Determining an Equilibrium Constant
INTRODUCTION: In this experiment an equilibrium constant for the formation of a
complex ion will be determined. In addition, experience will be gained in the
use of the spectrophotometer and Beer's Law.
Iron(III) ions and thiocyanate
ions combine in aqueous solution to form a complex ion, thiocyanatoiron(III)
ion:
Fe3+(aq) + SCN-(aq) 
FeSCN2+(aq)
(1)
The equilibrium constant for
this reaction is given by applying the law of mass action:
Kc = [FeSCN2+]
(2)
[Fe3+][SCN-]
where the square brackets
signify equilibrium concentrations. Measurement of these concentrations will
enable one to calculate the equilibrium constant.
As you observed in the previous
experiment, the product complex ion is the only one of the three species which
has an appreciable color (blood-red); therefore, spectrophotometry will be used
to measure the concentration of this species. Suppose that a monochromatic
(single-wavelength) light beam of intensity Io is directed
upon a sample of a light-absorbing (colored) species. A portion of this light
is absorbed by the sample and the emerging light beam has a lower intensity I.
The transmittanceT of the sample is defined as follows:
T = I/Io
or %T = I/Io
x
100%
(3)
The absorbance A
of a sample is defined as follows:
A = - log10(T)
= log(Io/I) =
2 -
log(%T)
(4)
Beer's Law states that absorbance is
directly proportional to the molar concentration of an absorbing species:
A =
ebc
(5)
where c stands for molar
concentration (molarity), b is the path length of the light through the
solution (1.27 cm), and e(epsilon) is a constant (units: L/mol cm) called the
molar absorptivity or molar extinction coefficient, which depends upon the
nature of the absorbing species, the wavelength, and the temperature. If eand b
are known, measurement of the absorbance of a solution enables one to calculate
the concentration. Since eand b are constant during an experiment, a plot of
absorbance versus molarity will have a slope of eb.
Read the description of the use
of the Spectronic 20 spectrophotometer from the NT Curriculum
Project. In order to view the videos you will need to install the Apple Quicktime program if
your computer does not have it installed.
Part I of this experiment
involves the preparation of a Beer's Law calibration plot for the FeSCN2+
complex ion. Five solutions containing known concentrations of the complex ion
will be prepared and their absorbance measured. A plot of absorbance versus
concentration will allow calculation of the extinction coefficient. This value
may then be used in conjunction with the absorbance of any solution containing
the ion to determine its concentration, i.e., once the calibration is made, the
absorbance of any solution is divided by the product of the extinction
coefficient and the path length to obtain the molarity. The goal of this
section of the experiment is to determine the values of the slope and the
extinction coefficient.
A problem arises in determining
the concentrations of the complex ion to use in the Beer's Law plot. Since the
reaction forming the ion is an equilibrium process, it does not proceed to
completion; solutions of the complex ion will generally also contain measurable
concentrations of the two reactant ions, and the concentration of the complex
ion will not be known. However, we can make use of Le Chatelier's Principle
(see Experiment 5) to overcome this obstacle. If a limited quantity of
iron(III) ion is combined with a large excess of thiocyanate ion, the
equilibrium will be shifted far to the product side, essentially to completion.
The number of moles of the complex ion formed will then be essentially equal to
the number of moles of iron(III) ion that were used initially. A series of five
different dilutions of the iron(III) ion will be used to prepare solutions of
the complex ion in accord with this principle and a Beer's Law plot will be
made in order to determine the extinction coefficient of the complex ion.
Part II of the experiment
involves the preparation of the complex ion under true equilibrium conditions
using several different sets of initial concentrations. The molarity of the
complex ion will then be calculated using the absorbance of the solutions and
the results of Part I. The equilibrium concentrations of the other two ions can
then be determined through mass balance considerations (stoichiometry).
The calculations in this
experiment are somewhat involved and will be illustrated by the following
example. In the equilibrium
A + B
C
the equilibrium concentrations
of all three species are required in order to calculate Kc. The
initial volumes and molarities of A and B are known; these molarities are not
the same as those existing after equilibrium is attained. The method of
analysis used in the experiment provides the molarity of C at equilibrium. The
numbers of moles of A and B at equilibrium are determined through
stoichiometry calculations. In converting back to molarity, the total
combined volume must be considered.
In the example, 10.0-mL portions
of 2.10 x 10-3 M solutions of A and B are combined and
allowed to reach equilibrium. Analysis of the mixture reveals that the
concentration of C at equilibrium is 1.50 x 10-4 M.
The initial numbers of moles
of A and B are required in order to do the stoichiometry calculations. Using
milliliters and millimoles:
(10.0 mL) (2.10 x 10-3 mmol/mL) = 2.10 x 10-2
mmol A
The calculation is identical for
B. For the product C, note that the volume is the total combined volume:
(20.0 mL) (1.50 x 10-4 mmol/mL) = 3.00 x 10-3
mmol C
Now consider the stoichiometry.
