450 Journal of Chemical Education • Vol. 75 No. 4 April 1998 • JChemEd.chem.wisc.edu
In the Laboratory
Kinetics-Based Indirect Spectrophotometric Method
for Simultaneous Determination of MnO4
–
and Cr2O7
2–
A Modern Instrumental Analysis Laboratory Experiment
Siddharth Pandey, Mary E. R. McHale, Ann-Sofi M. Horton, Sandra A. Padilla, Ashantè L. Trufant,
Noé U. De La Sancha, Ernesto Vela, and William E. Acree, Jr.*
Department of Chemistry, University of North Texas, Denton, TX 76203-5070
UV–visible absorption spectroscopy provides a very convenient
experimental means for determining percentage compositions
and solution concentrations of unknown samples,
for measuring reaction rate constants, and for determining
both the stoichiometry and equilibrium constant of metal–
ligand complexes. During the past few years many experimental
spectroscopic methods have appeared in this Journal
(1–10) and in standard laboratory manuals for use in general
chemistry, physical chemistry, or quantitative analysis.
Spectroscopic methods are based upon application of the
Beer–Lambert law, which states that the measured absorbance,
A, is directly proportional to the molar concentration
of the light-absorbing species i :
A = εibC (1)
where b is the path length (in cm) through the solution and ε is
the wavelength-dependent molar absorptivity (in M᎑1 cm᎑1). The
individual absorbances at the same wavelength are additive
when two light-absorbing species are present,
ATotal = Ai + Aj = εi b Ci + εj b Cj (2)
if no interaction or reaction between components i and j
occurs. Absorbance measurements at two different wavelengths
provide two equations in two unknowns. By solving
both equations simultaneously,
ATotal @ λ1
= εi @ λ1
b Ci + εj@ λ1
bCj (3)
ATotal@ λ2
= εi @ λ2
bCi + εj @ λ2
b Cj (4)
one can obtain concentrations of the two components. The
four ε-values needed in this computation are calculated
fromBeer–Lambert law plots (or linear-least squares analysis)
for the separate components in standard solutions of
known concentrations. This method has been used numerous
times in our quantitative analysis course to determine
MnO4
᎑
and Cr2O7
2᎑
concentrations in unknown liquid mixtures.
The two wavelengths selected for these analyses are 545
nm and 440 nm, which correspond to wavelengths of nearmaximum
absorbances for MnO4
᎑
and Cr2O7
2᎑
, respectively.
During the past two years we have continually upgraded
the laboratory experiments students perform in our undergraduate
instrumental analysis course to incorporate as much
as possible new analytical methods and data treatments published
in recent chemical literature. One of the experiments
designed involves a relatively interesting kinetics-based indirect
spectrophotometric method for the simultaneous determination
of MnO4
᎑
and Cr2O7
2᎑
. It draws heavily upon two published
analyses for permanganate and vanadate ions (11, 12), which
we have modified to enable quantitative determination of
Cr2O7
2᎑
concentration. From an educational point of view,
the modification affords our undergraduate chemistry majors
the rare opportunity to critically compare direct and indirect
analytical methods for a common unknown mixture. Most
students will have performed the direct analysis based upon
eq 2 as an experiment in our quantitative analysis course.
Method selection and method evaluation are two problems
that practicing analytical chemists routinely encounter.
The kinetics-based indirect spectrophotometric method
is relatively straightforward and takes advantage of the fact
that the oxidation of pyrogallol red (PGR) by permanganate
occurs much faster than oxidation of PGR by dichromate.
One follows the extent of oxidation by monitoring the absorbance
of the solution at 488 nm, which corresponds to
the broad band maximum in the PGR absorption spectrum.
Measured absorbances at two fixed times, At1
and At2
, are
directly proportional to the molar concentrations of the added
oxidizing agents
At1
= APGR + mt1,Cr2O7
2᎑ CCr2O7
2᎑ + mt1,MnO4
᎑ CMnO4
᎑ (5)
At2
= APGR + mt2,Cr2O7
2᎑ CCr2O7
2᎑ + mt2,MnO4
᎑ CMnO4
᎑ (6)
where APGR represents the solution absorbance in the absence
of both MnO4
᎑
and Cr2O7
2᎑
, and mti, j
is the numerical value
of the calibration curve slope for each time i and component
j. We have found 3 and 8 min to be suitable reaction times.
