Use of Flourescent Plate Reader: Sampling of Heterogenous Solids
✅ Paper Type: Free Essay  ✅ Subject: Chemistry 
✅ Wordcount: 7805 words  ✅ Published: 18th May 2020 
Abstract
A Gemini XPS microplate reader was used to determine if current mixing practices were able to produce uniform tablets capable of delivering a consistent quantity of the active ingredient, pyrenesulfonic acid (PSA). Only the second dilution was picked to be analyzed since it contained the most consistent data with the lowest variance. The variance of the second dilution tablet, ${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}$
= 8.53621E18 M^{2}, accounted for 8.037% of the total variance. The average concentration of PSA for the second dilution among 9 PSA fluorescence readings was 4.430E07 M ± 6.554E09 M. No outliers were present since no values fell outside of ±25% of the mean. The total variance (σ_{total}^{2}) was 1.06209E16 M^{2}; ${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}$
was 8.53621E18 M^{2}; σ_{measured}^{2} was 4.295E17 M2; σ_{preparation}^{2 }was 5.47224E17 M^{2}. Overall, the data analysis denotes significant variance in the concentration of PSA among the samples—proving that the current mixing process of solid sampling is inconsistent and in need of revision.
Introduction
The purpose of this experiment was to test the homogeneity of tablet samples provided, and to determine the efficacy of solid sample mixing in delivering a consistent and precise amount of the active ingredient within a standard tablet. PSA was used as the active ingredient due to its fluorescence quality, and Na_{2}SO_{4} was used as an inactive suspension medium. The setup for this experiment mimics the mixing process of pharmaceutical drugs. Since the active ingredient is potent in microgram dosages, a seemingly small error would still deliver too much or too little of the active ingredient. Delivering too much or too little of a high potency drug could cause unintended side effects or decreased efficacy—either case would mean endangering the life of the patient.
If you need assistance with writing your essay, our professional essay writing service is here to help!
Essay Writing ServiceFluorescence of PSA was measured using a Gemini XPS microplate reader, and samples were loaded onto a 96 well plate. Standards prepared by the TA, a blank, and the replicates of three samples and their varying dilutions were loaded onto the well plate. The fluorescence output from each cell is attained by bombarding the plate with photons. The electrons of the fluorophore (PSA) is excited to a higher energy state by absorbing the photon of a shorter wavelength. Energy is released, in this case light, as the PSA transitions from a higher energy state to a lower energy state. The wavelength emitted is a longer wavelength. This emission is picked up by the Gemini XPS reader and the intensity of the wavelength is reported.
The Gemini XPS reader utilizes light from an excitation source to emit photons at a sample. The light is passed through a monochromator so that a specific wavelength can be selected–excitation wavelength is unique for each compound. The sample would then absorb the photon and its valence electrons would then be excited to a higher energy state. The electrons would then fall back to ground state, and in that process emit a wavelength. A separate monochromator is used to separate the emission light from the excitation light. And a photomultiplier tube is used to detect the fluorescence values.
Using the standards premade by the TAs, fluorescence values obtained from the Gemini XPS were used to plot a standard curve of fluorescence vs concentration of PSA in the standards. A bestfit line can be obtained from the curve and concentration of the samples can be calculated using the bestfit line equation. Data analysis was then carried out for the concentrations of the samples.
Experimental Methods
Materials:
 Mixture of 0.05 % w/w/ pyrenesulfonic acid and sodium sulfate
 96 well plate
 Gemini XPS microplate reader
 Microliter pipet and tips (Eppendorf)
 Standard glassware
 Microfuge sample vials
Table of Physical Constants:
Substance 
M.W. (g/mol) 
BP (°C) 
Density (g/mL) 
Hazards 
Sodium Sulfate Na_{2}SO_{4}

