Sugar Hydrolysis
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One of the most important products that we have in our daily diet is sugar. The main type of sugar that we use is sucrose, which is a disaccharide consisting of glucose and fructose. The hydrolysis of sucrose to produce glucose and fructose occurs by the following overall reaction:
C12H22O11(s) + H2O(l) yields C6H12O6(aq) + C6H12O6(aq)
glucose fructose
A biochemist studies the kinetics of the process and obtains the following data that is consistent with a first order reaction:
[Sucrose]M Time(h)
0.501 0
0.451 0.50
0.404 1.00
0.363 1.50
0.267 3.00
a. Use the above data to determine the rate constant and half-time of the reaction.
b. How long does it take to hydrolyze 70% of the sucrose.
c. How do you explain the fact that other studies demonstrate this is a second order reaction with water as the second reactant? In other words, why isn't water in the rate expression above?
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The solution provides detailed explanations on the concept of sugar hydrolysis and step-by-step calculations. It also provides calculations and drawings in an Excel file.
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a) As summarized in the reference, for a first order reaction, the integrated rate laws can be written as:
[A] = [A]0 e- k t
or ln[A]=ln[A0] - kt
So we need to plot ln[A] vs. t to see if there is a linear relationship. If there is, the slope k could be found from the plot. The plot is ...
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