The University of Lethbridge
Department of Chemistry & Biochemistry
Chemistry 2740 Laboratory
Experiment 6
A KINETIC STUDY OF THE ACID CATALYZED HYDROLYSIS OF SUCROSE
The rate constant for a reaction that follows a first-order rate equation can be determined
relatively easily by measuring a suitable physical property of the reaction system that
varies in a linear fashion as the reaction progresses (refer to Appendix A on “First-order
Reactions”). We will demonstrate the process in this experiment. The reaction to be
followed is the inversion or hydrolysis of sucrose. The physical property that will be
measured is the optical rotation of the sucrose reaction solution.
Sucrose, or common table sugar, is a disaccharide derived from the monosaccharides
glucose and fructose and is thermodynamically unstable with respect to hydrolysis to
glucose and fructose. All three molecules are optically active and consequently rotate the
plane of polarization of plane polarized light by characteristic amounts. Sucrose is
dextrorotatory (rotates the plane of polarization clockwise) and the equimolar mixture of
glucose and fructose is levorotatory (rotates the plane of polarization anticlockwise). As a
result, as the hydrolysis of sucrose proceeds the optical rotation of the solution changes
from positive to zero to negative. (Because of this sign change the hydrolysis of sucrose is
also referred to as the inversion of sucrose and the product as invert sugar). The change
in optical rotation provides a convenient means of following the course of the reaction,
which is done with a polarimeter. The optical rotation α of a solution is directly
proportional to the concentration of the optically active species in solution. This
relationship between optical rotation and concentration allows one to use the first-order
integrated rate equation in the form
ln [(αo - α∞) / [(αt - α∞)] = k't
(1)
(For a description of polarized light, polarimeters and isomerism, see your introductory
organic chemistry textbook.)
The differential rate law for the reaction
H+
sucrose + H2O
is
-
d [sucrose]
dt
fructose + glucose,
= k [sucrose] [H+]
(2)
(3)
The hydrogen ion is a catalyst and so its concentration remains constant throughout the
reaction with the result that the reaction follows the observable rate law
Rate = k' [sucrose]
where k' = k [H+]
(4)
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Chemistry 2710 Laboratory
Experiment 6
and is consequently first-order in the concentration of sucrose. Thus for any particular
experiment the reaction follows first-order kinetics, however the rate constant will vary
from one reaction mixture to another depending upon the hydrogen ion concentration. In
order to demonstrate the order with respect to hydrogen ion it is necessary to carry out
runs at two or more hydrogen ion concentrations.
Apparatus
Polarimeter, polarimeter tubes and timer.
The polarimeter is outlined schematically below. It has a sodium vapour lamp that puts
out light that is predominantly of one wavelength, 589 nm (the so-called sodium D line).
The light from this travels through a Nicol prism to produce plane polarized light. This in
turn is passed through a sample cell held in a cell holder and from there the rotated light
travels to an analyzer Nicol prism and an optical device for detecting the "balance" point.
The analyzer Nicol prism must be rotated such that the prism axis aligns with the plane of
polarization of the light that exits from the sample. This is the "balance" point. The
optical detecting device allows the observer to determine the balance point.
rotated polarized
light
polarized light
detector optics
and eyepiece
•
lamp
polarizing Nicol
prism
sample cell
analyzer Nicol
prism
eye
Schematic diagram of a polarimeter
The polarimeter to be used in this experiment is relatively simple to operate. The sample
compartment has a hinged lid that allows access to the cell holder. The polarimeter tube
is simply laid in the V-trough in the compartment and then the lid is closed.
The view in the eyepiece of the optical detector consists of two separate images: on the
right is the scale for the analyzer prism angle and on the left is a circular image area for
determining the balance point. The analyzer prism is turned by the balancing knob on the
right hand end of the polarimeter and the angle shown in the eyepiece changes
accordingly. The angle scale for the analyzer prism has a vernier. See appendix B for
instructions on reading a vernier scale. Make sure that you can read the scale before
starting any experiments.
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Chemistry 2710 Laboratory
Experiment 6
The circular image area for determining the balance point is divided into two halves as
shown below.
When the instrument is not in balance (i.e., the analyzer prism direction (angle) does not
correspond to the direction of the plane of polarization of the light), one half of the circular
image is dark and the other half is bright. When the instrument is balanced, both halves
of the circular image area are equally bright. Thus one adjusts the balancing knob until
both halves of the circular image area are equally bright and then the corresponding angle
is read from the scale with the help of the vernier.
NOTE: Around the balance point the brightness of the split image is sensitive to changes
in the analyzer prism angle. There are other angles where both halves of the image are
equally bright but their relative brightness is insensitive to changes in prism angle. These
are not the balance point! In this experiment your initial reading should be between +10°
and +14°. If your reading is not in this range then try balancing the polarimeter again.
