Title Spectrophotometric Analysis of a Two-Component System Cartesian Coordinate System Mole (Unit) Absorbance Concentration Spectrophotometry 285.6 KB 5
```                            Spectrophotometric Analysis of a Two-Component System with Overlapping Spectra by Walter Rohr
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Spectrophotometric Analysis of a Two-Component System with
Overlapping Spectra by Walter Rohr

A number of methods have been developed to determine the composition of a binary
mixture spectrophotometrically. Most of these are directed at mixtures where one
component can be isolated from the other or they require a Beer’s law experiment to
measure the molar absorptivity of each of the substances in the mixture. However,
Blanco1, et. al. described a method of resolving mixtures with overlapping spectra, called
Multi-Wavelength Linear Regression Analysis or MLRA, without determining molar
absorptivities or complicated mathematics. Using Blanco’s method, the composition of a
binary mixture with overlapping spectra can be resolved with only three measurements,
the absorbance of a standard solution for each component, and the unknown mixture
itself. Vernier’s Logger Pro software is ideally suited for this experiment with the ease at
which one can manipulate data and its ability to prepare a graph even when the data are
out of order.

Here’s how MLRA works: Assuming additivity, the absorbance of a mixture is the sum
of the absorbances of its components. If we have a mixture consisting of two
components, #1 and #2, with an unknown concentration of #1x and #2x, then:

Absorbance of the unknown mixture, ( ) ( ) )2(#1# xAxAmixtureA +=
but applying Beer’s law: ( ) ( ) ( )xCbxA 1#1#1# ⋅⋅= ε and ( ) ( ) ( )xCbxA 2#2#2# ⋅⋅= ε

Substituting: ( ) ( ) ( ) ( )xCbxCbmixtureA 2#)2(#1#1# ⋅⋅+⋅⋅= εε

However, the absorbances of standard solutions of the same substances will follow the
same Beer’s law relationship and have the same molar absorbance, ε , and one centimeter
path length, b, as the unknown solutions under the same conditions. Therefore, we can
write:

( ) ( ) ( )sCbsA 1#1#1# ⋅⋅= ε and ( ) ( ) ( )sCbsA 2#2#2# ⋅⋅= ε

Rearranging these relationships: ( )
( )

)1(#
1#

1#
sC
sA

b =⋅ε and ( )
( )

)2(#
2#

2#
sC
sA

b =⋅ε

Substituting: ( )
( )
( )

( ) ( )
( )

( )xC
sC
sA

xC
sC
sA

mixtureA 2#
2#
2#

1#
1#
1#

⋅+⋅=

or: ( )
( )
( )

( ) ( )
( )

( )sA
sC
xC

sA
sC
xC

mixtureA 2#
2#
2#

1#
1#
1#

⋅+⋅=

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Dividing through by A(#1s) and simplifying we obtain:

( )
( )

( )
( )

( )
( )

( )
( ) 



⋅



+



=

sA
sA

sC
xC

sC
xC

sA
mixtureA

1#
2#

2#
2#

1#
1#

1#

Since the relationship follows the form: y = mx + b, then a plot of
( )

( )sA
mixtureA

1#
versus

( )
( )sA

sA
1#
2#

will give a line with a slope of
( )
( )sC

xC
2#
2#

and an intercept of
( )
( )sC

xC
1#
1#

.

That is, the concentration of the unknown component in the mixture #2x, equals the slope
times the concentration of the standard solution for component #2. Likewise, the
concentration of the unknown component in the mixture #1x, equals the intercept times
the concentration of the standard solution for component #1, or simply

( ) ( )sCmxC 2#2# ⋅= and ( ) ( )sCbxC 1#1# ⋅=

Let’s apply this method to the analysis of the metals in a United States five-cent coin.

