Tatiana Soboleva
3/18/14
“Optimization of Multicomponent UV-Vis Analysis of Analgesic Pharmaceuticals Using
Linear Least Squares Regression”
Introduction
In this experiment we are quantifying acetaminophen, aspirin, and caffeine in Excedrin®
Extra Strength, CVS®, and Blowfish® analgesic pharmaceuticals using spectrophotometric
method along with Linear Least Squares Regression computational estimations. Acetaminophen,
aspirin, and caffeine are known to absorb ultraviolet radiation over almost the same spectrum;
hence, the synchronic presence of the three analytes in a tested sample yields inconclusive results
as every species contributes to the overall absorbance curve due to spectral overlap. According to
the manufacturer, Excedrin® Extra Strength and CVS® sedatives contain acetaminophen
(250mg/tablet), aspirin (250 mg/tablet), and caffeine (65 mg/tablet); whereas Blowfish®
effervescent contains only aspirin (500 mg/tablet), and caffeine (60 mg/tablet). In order to
identify the concentration of individual species from a complex matrix of an analgesic
pharmaceutical, Linear Least Squares Regression method is applied. It estimates minimal sum of
squared deviations of experimental data from the “linear” model using iterative matrix of
equations that are solved simultaneously. The applied computational method of Linear Least
Squares Regression is a reliable tool in this analysis due to the short range of wavelengths
(100nm), and 200 analyzed equations which are considered to be an inherently linear system.
Besides, the concomitant quantitation of acetaminophen, aspirin, and caffeine species;
this report provides method optimization for analyte determination in Excedrin® Extra Strength,
CVS®, and Blowfish® analgesics.
Due to an insignificant spectral identity of the aspirin and a (at least) three component
matrix system (Figure1), the expected outcome of the experiment is that there will be a
significant systematic error associated with its quantitation that will be also impairing the
quantitation of acetaminophen and caffeine components in Excedrin® Extra Strength, CVS®, and
Blowfish® analgesic pharmaceutical tablet samples.
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Tatiana Soboleva
3/18/14
Experimental Methodology
The obtained absorbance of acetaminophen, aspirin, and caffeine from 20mg/L standards
over the wavelength range of 205-305nm reported at every half-wavelength (Figure 1), shows a
significant overlap among the analyzed species. Aspirin has no distinct picks that would identify
it from the other two analytes leading to a potentially poor accuracy in its quantitation.
Absorbance
Figure 1: Absorbance of aspirin, acetaminophen, and caffeine over 205-305nm range
Absorbance of aspirin, acetaminophen, and caffeine
over 205-205 nm
20 mg/L Aspirin
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
0.00
20 mg/L Acetaminophen
short, hardly distinguished
20 mg/L Caffeine
205
215
225
235
245
255
l (nm)
265
275
285
295
305
The extinction coefficients of acetaminophen, aspirin, and caffeine, were determined
from the standards with concentration range 4-16ppm using Beer’s Law equation A=b*C*ɛ,
where b is the path length 1cm, C- concentration, and ɛ-extinction coefficient. They were
ultimately used for the calculations of individual analyte concentration in the sample matrix of
specified analgesics. The multicomponent system requires execution of Linear Least Squares
Regression method. It is based on LinestTM Excel function that begins with a “guess” of the three
species concentration plugging this value into the provided 200 equations (205-305nm) and upon
iteration calculates the set of the three values which yield smallest sum of the squared deviations
between the observed and calculated absorbance. As a result, the application of LinestTM Excel
function provides a better quantitative estimation.
The Excedrin® Extra Strength, CVS®, and Blowfish® analgesics samples were tested at a
constant pH=1 due to the acid/base properties of the acetaminophen, aspirin, and caffeine
molecules (Figure2).
Figure 2: Structures and pKa values of acetaminophen, aspirin, and caffeine.
Acetaminophen pKa=9.71 Aspirin pKa=3.49 Caffeine pKa=0.6
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Tatiana Soboleva
3/18/14
Results
In order to determine the best concentration sequence and wavelengths’ ranges (i.e the ranges
with the least deviation between the observed and calculated absorbance), the 205-305nm wavelength
range was plotted for the following concentrations : acetaminophen (15ppm), aspirin (15ppm), caffeine
(15ppm) (see Figure 3); acetaminophen (5ppm), aspirin (15ppm), caffeine (5ppm) (see Figure 4);
acetaminophen (5ppm), aspirin (5ppm), caffeine (15ppm) (see Figure 5).
