Spectrophotometric Analysis of a Two
Component Solution
Starring:
In order of Appearance,
Meg “Sporty Spice” Chapman
Karen “The Madam” Costello
Dave “Wait 20 Minutes” Dulebohn
Zack “The Savior” Jarrett
Instructor: Barry “Thumbs Up” Husowitz
Purpose:
Using spectroscopy and the Beer-Lambert law,
determine experimentally the concentrations of
chromium (III) and cobalt (II) in an unknown mixture
of Cr(NO3)3 and Co(NO3)2.
Beer-Lambert Law
The Beer-Lambert law states “that the amount of light absorbed by a sample is
directly proportional to the concentration of the absorbing solution.”
A = kc
Where A is absorbance, k is a constant of proportionality known as the molar
absorptivity, and c is the concentration of the solution.
For a solution that is a mixture of two parts, the Absorbance (A) is equal to the
sum of kc for both parts:
A = k1c1 + k2c2
When working with two component solutions it is necessary to determine a
wavelength where one component absorbs strongly while the other absorbs
weakly, and vice versa. We call these two wavelengths 1 and 2 and use
them to form two equations, which when solved as a system can be used to
determine the concentration of each substance in the solution.
A1 = k11c1 + k12c2
A2 = k21c1 + k22c2
Procedure Summary:
1)
Determine 1 and 2.
2)
Create a calibration curve for the absorbance of each species at 1 and 2.
3)
Measure the absorbance of 3 solutions (labeled A, B, and C) of unknown
concentrations of Cr(NO3)3 and Co(NO3)2.
4)
Analyze the results to determine the concentration of each species in the
unknown samples.
Step 1: Determine 1 and 2
1) We measured the absorbance of solutions of 0.050 M Cr(NO3)3 and 0.188 M
Co(NO3)2 from 400 nm to 600 nm at 20 nm intervals using Spec20
spectrophotometers.
2) This data was plotted and used to determined the wavelengths where the two
components had opposite levels of absorbance (1 and 2).
Spe ctrophotome tric Analysis
0.900
400
420
440
460
480
500
520
540
560
580
600
Abdsorbance Absorbance
Cr(NO3)3
Co(NO3)2
0.756
0.064
0.722
0.121
0.470
0.286
0.251
0.533
0.170
0.697
0.217
0.850
0.330
0.846
0.493
0.542
0.634
0.256
0.664
0.104
0.573
0.072
0.800
0.700
Absorbance Cr(NO3)3
0.600
Absorbance
Wavelength
(nm)
Absorbance Co(NO3)2
0.500
Absorbance Co(NO3)2
0.400
Absorbance Cr(NO3)3
0.300
0.200
0.100
0.000
400
420
440
460
480
500
520
540
560
580
600
Wavelength (in nm)
3) We chose 400 nm for 1 and 500 nm for 2 because that is where there is
the greatest difference in absorbance between the species.
Step 2: Create a Calibration Curve
for each species at 1 and 2
1) We prepared dilutions of 0.01 M, 0.02 M, 0.03 M, and 0.04 M from the
standard solutions of each component.
Dilution Volumes, Cr(NO
3)3
Dilution Volumes, Co(NO
3)2
Desired Molarity Volume 0.050 M Cr(NO3)3 Volume H2O
Desired Molarity Volume 0.188 M Co(NO3)2 Volume H2O
0.01 M
2 mL
8 mL
0.01 M
1 mL
18.8 mL
0.02 M
2 mL
3 mL
0.02 M
1 mL
9.4 mL
0.03 M
6 mL
4 mL
0.03 M
1 mL
6.27 mL
0.04 M
6 mL
1.5 mL
0.04 M
1 mL
4.7 mL
2) We measured the absorptivity of each dilution at 1 and 2, then plotted the
data and fitted a best fit line to each series.