142.04 
2604 
2.66 
Hygroscopic Irritant 
Pyrenesulfonic Acid C_{16}H_{10}0_{3}S

282.3 
125129 
1.528 
Corrosive 
Procedure:
 Standard solutions made by the T.A.
10 total samples (9 standards + blank)
Standard 
Concentration 
1 
3.00E05 
2 
1.00E05 
3 
3.00E06 
4 
1.00E06 
5 
3.00E07 
6 
1.00E07 
7 
3.00E08 
8 
1.00E08 
9 
1.00E09 
Blank 
0.00E+00 
 Transferred 100 µL of each standard onto well plate, starting with cell A1 and progressing downwards in columns
 Weighed out three ~200 mg portions from precrushed tablet sample mixture—recorded weight
Dissolvee each ~200 mg portion into individual 25 mL volumetric flask using DI water
Transferred three 100 µL portions of each sample onto the 96 well plate (a total of 9 wells)—original concentration cells
 Successive dilutions:
Took 100 µL of each sample at original concentration and placed into a separate microfuge vial
Added 900 µL of DI water to each vial—agitated till combined
Transferred 3 – 100µL portions of each diluted sample onto the 96 well plate
 Repeated step 4 three more times to have four dilutions factors total.
 Randomization of the cells was omitted since it was experimentally determined that variance between the wells is less significant than variance between samples.
Because of this, samples were placed consecutively down the columns of the 96 well plate, starting a new column once last well was reached.
 Gemini XPS plate reader was set to an excitation wavelength = 314 and an emission wavelength = 376. The 96 well plate was processed, and data is reflected in Table 1.
 Data analysis was then ran on the recorded data
Table 1: Fluorescence Values of Samples and Their Subsequent Dilutions 

Sample 
Fluorescence 1 (RFU) 
Fluorescence 2 (RFU) 
Fluorescence 3 (RFU) 
Average Fluorescence (RFU) 
Standard Deviation (±RFU) 
1 – Original 
22985.303 
23442.467 
23530.316 
23319.362 
292.619 
1 – 1^{st} Dilution 
2479.750 
2527.904 
2506.833 
2504.829 
24.139 
1 – 2^{nd} Dilution 
314.598 
291.443 
306.807 
304.283 
11.782 
1 – 3^{rd} Dilution 
71.098 
64.540 
74.215 
69.951 
4.938 
1 – 4^{th} Dilution 
61.291 
38.943 
55.321 
51.852 
11.571 
2 – Original 
22442.906 
23335.652 
23303.484 
23027.347 
506.397 
2 – 1^{st} Dilution 
2478.135 
2348.605 
2428.256 
2418.332 
65.333 
2 – 2^{nd} Dilution 
318.878 
301.365 
305.894 
308.712 
9.090 
2 – 3^{rd} Dilution 
62.322 
58.119 
62.616 
61.019 
2.516 
2 – 4^{th} Dilution 
33.198 
69.227 
39.811 
47.412 
19.180 
3 – Original 
22994.227 
23104.609 
24104.549 
23401.128 
611.675 
3 – 1^{st} Dilution 
2495.604 
2500.077 
2456.324 
2484.002 
24.074 
3 – 2^{nd} Dilution 
311.308 
314.949 
308.632 
311.630 
3.171 
3 – 3^{rd} Dilution 
67.710 
67.550 
65.584 
66.948 
1.184 
3 – 4^{th} Dilution 
40.821 
54.270 
38.938 
44.676 
8.362 
Table 2: Fluorescence Values of Standards 

Standard Concentration 
Fluorescence (RFU) 
Standard 3.00E05 
57567.523 
Standard 1.00E05 
11789.262 
Standard 3.00E06 
2900.25 
Standard 1.00E06 
979.47 
Standard 3.00E07 
150.518 
Standard 1.00E07 
63.148 
Standard 3.00E08 
70.728 
Standard 1.00E08 
528.337 
Standard 1.00E09 
94.711 
Blank 0.00E+00 
72.766 
Results and Data Analysis
Fluorescence values of the standard solutions and one blank solution were used to construct a standard curve. The concentration of pyrenesulfonic acid (PSA) vs fluorescence was plotted. Standards highlighted in gold were used to construct the standard curve (Table 2). At high concentration and at very low concentration BeerLambert Law is not applicable. At high concentration solutesolute interactions dominate and a shift in absorption wavelength is observed. Similarly, at very low concentrations solventsolvent interactions dominate, also shifting the absorption wavelength. Extreme lows and highs in concentration would result in a deviation from the linear curve, making the standard curve less accurate by decreasing the correlation of absorption and concentration. Therefore, extreme highs and extreme lows in concentration were omitted to maximize the positive correlation between fluorescence and concentration of PSA.
*Note: The bestfit line does not intersect the origin because the fluorescence of the blank was not zero—due to scattered light.
R^{2} = 0.9969 denotes a strong positive correlation between fluorescence and concentration of PSA.
The bestfit line equation was determined to be: y = (1.19 E9)x – 217.82 (eq. 1)
Concentration of PSA was determined by using the bestfit line equation wherein average fluorescence value was used as the y input. Concentration can then be calculated by solving for x. The concentration of each sample was determined, and the concentration of the individual dilutions were also calculated in a similar fashion.
e.g. Avg Fluorescence = (1.19 E9)*[PSA] – 217.82 (eq. 2)
Table 3: Average Concentrations and Standard Deviation of Samples 