Figure 3: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (15ppm) over 205-305nm
range.
4
Absorbance
3
2
Observed
1
Calculated
Difference
0
205
225
245
-1
265
285
305
λ(nm)
Figure 4: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (15ppm), and caffeine (5ppm) over 205-305nm
range.
3
2.5
Absorbance
2
Significant deviation
1.5
Observed Abs
1
Claculated Abs
0.5
Difference
0
-0.5 205
-1
225
245
265
285
305
λ(nm)
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Tatiana Soboleva
3/18/14
Figure 5: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (5ppm), and caffeine (15ppm) over 205-305nm
range.
3
Absorbance
2.5
2
significant deviation
1.5
Observed
1
Calculated
0.5
Difference
0
-0.5205.0
225.0
245.0
265.0
285.0
305.0
λ(nm)
After the identification of the region of “significant deviation” (shown by blue brace in Figure 4
an 5) which according to Figure 4 and 5 is located in the 250-275nm range, this spectrum was eliminated
from the new graph sequence for the same concentrations (see Figures 6-8).
Absorbance
Figure 6: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (15ppm) over 210-250nm
and 285-290nm range.
3
2.5
2
1.5
1
0.5
0
210.0
Observed
Calculated
Difference
230.0
250.0
270.0
290.0
λ(nm)
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Tatiana Soboleva
3/18/14
Figure 7: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (5ppm) over 210-250nm and
285-290nm range.
Absorbance
2
1.5
Observed
1
Calculated
0.5
0
210.0
Difference
230.0
250.0
270.0
290.0
λ(nm)
Figure 8: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (5ppm), and caffeine (15ppm) over 210-250nm and
285-290nm range.
2.5
Absorbance
2
1.5
Observed
1
Calculated
0.5
Difference
0
210
230
250
270
290
λ(nm)
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Tatiana Soboleva
3/18/14
In order to check the “deviation” effect caused by the suspected 250-275nm spectrum that was
previously eliminated, the ranges of 210-275nm and 280-290 nm was tested for the same concentration
range (see Figures 9-11).
Figure 9: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (5ppm), and caffeine (15ppm) over 210-275nm and
280-290nm ranges.
Absorbance
2.5
2
1.5
Observed Abs
1
Calculated Abs
0.5
Difference
0
210
230
250
270
290
λ(nm)
Figure 10: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (15ppm) over 210-275nm
and 280-290nm ranges.
3
Absorbance
2.5
2
Observed
1.5
1
Calculated
0.5
0
210.0
Difference
230.0
250.0
270.0
290.0
λ(nm)
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Tatiana Soboleva
3/18/14
Figure 11: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (5ppm) over 210-275nm and
280-290nm ranges.
Absorbance
2
1.5
Observed
1
Calculated
0.5
Difference
0
210
230
250
270
290
λ(nm)
A closer look at the “deviation” graph region was performed by its isolation via the analysis of
the 245-260nm and 275-280nm wavelength ranges omitting the 210-245nm and 260-275nm ranges, data
was analyzed for the same concentrations (see Figures 12-14).
Absorbance
Figure 12: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (5ppm) over 245-260nm and
275-280nm ranges.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
240.0
Observed
Calculated
Difference
250.0
260.0
270.0
280.0
290.0
λ(nm)
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Tatiana Soboleva
3/18/14
Figure 13: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (5ppm), and caffeine (15ppm) over 245-260nm and
275-280nm ranges.
1.2
Absorbance
1
0.8
0.6
Observed
0.4
Calculated
Difference
0.2
0
240.0
250.0
260.0
270.0
280.0
290.0
λ(nm)
Absorbance
Figure 14: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (15ppm) over 245-260nm
and 275-280nm ranges.
