EXPERIMENT 2 - RATE CONSTANT OF A PSEUDO
EXPERIMENT 2 - RATE CONSTANT OF A PSEUDO-FIRST ORDER REACTION
OBJECTIVE To determine the rate constant of a pseudo-first order reaction
(ie - the hydrolysis of sucrose) by polarimetry.
THEORY
Sucrose, cane sugar, undergoes the following hydrolysis reaction. The reaction is catalyzed by acid.
C
12
H
22
O
11
+ H
2
O
[H ]
C
6
H
12
O
6
+ C
6
H
12
O
6 rxn (2-1)
sucrose D-glucose D-fructose
The rate of hydrolysis is given by the second order rate equation,
Rate = k
[sucrose] [H
+
].
If [H
+
] is present in great excess, the rate equation becomes, eqn (2-1)
Rate = k [sucrose] eqn (2-2) where k = k
[H
+
]. Under this condition, the hydrolysis of sucrose is said to follow a pseudo-first order reaction.
The purpose of the experiment is to accurately determine the apparent rate constant k for this reaction.
Let c = concentration of sucrose remaining at any time t. dc dt
= rate of hydrolysis of sucrose at any time t.
Then, the rate of hydrolysis is,
- dc dt
= k c eqn (2-3) where the negative sign shows the rate of hydrolysis of sucrose is decreasing. This differential equation can be integrated to yield the integrated rate equation, c = c o e
k t or eqn (2-4)
2-1
ln
c c o
= k t eqn (2-5) or log
c c o
= k
2.303
t eqn (2-6)
( y = mx ) where c o
= initial concentration of sucrose before hydrolysis.
We can calculate the concentration of sucrose remaining at any time t, if we know k and c o
.
Alternatively, we can use the integrated rate equation to accurately determine k , since a plot of
"log( c c o
) versus time" should be a straight line.
Optical Rotation
A sucrose solution is said to be optically active because it can rotate the plane of a beam of polarized light. The angle of rotation is proportional to the number of optically active molecules in the path of the polarized light. Expressed mathematically,
= [
eqn (2-7) where
= angle of rotation (plane of polarized light) b = path length of solution c = concentration of optically active species
[
] t
D
= proportionality constant called specific rotation constant. It is unique for a particular optically active species.
Substances which rotate the plane of polarized light in a clockwise direction are assigned positive values. Conversely, substances which rotate the plane polarized light in a counterclockwise direction are assigned negative values.
H
CH
2
O
OH
H
H
O
CH
2
OH H H
+
H
CH
2
O
OH
H
H
HO OH
H
H
OH
O H OH
OH H
CH
2
OH H
2
O HO OH
H
H
OH
OH
+
HO
O
CH
2
OH
H OH
OH H
H
CH OH
2
[
]
20
D sucrose D - glucose D - fructose
= + 66.5 o
[
]
20
D
= + 52.7 o
[
]
20
D
= - 92.4 o
2-2
The word inversion is commonly used to describe the above reaction. This is because at the end of the reaction the products consisting of equal amounts of glucose and fructose will have a net rotation in the negative direction. In this experiment the rate of inversion of sucrose will be determined with a polarimeter.
Polarimeter
A simplified diagram of principal components in a polarimeter is as follows:
Light source polarizer
Solution of optically active
Analyzer compound
Figure 2-1 Angular relationships and optical path of
Polarizer-Analyzer unit.
Light source from a sodium lamp is made to lie in a single plane by a polarizer which can be a polaroid filter or a Nicol prism. The horizontally polarized light is then passed through the sample cell containing the optically active solution and the angle of rotation
is measured with the help of the analyzer.
In effect, the analyzer splits the beam into two distinct regions. The angle of rotation
is then determined by rotating the analyzer until the two regions are of equal intensity (Figure 2-2). The rotation of the analyer is calibrated directly in
.
2-3
Adjustment
Incorrect
Adjustment
Correct
Adjustment
Incorrect
Figure 2-2 Patterns seen in adjustment of a polarimeter analyzer which splits the beam into two distinct regions.
2-4
PROCEDURE
1. Make a 100 mL stock sucrose solution containing 20.0 g of sucrose per 100 mL
in a volumetric flask.
2. Pipet 20.00 mL of the stock sucrose solution and pipet 20.00 mL of 4 M HCl in a flask and mix well.
4.
3. Immediately rinse out the 20 cm polarimeter tube with a few mL of the solution prepared in step 2, and then fill up the tube and seal the end, making sure no air bubbles are present.
5.
Focus the polarimeter by rotating the lever until the fields are equal in intensity
(Figure 2-2). Note the angle of rotation of the solution (ie - should be somewhere between +10
At o
and +15 o
).
60 seconds intervals for the
120 seconds first 600 seconds
intervals for the
, and then next 1200 seconds measure the angle of rotation of the solution and record the time at which each measurement is taken.
[ NB - It is impossible to obtain a reading at the instance the sucrose solution is mixed with the acid. This is quite all right. As soon as you can, take the first reading and we will call this reading time zero.]
6. Take a first reading and call the first reading time zero. Record the room temperature.
[ NB - The angle of rotation alters rather quickly during the first few minutes.]
7. Make another sample by pipetting 20.00 mL sucrose solution and pipetting
20.00 mL 4 M HCl into another flask and mix well. Put this solution in a water bath at 60 o
C for 15 minutes . Do not overheat.
Cool this solution to room temperature and measure its optical rotation. Call this angle
. This solution gives the final optical rotation after all the sucrose has been inverted.
2-5
360
420
480
540
600
120
180
240
300
DATA SHEET
Make of polarimeter used: _________________________________________
Average temperature of reaction: ____________________________________
Final optical rotation angle,
: _____________________________________
o -
= _________________
(*** : Do not need to calculate here.) time
(sec)
0 angle
o = c
(
-
) c / co
(
-
) / (
o -
)
*** log (c / co)
***
60
2-6
1200
1320
1440
1560 time
(sec)
720
840
960
1080
1680
1800 angle
c
(
-
) c / co
(
-
) / (
o -
) log (c / co)
2-7
INTERPRETATION OF DATA
For a first order reaction, the following equation holds true. ln c c o
= k t . eqn (2-8)
For an optically active substance, the amount of optical rotation is directly proportional to concentration. Thus, the initial concentration of sucrose co is proportional to (
o -
), where o is the initial optical rotation of the mixture at zero time, and
is the final optical rotation after all the sucrose has been inverted. Similarly, the concentration of the sucrose, c, at any time is proportional to (
-
), where
is the optical rotation of the mixture at time t.
Substituting for c and co in eqn (2-8), we obtain, ln
o
-
-
= k t eqn (2-9) or
log
o
-
-
= k
2.303
t
( y = mx ) eqn (2-10)
Acording to eqn (2-10), a plot of " log
o
-
-
versus time" should yield a straight line. The rate constant k can be determined by measuring the slope of the graph.
2-8
TREATMENT OF DATA
1. Plot a graph of "log
c c o
versus time". Determine the slope of the curve.
2. Calculate the rate constant k for the inversion of sucrose at the stated temperature.
Include the units for the slope of the curve and the rate constant k .