Sample 
Average Fluorescence (RFU) 
Average concentration (M) 
Fluorescence Standard Deviation (±RFU) 
Concentration Standard Deviation (±M) 
1 – Original 
23319.362 
1.98E05 
292.619 
2.464E07 
1 – 1^{st} Dilution 
2504.829 
2.29E06 
24.139 
2.033E08 
1 – 2^{nd} Dilution 
304.283 
4.40E07 
11.782 
9.922E09 
1 – 3^{rd} Dilution 
69.951 
2.42E07 
4.938 
4.159E09 
1 – 4^{th} Dilution 
51.852 
2.27E07 
11.571 
9.744E09 
2 – Original 
23027.347 
1.96E05 
506.397 
4.264E07 
2 – 1^{st} Dilution 
2418.332 
2.22E06 
65.333 
5.502E08 
2 – 2^{nd} Dilution 
308.712 
4.43E07 
9.090 
7.655E09 
2 – 3^{rd} Dilution 
61.019 
2.35E07 
2.516 
2.119E09 
2 – 4^{th} Dilution 
47.412 
2.23E07 
19.180 
1.615E08 
3 – Original 
23401.128 
1.99E05 
611.675 
5.151E07 
3 – 1^{st} Dilution 
2484.002 
2.28E06 
24.074 
2.027E08 
3 – 2^{nd} Dilution 
311.630 
4.46E07 
3.171 
2.670E09 
3 – 3^{rd} Dilution 
66.948 
2.40E07 
1.184 
9.970E10 
3 – 4^{th} Dilution 
44.676 
2.21E07 
8.362 
7.041E09 
Histogram
A histogram was not performed since there were only 3 samples measured. The lab procedure was altered so that four dilutions were made from each sample. Because the data obtained was not that of a single homogenous population, a histogram would be misleading to identify subpopulations as the varying levels of dilution factors themselves can be considered subpopulations.
Standard Deviation of Population
An overall average was taken of the average concentrations provided in Table 3. Original concentrations of all samples were averaged to obtain the overall average concentration; the same procedure was followed for the subsequent dilutions.
Standard deviation was calculated using: STDEV = $\sqrt{\frac{\sum _{\textcolor[rgb]{}{\mathrm{i}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{1}}^{\textcolor[rgb]{}{\mathrm{n}}}{\textcolor[rgb]{}{(}{\textcolor[rgb]{}{\mathrm{x}}}_{\textcolor[rgb]{}{\mathrm{i}}}\textcolor[rgb]{}{\u2013}\stackrel{\u0305}{\textcolor[rgb]{}{\mathrm{x}}}\textcolor[rgb]{}{)}}^{\textcolor[rgb]{}{2}}}{\textcolor[rgb]{}{\mathrm{n}}\textcolor[rgb]{}{\u2013}\textcolor[rgb]{}{1}}}$
(eq 3)
Coefficient of Variation (CV) at each various concentration was calculated using:
Coefficient of Variation (CV) = (STDEV/ Average) x 100 (eq 4)
The coefficient of variation of the second dilution was lowest—denoting that dilution 2 had the least amount of variation relative to its mean. Since dilution two had the least amount of variability, it was instructed that an ANOVA should be ran for only the second dilution.
Table 4: Standard Deviation of Overall Average Per Dilution Factor 