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
240.0
Observed
Calculated
Difference
250.0
260.0
270.0
280.0
290.0
λ(nm)
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Tatiana Soboleva
3/18/14
The analysis of the 210-250 nm range for the same concentrations was done to verify the
independence of the two previously split spectral areas (210-250nm and 285-290nm), see Figures 15-17.
Figure 15: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (5ppm) over 210-250nm
range.
1.2
Absorbance
1
0.8
0.6
Observed
0.4
Calculated
0.2
Difference
0
200.0
210.0
220.0
230.0
240.0
250.0
260.0
λ(nm)
Figure 16: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (15ppm), aspirin (15ppm), and caffeine (15ppm) over 210-250nm
range.
1.4
Absorbance
1.2
1
0.8
Observed
0.6
Calculated
0.4
Difference
0.2
0
200.0
210.0
220.0
230.0
240.0
250.0
260.0
λ(nm)
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Tatiana Soboleva
3/18/14
Figure 17: The figure displays the observed, calculated absorbance and their difference for the
solution containing acetaminophen (5ppm), aspirin (5ppm), and caffeine (15ppm) over 210-250nm
range.
1
Absorbance
0.8
0.6
Observed
0.4
Calculated
0.2
0
200.0
Difference
210.0
220.0
230.0
240.0
250.0
260.0
λ(nm)
The averages of absorbance difference were calculated for the following analyzed
concentration sequences (Table 1).
Table 1: The averages of absorbance difference for the analyzed concentration ranges
Average of abs
difference
5-15-5
0.051665
205-305
15-15-15
0.367430842
5-5-15
0.057872
5-5-15
0.019827708
210-250 &285-290
15-15-5
0.027108
15-15-15
0.043962
5-5-15
0.0286915
210-275 &280-290
15-15-5
0.031777
15-15-15
0.058994
15-15-5
0.039877
245-260 &275-280
15-15-15
0.05327
5-5-15
0.044732
15-15-5
0.025886
210-250
15-15-15
0.032602
5-5-15
0.015540508
*Yellow color- the biggest deviation value from a wavelength range.
Wavelength range
Concentrations
The biggest
deviation values
The smallest
deviation values
*Green-the lowest deviation value from a wavelength range.
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Tatiana Soboleva
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According to Table1 data, the optimal analgesics’ analysis template was determined as:
the 210-250 & 285-290nm wavelength ranges (see Figures 18-20).
Figure 18: The figure displays the observed, calculated absorbance and their difference
for the CVS® sample over 210-250nm and 285-290nm ranges.
0.4
Absorbance
0.3
0.2
Observed
0.1
Calculated
Difference
0
210
230
250
-0.1
270
290
λ(nm)
Absorbance
Figure 19: The figure displays the observed, calculated absorbance and their difference for the
Excedrin® Extra Strength sample over 210-250nm and 285-290nm ranges.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05 210
Observed
Calculated
Difference
220
230
240
250
λ(nm)
260
270
280
290
Figure 20: The figure displays the observed, calculated absorbance and their difference for the
Blowfish® sample over 210-250nm and 285-290nm ranges.
0.6
Absorbance
0.5
0.4
0.3
Observed
0.2
Calculated
0.1
Difference
0
-0.1210.0
220.0
230.0
240.0
250.0
260.0
270.0
280.0
290.0
λ(nm)
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Tatiana Soboleva
3/18/14
The analyte concentration/tablet was calculated for the 210-250nm and 285-290nm
wavelength ranges (Table 2-4).
Table 2: Acetaminophen, aspirin, and caffeine concentrations/tablet in CVS® samples
Tablet
Aspirin/Tablet (mg)
Dil. Factor
Std. Dev.
283.0
3.0
Acetaminophen/Tablet
(mg)
296.6
0.7
Caffeine/Tablet (mg)
81.0
1.0
Table 3: Acetaminophen, aspirin, and caffeine concentrations/tablet in Excedrin® Extra
Strength samples
Tablet
Aspirin/Tablet (mg)
Dil. Factor
Std. Dev.
255.0
3.0
Acetaminophen/Tablet
(mg)
272.2
0.7
Caffeine/Tablet (mg)
81.0
1.0
Table 4: Acetaminophen, aspirin, and caffeine concentrations/tablet in Blowfish® samples
Tablet
Aspirin/Tablet (mg)
Dil. Factor
Std. Dev.