Reagents
Sucrose, 4.0 M HCl.
Waste Disposal
A 4-litre bottle for the collection of wastes is supplied with the experimental set up.
Sucrose solutions not containing acid can be disposed of directly in the sink. Excess HCl
reagent and reaction solutions should be disposed of in the bottle. The glassware can then
be given a single small rinse into the waste container before being cleaned further in the
sink.
In preparing reaction solutions only remove as much reagent from the stock container as
is necessary to make the reaction mixtures.
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Experiment 6
Procedure
Prepare 100 mL of an aqueous solution containing 20 grams of sucrose.
Ensure that you know how to make a reading on the polarimeter. With no cell in the cell
compartment and with the lid down, adjust the analyzer prism angle (right hand knob)
until the polarimeter is in balance (see above). The field of view in the eyepiece can be
focussed by screwing the eye piece in or out. Read the angle. Repeat the procedure after
displacing the analyzer prism from balance. Successive readings of the balance point
should not vary by more than ca. ± 0.2°.
The polarimeter tubes are thermostated with water at 25.0°C circulating through their
jackets. The tubes will be clean and dry and ready for use. Please handle them carefully;
the glass filling port in the centre of the tube is easily broken.
To make a reading, place the polarimeter tube filled with solution in the cell compartment
so that the filling port is up, close the lid of the instrument cell compartment and follow
the procedure described above. Because of the rubber hoses attached to the polarimeter
tube jackets the lid of the cell compartment cannot be shut completely. Always put the
polarimeter tube into the cell compartment with the tube oriented in the same direction
each time. In other words, one end of the polarimeter tube should always point right or
always point left but not left one time and right the next. The reason for this is that the
glass windows of the polarimeter tube may rotate plane polarized light by a small amount
as a result of strains in the glass. By keeping the cell pointing in the same direction for
each reading this small error will always be of the same magnitude and sign, and when
the difference between two readings on the same cell is taken, the errors will subtract to
zero.
Carry out three runs at HCl concentrations of 0.96, 1.44 and 2.00 M. Do this by first
pipetting into three 50 mL volumetric flasks the amounts of 4 M HCl solution required to
produce these concentrations when the flasks are filled to the marks. Naturally the
reaction begins as soon as the sucrose is added to the HCl so that the complete solution
should not be prepared until you are ready to make measurements. When you are ready
to start a run, pipette in 25 mL of the sucrose solution and then quickly fill the flask to the
mark. For the run using 2 M HCl simply fill the flask to the mark with sucrose solution
(i.e., a pipette is not needed).
Start with the reaction mixture that reacts slowest, i.e., the 0.96 M HCl solution. Pipette
25 mL of the sucrose solution into the volumetric flask containing the required amount of
4.0 M HCl and quickly fill the flask to the mark with water. Ensure that the reaction
mixture is well mixed. Pour the mixed solution into the central opening in the polarimeter
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Chemistry 2710 Laboratory
Experiment 6
tube until the tube is filled and ensure that there are no air bubbles in the light path.
Place the tube in the polarimeter, balance the polarimeter, immediately note the time of
balancing and then read the optical rotation, α. Repeat the readings at intervals of
approximately 8 to 10 minutes. When you feel that you have control of the situation you
can start the next slowest reaction and make readings on the two solutions as needed. For
the second solution take readings at 4 to 5 minute intervals. Finally, start the fastest
reaction mixture and take readings for it at 2 to 3 minute intervals. Discontinue making
readings for a particular reaction mixture when the value of the optical rotation drops to
zero.
Leave the reaction mixtures in the polarimeter tubes overnight and return the next day to
take readings for each solution. These readings will provide values for the optical rotation
at complete reaction, α∞. The values will be around -4 to -5°. Be careful reading the
vernier at angles below 0°. If the vernier zero mark is between 0° and -1° on the main
scale and the reading on the vernier is 0.65, the angle is -0.35° (i.e., -1 + (+0.65)) and not 0.65°.
Before leaving the laboratory, please enter names, date, and experimental data
into the computer.
Calculations and Report
Calculate the first-order rate constants for each run from the rotation readings αo, αt and
α∞ using an appropriate plot. Calculate the second-order rate constants at each hydrogen
ion concentration.
It is likely that the second-order "constants" will increase as the concentration of acid
increases despite the fact that the reaction is accurately first-order with respect to
hydrogen ion concentration in dilute acid solutions. This same behaviour is often observed
in other acid catalyzed reactions carried out in concentrated acids (i.e. > ~0.1 M). Can you
think of a possible explanation for this fact?
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