Concentration 
Overall AVG Concentration [M] 
STDEV of Overall AVG Concentration [±M] 
Coefficient of Variation 
Original 
1.976E05 
3.621E07 
1.832E+00 
1st Dilution 
2.263E06 
4.265E08 
1.885E+00 
2nd Dilution 
4.430E07 
6.554E09 
1.479E+00 
3rd Dilution 
2.390E07 
3.851E09 
1.611E+00 
4th Dilution 
2.238E07 
9.812E09 
4.384E+00 
To identify any outliers, it was decided to isolate concentrations that is greater than +/ 25% from the mean. The procedure is the same for the original concentration and all the subsequent dilutions. Calculations for the original concentration will be used as an example.
Upper Boundary of [Original] = Mean + (.25)(Mean) (eq 5)
Upper Boundary of [Original] = 1.976E05 + (.25)( 1.976E05) = 2.470E05 M
**No concentration values fell above the upper boundary for the [Original] concentration data pool.
Lower Boundary of [Original] = Mean – (.25)(Mean) (eq 6)
Lower Boundary of [Original] = 1.976E05 – (.25)( 1.976E05) = 1.482E05 M
**No concentration values fell below the lower boundary for the [Original] concentration data pool.
It was determined that there were no outliers within the data. Refer to Table # in appendix for the lower and upper bounds of each dilution.
ANOVA
An ANOVA: Single Factor Analysis was performed to determine the level of variance between the tablet samples. It was instructed that ANOVA would be run for the second dilution only since the concentration fits within the standard curve; the second dilution also has the lowest coefficient of variation (i.e. 1.479% error)(Table 4).
The concentrations of all the replicates of the second dilution were calculated using the line of bestfit equation (eq 1); the data is shown in Table 3. Using the average concentrations, Table 5 represents the sum, average, and variance of each sample’s second dilution.
Table 5: Statistical Summary for Second Dilution of Tablet 

Groups 
Count 
Sum 
Average 
Variance 
Sample 1 
3 
1.31899E06 
4.39664E07 
9.84399E17 
Sample 2 
3 
1.33018E06 
4.43394E07 
5.8598E17 
Sample 3 
3 
1.33755E06 
4.45851E07 
7.1294E18 
Table 6 is a summary of the ANOVA output. MS_{within} represents an estimate of the variance in measurement technique, σ^{2}. MS_{between }represents σ^{2}+n σ_{tablet}^{2}, where n is the number of replicates and σ_{tablet}^{2} is the variance due to the differences among the tablet samples (1).
Table 6: ANOVA Output For All Replicates of Second Dilutions 

Source of Variation 
SS 
df 
MS 
F 
Pvalue 
F crit 
Between Groups 
5.82276E17 
2 
2.91138E17 
0.532026526 
0.612762098 
5.14325285 
Within Groups 
3.28335E16 
6 
5.47224E17 