1183.0
6.0
Acetaminophen/Tablet
(mg)
8.0
1.0
Caffeine/Tablet (mg)
118.0
3.0
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Tatiana Soboleva
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%Agreement calculations for aspirin:
CVS® samples: [(283.0 mg-250.0mg)/ 250.0mg]*100%=13.2% (overestimation)
Excedrin® Extra Strength samples: [(255.0mg-250.0mg)/ 250.0mg]*100%=2.0%
(overestimation)
Blowfish® samples: [(1183.0mg-500.0mg)/ 500.0mg]*100%=136.6% (overestimation)
%Agreement calculations for acetaminophen:
CVS® samples: [(296.6mg-250.0mg)/ 250.0mg]*100%=18.6% (overestimation)
Excedrin® Extra Strength samples: [(272.2mg-250.0mg)/ 250.0mg]*100%=8.8%
(overestimation)
Blowfish® samples: should not be detected.
%Agreement calculations for caffeine:
CVS® samples: [(81.0mg-65.0mg)/ 65.0mg]*100%=24.6% (overestimation)
Excedrin® Extra Strength samples: [(81.0mg-65.0mg)/ 65.0mg]*100%=24.6%
(overestimation)
Blowfish® samples: [(118.0-60.0mg)/ 60.0mg]*100%=96.7%
Discussion/Conclusions
The quantitation of acetaminophen, aspirin, and caffeine in Excedrin® Extra Strength,
CVS®, and Blowfish® analgesic pharmaceuticals was systematically overestimated in the Least
Squares Regression method due to the absorbance overlap among the analytes under study.
According to the applied computational method, it was found that CVS® contains: aspirin
(283.0±3.0)mg/tablet, acetaminophen (296.6±0.7) mg/tablet, caffeine (81.0±1.0) mg/tablet;
Excedrin® Extra Strength contains: aspirin (255.0±3.0)mg/tablet, acetaminophen
(272.6±0.7)mg/tablet, caffeine (81.0±1.0)mg/tablet; and Blowfish® contains: aspirin
(1183.0±6.0)mg/tablet, acetaminophen (8.0±1.0) mg/tablet, caffeine (118.0±3.0) mg/tablet. The
system was optimized via the elimination of 245-250nm and 275-280nm wavelength ranges from
absorbance spectrum analyses.
Despite the fact that Least Squares Regression method is effective over short ranges,
relatively small data sets, and allows an easier statistical interpretation of calibration simulations;
it is limited in the function shapes, having poor extrapolation properties, and sensitivity to
outliers. According to Figures 6-11 and 15-17 the “tuning knob” in method optimization is the
number of analyzed wavelengths which is directly proportional to the accuracy of quantitation.
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Tatiana Soboleva
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Moreover, the best concentration range for “tuning” was determined to be acetaminophen
(5ppm), aspirin (5ppm), and caffeine (15ppm).
Future research direction



In order to diminish the possible absorbance interference of tablet capsule components,
the crushed, homogenized, and digested aliquots should be filtered 3-5 times prior to the
UV-Vis analysis.
Standard Additions method might be applied for two of the three components during two
separate experimental analyses: one standard additions target might be caffeine
component which is ~4 times less concentrated than the other two analytes; and the otheraspirin which has a poor distinctive absorbance feature. The obtained results should be
compared to this experiment. While designing the Standard Additions experiment, the
final analyte concentration (caffeine or aspirin) must be less than the concentration of the
other system components (Figures 3,6,10,14,16)1.
Internal standards method might be designed for this experiment.
Caffeine or
Aspirin
Excedrin® Extra Strength/
CVS®/ Blowfish®
1
Note that enhance in the signal via Standard Additions method will lead to the increase in the total absorbance
curve amplitude that might impair the accuracy of the obtained results. Moreover, if the design of the experiment
has a final analyte concentration close to the concentration of the other two components, the system will be
approaching limits of quantitation again leading to erroneous results. Another aspect that should be taken into
account is related to the efficiency of the Least Squares Regression model which is not designed for data
extrapolation needed for “unknown” concentration determination.
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