Oxidation of PGR by permanganate is complete in the first
three minutes. Reduction in the observed absorbance between
3 and 8 min results entirely from the oxidation of PGR by
the dichromate ion. The above method generates the two
equations that must be solved simultaneously from absorbance
measurements at two fixed times, rather than at two
different analysis wavelengths. This can potentially eliminate
problems encountered in the analysis of mixtures containing
components having severely overlapping absorption spectra
(10), as is the case with Cr2O7
2᎑
and MnO4
᎑
(see Fig. 1). The
permanganate ion has an appreciable absorbance at both 350
and 440 nm, which are the analysis wavelengths for the
dichromate ion. Moreover, students are shown that chemical
reactions need not occur instantaneously to be of analytical
significance. Kinetics-based techniques represent an important
part of the experimental methods available to practicing*Corresponding author. Email: acree@unt.edu; fax: 940/565-
4318.
JChemEd.chem.wisc.edu • Vol. 75 No. 4 April 1998 • Journal of Chemical Education 451
In the Laboratory
analytical chemists (13–16).
Experimental Methods
The experimental work can easily be completed in a
three-hour laboratory period. We suggest that students work
in groups of two in order to reduce the time needed to prepare
solutions. Each group is given 25 mL of an unknown solution
containing between 5.00 × 10᎑5
and 2.00 × 10᎑4
M KMnO4
and 2.50 × 10᎑5
to 1.00 × 10᎑4
M K2Cr2O7. Separate stock
solutions of 2.00×10᎑4
M KMnO4 and 1.00 ×10᎑4
M K2Cr2O7
are prepared ahead of time by the instructor or laboratory
assistant. Each group will also need approximately 300 mL
of “reaction” solvent. The reaction solvent is prepared by
transferring 250 mL of pH 4.0 acetic acid–sodium acetate
buffer (2.2 M acetic acid + 0.5 M sodium acetate) and 75 mL
of 8.0×10᎑4
M pyrogallol red (dissolved in ethanol) to a 500mL
volumetric flask and diluting to the mark with deionized
water.
Students are instructed to use a buret to transfer 20.00 mL
of the reaction solvent into each of twelve 25-mL volumetric
flasks. The first flask is filled to the mark with deionized water
and the absorbance is measured after 3 and 8 min have
elapsed. To the next five flasks are added 1.0, 2.0, 3.0, 4.0,
and 5.0 mL, by pipet, of 1.00 × 10᎑4
M K2Cr2O7 stock solution.
Each flask is then filled to the mark with deionized water
and the absorbances are recorded at the two fixed times. Students
are cautioned that the fixed time intervals are critical
and that all solutions should be analyzed in a stepwise manner.
The oxidizing agent is added to the next solution in the series
only after the 8-min data point has been recorded for
the preceding solution. The five KMnO4 standard solutions
and unknown solution (3-mL aliquot) are prepared and analyzed
in a similar manner. If necessary, the aliquot size of the
unknown can be increased (or decreased) to give a suitable
reduction in the measured absorbance. (NOTE: All chemical
and waste solutions should be discarded according to proper
disposal procedures; see refs 17 and 18.) The ambient room
temperature is maintained fairly constant in our laboratory.
If temperature fluctuations become a problem, our spectrophotometers
are equipped with a thermostated, waterjacketed
cell holder that can be used to maintain better
temperature control.
Discussion of Results
Typical student results are listed in Table 1 for the determination
of MnO4
᎑
and Cr2O7
2᎑
by means of the kineticsbased
indirect spectrophotometric method. The first six
solutions pertain to the calibration curves for dichromate,
needed to determine the numerical values of the two proportionality
constants, mt1,Cr2O7
2᎑ and mt2,Cr2O7
2᎑, that govern the
change in the measured absorbance. Solutions 7–11 are standards
containing known amounts of MnO4
᎑
. Linear leastsquares
analysis of the experimental data for the two sets of
standard solutions yields slopes of mt1,Cr2O7
2᎑ = ᎑16,060 ± 730
(r 2
= .9917), mt2,Cr2O7
2᎑ = ᎑23,550 ± 940 (r 2
= .9936) and
mt1,MnO4
᎑ = mt2,MnO4
᎑ = ᎑18,560±210 (r 2
= .9995). Near-unity
squared correlation coefficients indicate that the measured
absorbance does decrease linearly with the molar concentrations
of both added oxidizing agents. By solving eqs 5 and 6
simultaneously, one obtains numerical values of CCr2O7
2᎑ = 5.87
× 10᎑6 M and CMnO4
᎑ = 1.19 × 10᎑5 M for the molar concentrations
of the diluted unknown solution.