Figure 1 - Absorbance spectra of nickel, copper and five-cent coin

To this end, the absorption spectra of the standard solutions with known concentrations
and that of the coin are obtained as three overlapping curves on a single graph. (See
Figure 1.)

In order to apply this method, data columns for
( )

( )sA
mixtureA

1#
and

( )
( )sA

sA
1#
2#

will be created

and plotted where the vertical axis becomes the absorbance of the mixture divided by the
absorbance of one of the components, and the horizontal axis becomes the ratio of

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absorbances of the two standard solutions. The divisor is constant in both calculations,
and should be the standard substance with the maximum absorbance, lambda max, closest
to the optimum absorbance2 of 0.434. In this example, nickel was chosen as the divisor.
Figure 2 is an example of the experiment at the end of the process.

Figure 2 - Linear regression analysis of absorbance ratios

���������
1. The components of an unknown mixture are identified by qualitative analysis,

chromatography, or another method.

2. A solution of the unknown is prepared and diluted quantitatively until the

maximum absorbance is in the optimum 0.15 to 0.70 range (20% to 70%
transmission). Likewise, standard solutions of each component are prepared
having absorbances in the optimum 0.15 to 0.7 range.

3. The spectrophotometer, calibrated using a distilled water blank, is used to
measure the absorbance vs. wavelength for each of the three solutions prepared
above.

4. Now that the absorbance of each solution has been measured, remove from
consideration absorbance values which are the most unreliable (those at the
extreme ends of the spectra or those outside the optimum 0.15 - 0.70 absorbance
range3). This is achieved by highlighting the number of the column on the far left
of the data table and scrolling through the unreliable data. All three data sets will
be selected by this process even though the data in only one column is suspect.

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The data are then eliminated from consideration by choosing Strike Through Data
Cells from the Edit menu. The selected data in those data sets will no longer be
graphed or figured in when calculating the absorbance ratios. Continue this
process of highlighting data and striking through unwanted data until the entire
table has been processed.

5. The next step in the process is to calculate the absorbance ratios which are the key
to this method. Using the Vernier Logger Pro software, choose New Calculated
Column from the Data menu. Type in your description of the calculation that will
also be used as the label for the vertical axis. In this example, Absorbance(coin))/
Absorbance(Ni) was entered. Next, enter a short name for your data column.
“Coin/Ni” was entered in this example. Note: You can uncheck the box which
states, “Add to Similar Data Sets.”

6. Enter the equation for the absorbance of the mixture divided by the absorbance of
one of the standards. This is accomplished by clicking the “Variables
(Columns)”menu, followed by “Choose specific column.” Next, check the
“Nickel coin solution│Absorbance,” followed by “OK.” The “Nickel coin
solution│Absorbance” should appear in the equation box. Type in a “/,” the
symbol for divide. Finally, check the “Variables (Columns)” option again, and
select “0.166M Ni│Absorbance,” then “OK.” The equation will now read, “Five-
cent coin solution│Absorbance”/ “0.166 M Ni│Absorbance.” Click
“Done.” (Note: In this example, the absorbance of the standard nickel solution is
used as the divisor.)

7. This process is repeated for the second calculated column, the ratio of the
absorbance of the 0.0595 M Cu solution to the absorbance of the 0.0166 M nickel
standard. The absorbance of the nickel solution being chosen as the standard will
again be the divisor.

8. Once the absorbance ratios are calculated, they must then be plotted. To select the

data to be plotted on the y-axis, click on the vertical axis, select more, then check
the absorbance(nickel coin solution)/ absorbance(standard nickel). Uncheck all
other data sets.

9. To select the data to be plotted on the x-axis, click on the horizontal axis checking
absorbance(Cu standard)/ absorbance(Ni standard). Autoscale the graph.

10. Click on the Linear Fit icon, . The best linear fit will appear for the data
selected (See Figure 2).

11. Calculate the concentration of the components of the mixture using the slope and
intercept of the line of best fit found in step 10. Use this information to determine
the percentage composition of the metals in a U.S. five-cent coin based on the
MLRA.