Download Expt RO 1 Determination of Reaction Order (RO) Background Bonds

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Determination of Reaction Order (RO)
Background
Bonds between sugar molecules such as glucose can be broken using selected enzymes. Cellulose is
made of long fibers of glucose molecules, but humans lack the enzymes to digest cellulose. However, if
cellulose can be broken down into glucose molecules using appropriate enzymes, then yeast
subsequently can be used to convert these sugar molecules to carbon dioxide and ethanol. This ethanol
can be separated from water and used as a fuel or fuel additive.
The University of Tennessee has partnered with DuPont to build a biorefinery and research facility
to convert cellulose to ethanol in Vonore, Tennessee. The plan involves growing switchgrass in
Tennessee. Switchgrass is a rapid growing, perennial, drought resistant plant that requires little care. If
economic methods to break down cellulose into its component glucose molecules can be worked out
then switchgrass will be a far better source of ethanol than the corn that is currently grown and its sugar
used to make ethanol. In this experiment we will explore the kinetics involved in using not an enzyme
but an acid to break the bond holding two sugar molecules together. Fructose and glucose are linked
together in the disaccharide molecule called sucrose (also known as common table sugar).
Objective
The purpose of this experiment is to determine the reaction order (first, second, or third) with
respect to sucrose for the acid catalyzed hydrolysis of sucrose.
Instructions
You will use the JASCO Automated Polarimeter in this experiment. Turn it on and allow it to
warm up while you prepare your solutions. See instruction pages kept with instrument for specific
instructions for operating the Jasco Automated Polarimeter.
Prepare a sucrose solution by
dissolving 20 grams of sucrose in water and diluting to 50 mL.
Fill the 10mL polarimeter cell with distilled water and place it in the instrument. The
polarimeter cell is very expensive and fragile.
Please be careful when handling it. The cell
must not be dropped. Program the instrument to take readings every 30 seconds for a total of 2
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minutes. The polarimeter is a bit tricky to program, and this step will insure that you are setting up
the instrument correctly. The only purpose of this part is to practice programming instrument to take
readings at timed intervals. Confirm that you are able to successfully program the polarimeter to
take a series of timed readings prior to continuing with the rest of the experiment.
Set up the polarimeter to take angle of rotation measurements, Q, at 3-minute intervals for a total
time of 90 minutes. This will give you a total of 30 data points. Mix precisely 10 mL of 1.0 M HCl
with 10 mL of the sucrose solution. Stir this mixture thoroughly for 60 seconds in a beaker. The
acid and sucrose solution must be well mixed prior to placing in the polarimeter cell. Now fill the
polarimeter cell (no air bubbles) with this acid and sucrose solution mixture. Initial Readings of
angle Q should begin around +9 to +12o and Q should decrease with time. Begin the readings and
watch to make sure everything is working correctly. If Q is too low or instrument not taking readings
then you will need to start again.
While the polarimeter is taking readings, prepare another acid/sucrose mixture using the same
amounts as before. Heat this mixture in a flask in a water bath at 50oC for 60 minutes. After
heating, allow this mixture to cool to room temperature. When the timed measurements are
completed, place this second solution in the polarimeter and measure the angle of rotation. This
determination will be just a single measurement. This measured angle of rotation is for the reaction
after it has reached equilibrium and is referred to as the Qz value. Your measured Qz value should
be a slightly negative value. Notice Qz was obtained by running the reaction at a higher temperature
so it would reach equilibrium faster. It could take about 6 hr or so to reach the equilibrium Qz value
at 25oC.
Analysis
Part I – Integrated rate law review during lab
While the polarimeter is collecting data, you have some time available, and this is an excellent
opportunity to review integrated rate laws. Read the section in your physical chemistry text on
integrated rate laws. Use your knowledge of calculus to derive the integrated rate laws for First,
Second, and Third Order kinetics. During lab while the data is being collected, clearly write out
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these derivations in your notebook and show them to your instructor. Consider reaction dx/dt =
–k´ xN where x is the concentration of a chemical reactant decreasing with time, rate = dx/dt, and k´
is the rate constant. The rate at which x decreases is proportional to the order of the reaction where
N =1 is first order, N = 2 is second order, N = 3 is third order, and so forth. Group terms so that
x–N dx = – k´ dt
and then integrate over the concentration range from Ao to A and over the time
range from 0 to t. Show each step of these three derivations (don’t skip steps). Compare your
results to the expected integrated rate law forms shown below where A represents the concentration
at some time t.
First Order
ln[A] versus time (min)
Second order
1/[A] versus time (min)
Third Order
0.5 /[A]2 versus time (min)
In other words complete the following equations:
First Order
ln[A] =
Second order
1/[A] =
Third Order
0.5 /[A]2 =
where each is written as linear equation of the general form y = m t + b where m is the slope, b is the
intercept and t is the time plotted along the x-axis. If you do not get equations of the forms shown
above then you know you have made a mistake. Refer to your physical chemistry textbook, calculus
book, or a general chemistry textbook if you need help. Lab partners compare your results and then
show to your instructor.
Part II – determination of order from collected data
Use the data collected by the polarimeter to determine the actual order of the sucrose reaction.