Calibration Curves
Absorbance of Standard Solutions
0.00 M
0.01 M
0.02 M
0.03 M
0.04 M
Cr(NO3)3 @ 400 nm
0.000
0.146
0.303
0.451
0.602
Cr(NO3)3 @ 500 nm
0.000
0.037
0.078
0.127
0.169
Co(NO3)2 @ 400 nm
0.000
0.000
0.007
0.012
0.037
Co(NO3)2 @ 500 nm
0.000
0.044
0.093
0.121
0.154
Calibration Curves
0.700
y = 15.09x
0.600
C r(N O 3 )3 @ 5 0 0 nm
0.500
Absorbance
C r(N O 3 )3 @ 4 0 0 nm
C o(N O 3 )2 @ 4 0 0 nm
C o(N O 3 )2 @ 5 0 0 nm
0.400
C r(N O 3 )3 @ 4 0 0 nm
0.300
C r(N O 3 )3 @ 5 0 0 nm
0.200
C o(N O 3 )2 @ 5 0 0 nm
y = 4.28x
y = 3.85x
0.100
y = 0.86x
0.000
0.00 M
0.01 M
0.02 M
0.03 M
Solution Concentration (Molarity)
0.04 M
C o(N O 3 )2 @ 5 0 0 nm
Measure the Absorbances of
Unknown Solutions
1) We measured the absorbances of 3 solutions of unknown concentration of
Cr(NO3)3 and Co(NO3)2.
Absorbance of Unknown Samples
Wavelength Unknown A Unknown B Unknown C
400 nm
0.193
0.081
0.194
500 nm
0.171
0.084
0.121
Analysis
In order to determine the concentration of each substance in a sample of
solution we must solve the following equations together as an algebraic system.
A1 = k11c1 + k12c2
A2 = k21c1 + k22c2
For the purpose of the following analysis, c1 refers to the concentration of
Cr(NO3)3 and c2 refers to the concentration of Co(NO3)3. k11 is the molar
absorptivity of Cr(NO3)3 at the wavelength 1, k12 is the molar absorptivity of
Co(NO3)3 at the wavelength 1. k21 and k22 are the molar absorptivities for
the wavelength 2. These constants are determined by calculating the slope of
the best fit lines on the calibration curves.
k11 = 15.09
k12 = 0.86
k21 = 4.28
k22 = 3.85
Analysis, Sample A
{
{
A1 = k11c1 + k12c2
A2 = k21c1 + k22c2
0.193 = 15.09c1 + 0.86c2
0.171 = 4.28c1 + 3.85c2
When solved, we find the following concentrations:
Cr(NO3)3 = 0.00943 M
Co(NO3)3 = 0.0339 M
Analysis, Sample A;
Percent Error
A simple percent error calculation shows us that
something is very wrong:
Concentrations of Unknowns (provided by instructor)
Concentration Cr(NO
3)3
Concentration Co(NO
3)2
0.025 M
0.05 M
Unknown A
% Error =
Molarity experimental
x 100
Molarity known
% Error Cr(NO3)3 =
0.00943 M
x 100 =
0.025 M
37%
% Error Co(NO3)2 =
0.0339 M
x 100 =
0.05 M
68%
Analysis; Source of Error
Sanity checking the calibration curve data reveals that the calibration curve for
Co(NO3)2 is incorrect.
Beer’s law states that A = kc. We can check our calibration curve against the
initial spectroscopic analysis results by seeing if the absorbance of 1.88M
Co(NO3)2 at 1 (400 nm) is equal to the product of the molar absorptivity (k) at 1
and the concentration (0.188 M):
Absorptivity0.188 M Co(NO3)2 @ 1 = k1 x Concentration
0.064  0.86 x 0.188
0.064  0.162
Absorptivity0.188 M Co(NO3)2 @ 2 = k2 x Concentration
0.850  3.85 x 0.188
0.850  0.724
Analysis; Source of Error
When we perform the same set of calculations for Cr(NO3)3, the equations are true.
We can conclude from this that the molar absorptivities derived for Cr(NO3)3 are
correct.
Absorptivity0.050 M Cr(NO3)3 @ 1 = k1 x Concentration
0.756 ≈ 15.09 x 0.050
0.756 ≈ 0.755
Absorptivity0.050 M Cr(NO3)3 @ 2 = k2 x Concentration
0.217 ≈ 4.28 x 0.050
0.217 ≈ 0.214
Conclusions
1.
Our percent error was far too high for this experiment to produce
trustworthy data.
2.
The molar absorptivity for Cr(NO3)3 was correct, but the molar
absorptivity for Co(NO3)2 was not.
3.
Without accurate molar absorptivities for each species it is impossible
to accurately perform the analysis needed to identify the
concentrations of each species in the solution
4.
There are 3 possible causes for our molar absorptivity of Co(NO3)2
being incorrect:
1.
Error when preparing the dilutions.
2.
Error when operating the Spectrometer.
3.
A mix of both of these.