J . S o p o u š e k e x e r c i s e
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7.a-c
1. Chemical kinetics
1.a. Measurement of sucrose inversion in acidic solution
The decomposition of sucrose into glucose and fructose in water (so-called
inversion of sucrose) is a reaction that can be accelerated by acidic catalysis:
C H O H O C H O C H O
H
12 22 11 2 6 12 6 6 12 6+  → +
+
(1.1.)
In excess of water, it is a pseudo-first order reaction and the rate equation is given by
the expression:
v
dc
dt
k c= − = ⋅ (1.2.)
where 𝑐𝑐 is the sucrose concentration, 𝑡𝑡 means time, and 𝑘𝑘 is the velocity constant of the
acid catalysed reaction. With respect to the catalyst concentration, the following applies:
[ ]k k k H= + +
0 1 (1.3.)
where 𝑘𝑘0 is the rate constant in pure solvent (H2O) that is practically negligible, 𝑘𝑘1 is the
rate constant of the reaction that is homogeneously catalysed by hydrogen ions of
concentration [H+].
The first-order rate constant is given by the relationship:
k
t
c
c
=
1 0
ln (1.4.)
where 𝑐𝑐 is sucrose concentration at time 𝑡𝑡 from the reaction beginning (ie from
acidification of the solution), 𝑐𝑐0 is the initial sucrose concentration.
The sucrose solution turns the plane of polarized light clockwise while the equimolar
mixture of the fructose and glucose turns the light counter-clockwise after complete
reaction. We can detect a shift from initial angle α0 of polarized light to final angle α∞.
The fraction 𝑐𝑐0 𝑐𝑐⁄ in relation (1.4.) can be replaced by a fraction, which depends on the
angle rotation of the plane of light α𝑡𝑡 at time 𝑡𝑡:
We obtain relationship:
k
t t
=
−
−
∞
∞
1 0
ln
α α
α α
(1.5.)
where α∞ can be determined either after a few days when the reaction is completed, or
by computing using empirical equation:
α∞ = −[0.20695 + 0.00004⋅𝑐𝑐0 − 0,0032(τ − 20)]⋅𝑐𝑐0⋅𝑙𝑙 (1.6.)
where 𝑐𝑐0 is given in unit g/dm3
, τ is the solution temperature in °C and 𝑙𝑙 is the
polarimetric tube length in meters.
The rearranging of eqn (1.5.) gives:
( ) ( )t
k k t= − − −∞ ∞
1 1
0ln lnα α α α (1.7.)
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e x e r c i s e J . S o p o u š e k
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7.a-c
which is a linear dependence 𝑡𝑡 on 𝑙𝑙𝑙𝑙(α0 − 𝑎𝑎∞) that allows to determine the rate
constant 𝑘𝑘 from the slope of the regression line.
TASK: Measure the turning of the polarized light during the inversion reaction of
sucrose and evaluate the rate constant at two different concentrations of the
catalyst.
LABORATORY AIDS AND CHEMICALS: polarimeter, 2 polarimetric cells, weighting
boat, stopwatch, 2 volume pipettes (20 cm3
), volumetric flask (100 cm3
), 3
Erlenmeyer flasks (100 cm3
), sucrose, 4 M HCl and 2 M HCl.
INSTRUCTIONS: Switch polarimeter on and get to know with instrument operating
manual.
Prepare 100𝑚𝑚𝑚𝑚 of stock solution by dissolving 20 g (accurate to 0.05g) of sucrose in
water (use 100 cm3
volumetric flask).
Take in Erlenmeyer flask and mix 20 cm3
of sucrose stock solution with 20 cm3
of water
and mix thoroughly. Fill the polarimetric cuvette with the solution. Insert the cuvette into
the polarimeter (see scheme in FIGURE 1) and measure the starting angle of the plane of
polarized light for the sucrose solution. Empty the polarimetric cuvette and rinse it with
distilled water.
Prepare the reaction
solution in Erlenmeyer
flask by mixing 20 𝑐𝑐𝑐𝑐3
of
stock solution of sucrose
and 20 𝑐𝑐𝑐𝑐3
of 4 𝑀𝑀 𝐻𝐻𝐻𝐻𝐻𝐻.
Mix the solutions quickly
and intensively. Start the
stopwatch immediately.
Rinse out the
polarimetric cell with
small amount of reaction
solution. Finally, pour the
reaction solution up to
cuvette marking and do measuring the plane of the polarised plane of light in 5 minute
intervals within one hour. Measure the angle also at time 80, 100 and 120 minutes.
Similarly prepare a reaction solution applying 2 𝑀𝑀 𝐻𝐻𝐻𝐻𝐻𝐻 and use same procedure as
before. The rotation changes of both reaction mixtures can be measured simultaneously
at shifted times.
REPORT: weight of sucrose, value α∞ and temperature τ used for evaluation of it.
Table 1a and 1b: for both experiments at different [H+] concentration: time t,
angle tα , ln( )∞− ααt . Common graph 1: for both [H+] concentrations: time
dependency of angle tα . Common graph 2: for both [H+] concentrations: dependency
𝑡𝑡 on ln( )∞− ααt . Next: Evaluation of rate constants 𝑘𝑘 at variable [H+] and their
confidence intervals. Evaluation of rate constants k0 and k1 by solution of two equations
with two unknowns (use eqn (1.3.)).
?


FIGURE 1: Scheme of polarimetric measurement. L-sodium lamp,
P-polarizer, A-analyser, K-cuvette with sucrose solution.