Try the following plots on the computer, where Q is the angle of rotation and
(Q-Qz) is proportional to the concentration of sucrose (this is shown in the theory section below).
First Order
ln[Q-Qz] versus time (min)
Second order
1/[Q-Qz] versus time (min)
Third Order
0.5 /[Q-Qz]2 versus time (min)
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The graph with a correlation coefficient closest to 1 is the best of the three. Calculate the rate
constant, k´, for each curve reporting answers in units of min-1, M-1 min-1,or M-2 min-1 as
appropriate for first, second, or third order kinetics. Include all three graphs in your report and
make a table listing the orders, k´ values and units, and correlation coefficients so the three linear
plots may be compared. Show how k´ values are calculated on each graph. Compare the order you
found to the reported order (literature value) with respect to the sucrose concentration. Note you are
trying to find first, second, or third order with respect to sucrose only and not the overall order of the
reaction. For further hint look at the theory section that follows to see order predicted for sucrose.
Be sure to include a table with columns for t, Q, [Q – Qz], ln[Q-Qz], 1/[Q-Qz], and 0.5/[Q–Qz]2,
three graphs (one for each order), and a fourth table that gives summary of your results ( order, r2,
slope and calculated k´ value). If possible compare rate constant, k´, for best selected order plot to
reported literature value for the rate constant. Note that literature value would be for k´ if given as
rate= k´ [S]N
and k if given as rate = k [H+][ S]N
Theory
In this experiment, the rate law for the acid catalyzed hydrolysis of sucrose will be determined.
Recall that the rate law may be expressed as
(1)
d[S]/dt = – k´ [S]N
where [S] is the concentration of sucrose, d[S]/dt is the rate at which sucorse disappears, k´ is the
rate constant, which varies with temperature, and N is an integer 1, 2, or 3, indicating the order of the
reaction as first, second, or third, respectively.
The general reaction is
Sucrose + H2O
--- H+--->
Fructose + Glucose
(2)
The reactant and the two products, invert sugar, are optically active, and their aqueous solutions
rotate polarized light. The specific rotation of sucrose is +66.4 degrees, and that of invert sugar is 19.7 degrees. The specific rotation is defined as the degrees of rotation per gram of solute per cubic
centimeter of solution per 10 cm path length. The rotation changes from clockwise to
counterclockwise as the reaction proceeds, and this process is what is monitored with the
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polarimeter. The angle of rotation of light which we are calling Q is proportional to the
concentration of sucrose, [S].
The reaction is first order in hydrogen ion concentration and is thought to proceed through the
reversible formation of a protonated sucrose complex, which may be represented as
k1
k3
(3)
H3O+ <=====> S-H3O+ ----->
F + G + H+
k2
where S, F, and G are abbreviations for the sugars involved. If one assumes that the reaction is first
S +
order in sucrose and applies the steady state approximation, one has
d[S-H3O+]/dt = 0 = k1[S][H3O+] - k2[S-H3O+] - k3[S-H3O+]
(4)
Solving for [S-H3O+] and substituting for
d[products]/dt = -d[S]/dt = k3[S-H3O+]
(5)
gives the following rate equation,
-d[S]/dt = k[S][H3O+]
where k = (k1)(k3)/(k2+k3)
(6)
Since the hydronium ion concentration remains constant except for the very small amount involved
in the activated complex, one can write from above -d[S]/dt = k [H+] [S] and therefore
-d[S]/dt = k´ [S]
(7)
k´ = k[H+]
(8)
if
or k = k´/[H+].
Integration of the above equation gives
ln[S/So] = -k´t
(9)
where t is the time and k is the rate constant.
The angle, Q, by which plane polarized light is rotated by the reaction mixture varies linearly
with the concentration of sucrose. This follows from the linear dependence of Q on the
concentrations of the three sugars, where
Q = a[S] + b[F] + c[G]
(10)
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and a, b, and c are functions of the polarimeter cell length, the specific rotation of the particular
sugar, and the concentration units chosen. Since, as S is decreased F and G are formed, then
stoichiometry requires
[F] = [G] = [So] - [S]
(11)
where [So] is the initial concentration of S. Combining the two previous equations gives
Q = (a-b-c)[S] + (b+c)[So]
(12)
and thus Q is linear in [S]. After a sufficient length of time for the reaction to go to completion one
can define a value of Q such that
Qz = (b + c) [So]
(13)
and using the proportionality [S] = Q - Qz the integrated rate equation becomes
-k´t = ln( [Q-Qz]/[Qo-Qz] )
(14)
ln [Q-Qz] = -k´t + ln [Qo- Qz]
(15)
or
Note that the value of Qo is not needed, and thus the point t=0 is arbitrary and may be taken at
the point in time at which the measurement of Q commenced. This is a general property of all first
order reactions.
Note that if the assumption that the reaction is first order with respect to sucrose is correct, a plot
of ln [Q-Qz] versus t will yield a straight line with -k´ as the slope. What do your plots based on
your experimental data give you for the rate law and how do they compare to the literature value for
the order of the reaction? Note if this reaction was first order with respect to the acid concentration
and first order with respect to sucrose then we could say the reaction was second order overall.
However, usually we are interested here in the order with respect to only an individual reactant–
sucrose.