Total 
3.86562E16 
8 
**Note: SS = Sum of Square, df = Degree of Freedom, MS = Mean Square, F = F_{calculated}
Since F_{calculated} < F_{critical} and PValue(0.612762098) > α(0.05), there is significant probability that the variance between groups were due to random data fluctuations—on a 95% confidence interval.
The total variance can be calculated by (2):
σ_{total}^{2} = σ_{tablet}^{2} + σ_{preparation}^{2} + σ_{measured}^{2} (eq 7) (2)
σ_{preparation}^{2}
σ_{preparation}^{2} = MS_{within} (eq 8) (1)
σ_{preparation}^{2 }= 5.47224E17 M^{2}
σ_{measured}^{2}
σ_{measured}^{2} = (6.554E09M)^{2} = 4.295E17 M^{2} (eq 9) (1)
*using standard of deviation value from Table 4
σ_{tablet}^{2}
${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{\left}\frac{{\textcolor[rgb]{}{\mathrm{MS}}}_{\textcolor[rgb]{}{\mathrm{between}}}\textcolor[rgb]{}{\u2013}{\textcolor[rgb]{}{\mathrm{MS}}}_{\textcolor[rgb]{}{\mathrm{within}}}}{\textcolor[rgb]{}{\mathrm{n}}}\textcolor[rgb]{}{\right}$
(eq 10) (1)
${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{\left}\frac{\textcolor[rgb]{}{(}\textcolor[rgb]{}{2}\textcolor[rgb]{}{.}\textcolor[rgb]{}{91138}\textcolor[rgb]{}{\mathrm{E}}\textcolor[rgb]{}{\u2013}\textcolor[rgb]{}{17}\textcolor[rgb]{}{)}\textcolor[rgb]{}{\u2013}\textcolor[rgb]{}{(}\textcolor[rgb]{}{5}\textcolor[rgb]{}{.}\textcolor[rgb]{}{47224}\textcolor[rgb]{}{\mathrm{E}}\textcolor[rgb]{}{\u2013}\textcolor[rgb]{}{17}\textcolor[rgb]{}{)}\textcolor[rgb]{}{}}{\textcolor[rgb]{}{3}}\textcolor[rgb]{}{\right}$
${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{\mathrm{}}$
8.53621E18 M^{2}
^{ }
σ_{total}^{2}
σ_{total}^{2} = 8.53621E18 M^{2 }+ 5.47224E17 M^{2 }+ 4.295E17 M^{2} (eq 7) (2)
σ_{total}^{2} = 1.06209E16 M^{2}
Therefore, %variance due to tablet variance = $\frac{{\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}}{{\textcolor[rgb]{}{\mathrm{\sigma}}}^{\textcolor[rgb]{}{2}}\textcolor[rgb]{}{\mathrm{total}}}$
x 100 = 8.037181406 %. (eq 11)
Discussion
The purpose of this experiment was to test if each tablet sample consistently delivered the same amount of the active ingredient in a drug. PSA, a fluorophore, was used to represent the active ingredient in a drug. A Gemini XPS reader was used to detect the fluorescence of PSA in each sample. Concentration was then calculated using the bestfit equation of the standard curve, y=(1.19 E9)x – 217.82, wherein the standards of PSA was plotted against their fluorescence output. An R^{2} = 0.9969 confirms a positive correlation between the standard’s PSA concentration and its fluorescence output. It is important that the concentration of Na_{2}SO_{4} is equivalent in the standard and the sample tablets so as to not introduce errors in the fluorescent output. Additionally, deionized water should be used to make the solutions so that there is not additional errors via ionion interactions.
Our academic experts are ready and waiting to assist with any writing project you may have. From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs.
View our servicesFive separate concentrations were made of PSA; the first being the original concentration, and then four subsequent dilutions of each sample diluted by a factor of 10. The various concentrations of each sample was labeled original, 1^{st} dilution, 2^{nd} dilution, 3^{rd} dilution, 4^{th} dilution. After computing the coefficient of variation (CV) for the overall average of all the samples (i.e. CV was calculated from average original concentration of all the samples, same procedure for subsequent dilutions), dilution 4 was omitted. The coefficient of variation (CV) for most of the concentrations were similar, with the exception of the 4^{th} dilution—which was too dilute to yield good data so was therefore omitted. More importantly, since the CV of the second dilution was close to that of the original concentration, analyzing the variance of the second dilution would yield good correlation on the whether or not the homogeneity of the tablets are consistent at their original concentration.
Only the second dilution was picked to be analyzed since it contained the most consistent data with the lowest variance. The average concentration of PSA for the second dilution among 9 PSA fluorescence readings was 4.430E07 M ± 6.554E09 M. No outliers were present since no values fell outside of ±25% of the mean. The total variance (σ_{total}^{2}) was 1.06209E16 M^{2}; ${\textcolor[rgb]{}{\mathrm{\sigma}}}_{\textcolor[rgb]{}{\mathrm{tablet}}}^{\textcolor[rgb]{}{2}}$
= 8.53621E18 M^{2}; σ_{measured}^{2} = 4.295E17 M2; σ_{preparation}^{2 }= 5.47224E17 M^{2}; and 8.037% of the total variance was from variance within the tablet samples. Overall, the data analysis denotes significant variance in the concentration of PSA for the second dilution. Considering that the second dilution had the lowest variance out of all the dilutions and the original concentration, it stands that variance is even worse for the original concentration and the other dilutions.
ANOVA was ran and a pvalue of 0.613, with an F_{calculated} of 0.532026526 and an F_{critical} of 5.14325285 . Since PValue(0.612762098) > α(0.05), there is significant probability that the variance between groups were due to random data fluctuations (on a 95% confidence interval).
It is clear from the data that nonhomogeneity is an issue. Variations of the tablets can be from ineffective mixing and/or imprecise sampling. Since the drug is high potency, variation in a milligram tablet would cause a significant variation when the active ingredient is on a microgram scale. Delivering too much or too little of a high potency drug would mean endangering the life of the patient. A way to troubleshoot this issue is to individually compound the tablets and have the process automated. In this case, an exact dose of the active ingredient is added to an exact amount of carrier compound. Cost and time, however, would be mitigating factors since tablets are compounded individually.
References
 CHEM 3472002 Lab reading, “Use of Fluorescent Plate Reader/ Sampling of Heterogenous Solids”
 Guy, Robert D., et al. “An Experiment in the Sampling of Solids for Chemical Analysis.” ACS Publications, pubs.acs.org/doi/abs/10.1021/ed075p1028
 “Microplate Reader: Plate Reader – BMG LABTECH.” BMGLabtech.com, www.bmglabtech.com/microplatereader/.
 Newton, et al. “UltravioletVisible (UVVis) Spectroscopy – Limitations and Deviations of BeerLambert’s Law: Analytical Chemistry.” PharmaXChange.info, 27 June 2016, pharmaxchange.info/2012/05/ultravioletvisibleuvvisspectroscopy%E2%80%93limitationsanddeviationsofbeerlambertlaw/.
Appendix
Table 7: Mass of Samples 