Each mole of C formed requires that one mole of A and one mole of B be
consumed. Thus, the amounts of both A and B remaining at equilibrium are
2.10 x 10-2 mmol - 3.00 x 10-3
mmol = 1.80 x 10-2 mmol
Convert these values to
molarities by dividing by the total solution volume:
[A] = [B] = 0.0180 mmol / 20.0 mL
= 9.00 x 10-4 M
Thus, Kc
= [C] / [A] [B] = (1.50 x 10-4 ) / (9.00 x 10-4
)2 = 185
PRE-LAB
EXERCISES (It will
be helpful to read the entire experiment first.)
1. A 0.010 M solution of
a complex ion had an absorbance of 0.25 when measured in a 1.0-cm path-length
cuvette. A 0.020 M solution of the same ion had an absorbance of 0.50.
What is the molar extinction coefficient of this ion?
2. Ions A and B react to form a
complex AB. If 10 mL of 1.0 M A is combined with 10 mL of 1.0 M
B, 0.0030 mol of AB is formed. Determine the equilibrium constant for this
reaction.
EQUIPMENT: 100-mL volumetric flask, wash
bottle, Pasteur pipet and bulb, 11 medium test tubes, burette and stand,
burette funnel, 150-mL beaker, test tube rack, spectrophotometer, 6 cuvettes
EXPERIMENTAL
The general procedure for using
the spectrophotometer is as follows. The instrument is turned on by rotating
the left-hand knob on the front until it clicks; this should be done at least
20 minutes before any measurements are to be made. The wavelength is set using
the dial on top of the instrument; in this experiment we will use a wavelength
of 450 nm, the wavelength of maximum absorbance of the complex ion. The meter
should indicate a reading of 0% transmittance with no sample present and the
cover closed. Rotate the left-hand knob on the front of the instrument
to adjust the 0% setting. The sample is contained in special test tubes called cuvettes.
Fill a clean cuvette half-full with deionized water and wipe the outer surface
clean. Insert the cuvette in the sample compartment on top of the instrument
such that the index line on the top of the cuvette points toward the front of
the instrument (there is a matching mark on the sample compartment). Close the
cover. Rotate the right-hand knob until the meter indicates 100%
transmittance. For sample measurements, fill a clean cuvette half-full with the
sample, wipe the outside, place it in the sample compartment, close the cover,
and record the percent transmittance. The %T may be read to more
significant figures than the absorbance; the absorbance will be calculated from
the %T. If the cuvette is wet from previous use, first rinse it with a
small portion of the new solution and discard the rinsings before filling. The
0% and 100% settings should be checked often and readjusted if necessary during
the course of the experiment. All measurements should be carried out using the
same spectrophotometer.
CAUTION: Two different molarities of
iron(III) nitrate solution and two different molarities of potassium thiocyanate
are used in this experiment. Be sure that you take the correct solution. Read
labels carefully!
Label 11 clean, dry test tubes
with the numbers 1-11. Use your diluted iron(III) nitrate solution to make up
solutions 1-5 according to the information in Table I. The 1.00 M KSCN
is contained in a dispenser in the hood. Simply raise the piston all the way
and push it down to dispense the required amount of solution. Be careful in
measuring out the reagents, as the quality of your results will depend directly
upon your accuracy here. Cover each test tube with Parafilm, mix well, and
allow to stand for a few minutes before measuring the %T of each
solution. Record as many significant figures as possible, being careful
to avoid parallax errorsl
Part
II. Make up
solutions 6-11 using the amounts given in Table II. Be sure that you use the
reagents with the correct molarities. Measure the %T of these solutions at 450
nm.
|
Soln. No. |
Diluted
Fe(NO3)3 , mL |
1.00 M KSCN, mL |
0.1 M HNO3 , mL |
|
1 |
1.00 |
5.00 |
4.00 |
|
2 |
2.00 |
5.00 |
3.00 |
|
3 |
3.00 |
5.00 |
2.00 |
|
4 |
4.00 |
5.00 |
1.00 |
|
5 |
5.00 |
5.00 |
0.00 |
Table II. Solutions for
Equilibrium Constant Determination
|
Soln. No. |
0.00250 M Fe(NO3)3
, mL |
0.00250 M
KSCN, mL |
0.1 M HNO3 ,
mL |
|
6 |
1.00 |
1.00 |
5.00 |
|
7 |
1.00 |
2.00 |
4.00 |
|
8 |
1.00 |
3.00 |
3.00 |
|
9 |
2.00 |
1.00 |
4.00 |
|
10 |
2.00 |
2.00 |
3.00 |
|
11 |
2.00 |
3.00 |
2.00 |
CALCULATIONS
Part
II. Use the
absorbances of solutions 6-11 along with the slope (and intercept, if nonzero)
of the Beer's Law plot to calculate the molarity of FeSCN2+ in each
solution. The number of moles of the complex ion is then equal to the product
of the molarity and the total volume of the solution. The numbers of
moles of Fe3+ and SCN- remaining must be calculated using
the numbers of moles of each species initially present and the number of moles
of FeSCN2+ formed (moles of reagent remaining = initial moles of
reagent minus number of moles reacted). These are also converted to molarity by
dividing each by the total volume of the mixture. Calculate the value of Kc
for each solution and the average value of the equilibrium constant. Calculate
the relative average deviation of the results.
REPORT: Combining the skills you have learned in
writing each of the sections of a formal lab report over the past two months,
write a formal lab report for today’s experiment.