Students are reminded during the brief pre-laboratory
lecture that analytical chemists always report the concentrations
in the original unknown samples, and that one must
always take into account any dilutions that may have been
made during the course of the chemical analysis. The experimentally
determined molar concentrations of Cr2O7
2᎑ and
MnO4
᎑ in the original unknown sample, CCr2O7
2᎑ = 4.90× 10᎑5
M and CMnO4
᎑ = 9.91 × 10᎑5 M, are in agreement with the
so-called “true” values of CCr2O7
2᎑ = 5.00 × 10᎑5 M and CMnO4
᎑
= 1.00 ×10᎑4 M. Other student values reported for this sample
were CCr2O7
2᎑ = 4.81 × 10᎑5, 5.13 × 10᎑3, and 5.17 × 10᎑5 M
and CMnO4
᎑ = 9.71× 10᎑5, 9.89 × 10᎑5, and 1.03 × 10᎑4 M for
the molar concentrations of the dichromate and permanganate
ions. On the basis of our past experiences with the kineticsbased
indirect spectrophotometric method, students should
be able to get within ± 5% of the correct values.
Figure 1. Absorbance spectra of (A) MnO4
᎑
; (B) Cr2O7
2᎑
; (C) PGR
and (D) its oxidized form.
a Measured absorbances recorded at 488 nm on a Bausch and Lomb
Spectronic 2000.
b A 3-mL aliquot of the unknown solution was used.
suoenatlumiSrofataDecnabrosbA.1elbaT
OnMfonoitanimreteD 4
– rCdna 2O7
–2 -sciteniKyb
dohteMcirtemotohportcepStceridnIdesaB
nloS C rC( 2O7
2᎑)
)M(
C ( OnM 4
᎑)
)M(
ecnabrosbA a
nim3 nim8
1 0 0 32.1 32.1
2 00.4 × 01 ᎑6 0 171.1 631.1
3 00.8 × 01 ᎑6 0 301.1 330.1
4 02.1 × 01 ᎑5 0 140.1 859.0
5 06.1 × 01 ᎑5 0 459.0 728.0
6 00.2 × 01 ᎑5 0 329.0 177.0
7 0 00.8 × 01 ᎑6 490.1 390.1
8 0 06.1 × 01 ᎑5 939.0 839.0
9 0 04.2 × 01 ᎑5 787.0 687.0
01 0 02.3 × 01 ᎑5 236.0 136.0
11 0 00.4 × 01 ᎑5 894.0 794.0
21 nwonknU b nwonknU b 519.0 178.0
452 Journal of Chemical Education • Vol. 75 No. 4 April 1998 • JChemEd.chem.wisc.edu
In the Laboratory
As part of the laboratory instruction, students in our
instrumental analysis course are given the analytical results
(CCr2O7
2᎑ and CMnO4
᎑ values) for their unknown sample, which
were determined using the more conventional two-wavelength
spectrophotometric method (see eqs 3 and 4) by undergraduate
students enrolled in the preceding semester’s quantitative
analysis course. They are asked to statistically analyze data
from the kinetics-based and two-wavelength methods and to
determine if there is a significant difference between the two
methods. The statistical treatment is discussed in most standard
analytical textbooks (19–21). Rarely are undergraduate students
afforded the opportunity to actually apply the treatment to
their experimental data. Such analysis leads into a discussion of
factors that are considered in selecting an analytical method.
Selection of an appropriate analytical method is a decision that
practicing analytical chemists encounter daily.
From an educational standpoint, we prefer the kineticsbased
experiment to the more traditional two-component,
two-wavelength spectrophotometric methods published in
standard laboratory manuals. The experiment not only incorporates
the important fundamental principles associated
with spectroscopic analysis, but it also exposes students to
kinetics-based techniques, which are often encountered in
enzyme and drug determinations. Moreover, the kineticsbased
method presented above provides students who have
already performed a two-component spectroscopic analysis
based upon eq 2 in their quantitative analysis course a suitable
alternative laboratory experiment. If desired, the experiment
can be shortened so as to analyze only one of the two ions.
Acknowledgment
Sandra Padilla, Ashantè Trufant, Noé De La Sancha, and
Ernesto Vela thank the U.S. Department of Education for
support provided to them under the Upward Bound Math
and Science Program.
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