon recording the last angle of rotation in the allotted time span, the polarimeter was switched off, and the reaction mixture was left in the polarimeter tube to allow it to run to completion. Approximately two days later, the polarimeter was switched back on, recalibrated with air, and used to take an additional reading of the mixture’s angle of rotation. This final value was recorded as the angle of rotation at “infinite” time. Upon completing the experiment, the reaction mixture was discarded in the appropriate waste container, the polarimeter tube was rinsed with distilled water, and the polarimeter was switched off.

Ruscitti 4 Results:

Ruscitti 5

Figure 1:Traditional Method of Polarimetric Analysis 2.50 2.00

f(x) = − 0.03 x + 2.11 R² = 1

1.50

ln(αt-α∞)

1.00 0.50 0.00 -0.50 -1.00 -1.50 0

20

40

60

Time (min)

80

100

120

140

Ruscitti 6

Ruscitti 7

Figure 2: Guggenheim Method of Polarimetric Analysis 2.5

2 f(x) = − 0.03 x + 1.91

ln(α1-α2)

1.5

1

0.5

0

-0.5 0

10

20

30

40

Time (min)

50

60

70

80

Ruscitti 8

Rate Constant from the Traditional Method: −1

k t =−slope=0.0282 s

(4)

Rate Constant from the Guggenheim Method: k g=−slope=0.0305 s−1

(5)

Percent Difference:

% Difference=

k g −k t ∗100 %=8.1 % Difference kt

(6)

Discussion: Overall, the experimental findings indicate that the rate constant for this pseudo firstorder reaction is 0.0282 s-1 by the traditional method and 0.0305 s-1 by the Guggenheim method. These values are displayed on Figs. (1) and (2), which present the linear plots of the polarimetric data taken during the experiment. For convenience, these values are also included in Eqs. (4) and (5), which distinguish the rate constants of the traditional method and the Guggenheim method as kt and kg, respectively. By comparing the two values, an 8.1% difference can be seen between the kt and kg, meaning that the results of both data treatments were consistent. Of the two

Ruscitti 9 methods, the Guggenheim approach is probably more accurate since it does not rely on a value for α∞, whereas the traditional method does require this measurement. In utilizing this value, kt must be less accurate because the reaction might not have reached completion in the allotted two days that it was left in the polarimeter. One could conceivably reduce this error by using an α∞ value that was measured a week or more after the experiment was started. By this point, the angle of rotation could better reflect the value at “infinite” time, and by extension the rate constant would become more accurate. References: 1

2

Garland, Carl W., et al., Experiments in Physical Chemistry Eighth Edition, 612, 2009.

Whitten, James. Chemical Kinetics-Inversion of Sucrose. University of Massachusetts, Lowell....