EXPERIMENT 3 - KINETICS OF A SECOND-ORDER REACTION
OBJECTIVE
To determine accurately the rate constant of a second-order
reaction, the saponification of ethyl acetate.
THEORY
The alkaline hydrolysis of fats is referred to as saponification (literally, "soap-making"). Over
the years the term has come to be used also in referring to the alkaline hydrolysis of any type of
ester.
The saponification of ethyl acetate
CH3COOC2H5 + OH-  CH3COO- + C2H5OH
rxn (3-1)
proceeds by a second-order reaction.
Rate = k[CH3COOC2H5][OH-]
eqn (3-1)
We can write the rate equation in terms of calculus notations,

d cA
= k cA  cB
dt
eqn (3-2)
where cA = concentration of ethyl acetate at time 't', and
cB = concentration of OH- at time 't'.
In this experiment, the initial concentration of hydroxide ion is adjusted to be the same as that of
ethyl acetate. Since their initial concentrations are the same and since the mole ratio of OH- :
CH3COOC2H5 is 1 : 1, then at any time t, the concentration of ethylacetate must be the same as
hydroxide ions. That is,
cA = cB
eqn (3-3)
Equation (3-2) becomes

d cA
2
= k cA
dt
eqn (3-4)
The concentration of ethylacetate (or OH-) remaining at any time can be determined by
integration.
cA d c
t
A
eqn (3-5)
co c 2 = - k 0 dt
A
3-1
or
1
1
=k t+
cA
co
( y = mx + b )
eqn (3-6)
where co = initial concentration of ethylacetate and
cA = concentration of ethylacetate at time t.
1
Thus, according to equation (3-6), a plot of "
versus time" should be a straight line. The rate
cA
constant k can be accurately determined by measuring the slope of the graph.
Conductivity and Conductivity Bridge
As reaction (3-1) progresses, the amount of OH- ions in solution diminishes as CH3COO- ions
are produced. It is known that the electrical conductivity of OH- ions is much greater than that of
CH3COO- ions. Equivalent ionic conductivity at infinite dilution, at 25oC, for OH- and
CH3COO- are 198.6 mhos and 40.9 mhos respectively. Therefore, the progress of reaction (3-1)
can be followed conductometrically.
Conductance L is a measure of the ability of a substance to conduct electricity and is defined to
be the reciprocal of resistance. Thus, Ohm's law may be expressed as
E
R
eqn (3-7)
i=EL
eqn (3-8)
i =
or
where i = current, E = voltage, and R = resistance. The unit of conductance is Siemens.
The conductance of a solution is measured by dipping a cell containing two platinum electrodes
into the solution. The electrodes are connected to one arm of a Wheatstone bridge and an
alternating voltage is applied to the bridge. The conductance is then obtained from the scale by
nulling the bridge. An alternating voltage is used to prevent polarization of the electrodes.
Accurate measurements are obtained only with properly prepared electrodes.
The equivalent ionic conductivity is unique for each ion and is a measure of the velocity or
mobility of the ions under the influence of an electric field. Conductance of a solution is directly
proportional to its ionic concentration, the surface area of the electrode and is inversely
proportional to the distance between electrodes. Expressed mathematically,
3-2
L = 
CA
d
eqn (3-9)
where C = concentration (equivalents per cm3),
d = distance between electrodes (cm),
A = area of electrode (cm2),
 = equivalent ionic conductivity constant.
 is unique for each solvent and is dependent on temperature.
3-3
PROCEDURE
1.
Prepare a common solution of 0.100 M ethylacetate for the BOTH groups.
Pipet 0.49 mL of ethylacetate from the reagent bottle and make up to 50 mL in a
volumetric flask.
2.
Into a 250 mL Erlenmeyer flask (flask #1),
(i) pipet in 10.00 mL of 0.100 M ethylacetate,
(ii) add 40.00 mL distilled water from a burette.
3.
Into another 250 mL Erlenmeyer flask (flask #2),
(i) pipet in 10.00 mL of 0.100 M NaOH,
(ii) add 40.00 mL distilled water from a burette.
4.
Into a 100 mL volumetric flask (flask #3), prepare 0.0100 M NaOH by
pipetting in10.00 mL of 0.100 M NaOH and diluting with water to 100.0 mL.
5.
Using lead donuts to stabilize the flasks, place all three flasks in a water bath at
approximately 25oC to obtain thermal equilibrium. Record the temperature of the
water bath.
6.
Measure the conductance of flask #3, the 0.0100 M NaOH. This conductance value is
Lo, measured at time = 0 sec.
[Lo should be approximately 2500 to 3500 mhos, or
2.500 x 10-3 to 3.500 x 10-3 Siemens, or
2500 to 3500 Siemens.]
7.
Start the saponification reaction by mixing together the entire contents of flasks
#1 and #2 containing the ethylacetate and sodium hydroxide respectively. Stir
the mixture and start the timer. Measure the first conductance reading after 300
seconds and continue collecting data at 300 seconds intervals for one hour.
3-4
DATA SHEET
Temperature of reaction = _______________________________
Conductance of 0.0100 M NaOH, Lo =
Time [sec]
L [S]
Lo - L [S]
Siemens
(Lo - L)/t [S/sec]
300
600
900
1200
1500
1800
2100
2400
2700
3000
3300
3600
3-5
INTERPRETATION OF DATA
According to eqn (3-6),
1 1
=k t
cA co
eqn (3-6)
we can accurately determine the rate constant, k, of a second-order reaction by plotting
1
"
versus time" where cA is the concentration of ethylacetate or hydroxide ion, at any time t.
cA
Since 'cA' is proportional to L - L and co is proportional to Lo - L, it follows that
co - cA  (Lo - L) - (L - L)
 Lo - L
eqn (3-10)
Rearranging eqn (3-6) gives
co  k  t =
co - cA
cA
eqn (3-11)
co  k  t =
Lo - L
L - L
eqn (3-12)
Substitute into eqn (3-11),
Rearranging eqn (3-12),
1  Lo - L 

 + L
co k  t 
(y = m x
+ b)
L=
 Lo - L 

t 
eqn (3-13)
1
. If
cok
we measure the slope of the line, we can calculate k provided we know the initial concentration,
co.
A plot of " L versus 

" should yield a straight line. The slope of the line, m, is
3-6
TREATMENT OF DATA
1.
2.
Enter your data neatly in the data sheet.
L - L
Plot a graph of "L versus o
".
t
3.
Measure the slope in the straight portion of the curve and calculate the rate
constant for the second-order reaction. Note that the initial concentration, co,
of ethylacetate is not 0.02 M.
4.
In your lab report, comment on the difference between the value of conductance
'L' measured at the so-called t = 0 and, the value that might have been obtained at
the exact moment of mixing.
3-7