Sample 
Mass (mg) 
1 
202 
2 
203 
3 
204 
Table 8: Concentrations of Samples 

Sample 
Concentration 1 [M] 
Concentration 2 [M] 
Concentration 3 [M] 
Average Concentration [M] 
1 – Original 
1.954E05 
1.992E05 
2.000E05 
1.982E05 
1 – 1^{st} Dilution 
2.272E06 
2.312E06 
2.294E06 
2.293E06 
1 – 2^{nd} Dilution 
4.484E07 
4.289E07 
4.418E07 
4.397E07 
1 – 3^{rd} Dilution 
2.433E07 
2.378E07 
2.459E07 
2.423E07 
1 – 4^{th} Dilution 
2.350E07 
2.162E07 
2.300E07 
2.271E07 
2 – Original 
1.908E05 
1.983E05 
1.981E05 
1.957E05 
2 – 1^{st} Dilution 
2.270E06 
2.161E06 
2.228E06 
2.220E06 
2 – 2^{nd} Dilution 
4.520E07 
4.372E07 
4.410E07 
4.434E07 
2 – 3^{rd} Dilution 
2.359E07 
2.324E07 
2.362E07 
2.348E07 
2 – 4^{th} Dilution 
2.114E07 
2.417E07 
2.170E07 
2.234E07 
3 – Original 
1.955E05 
1.964E05 
2.048E05 
1.989E05 
3 – 1^{st} Dilution 
2.285E06 
2.289E06 
2.252E06 
2.275E06 
3 – 2^{nd} Dilution 
4.456E07 
4.486E07 
4.433E07 
4.459E07 
3 – 3^{rd} Dilution 
2.404E07 
2.403E07 
2.387E07 
2.398E07 
3 – 4^{th} Dilution 
2.178E07 
2.291E07 
2.162E07 
2.210E07 
Table 9: Tablets +/ 25% Bounds 

Concentration 
Overall AVG [M] 
STDEV Overall AVG [M] 
% Error 
Upper Boundary 
Lower Boundary 
Original 
1.976E05 
3.621E07 
1.832E+00 
2.470E05 
1.482E05 
1st Dilution 
2.263E06 
4.265E08 
1.885E+00 
2.828E06 
1.697E06 
2nd Dilution 
4.430E07 
6.554E09 
1.479E+00 
5.537E07 
3.322E07 
3rd Dilution 
2.390E07 
3.851E09 
1.611E+00 
2.987E07 
1.792E07 
4th Dilution 
2.238E07 
9.812E09 
4.384E+00 
2.798E07 
1.679E07 
Cite This Work
To export a reference to this article please select a referencing stye below:
Related Services
View allDMCA / Removal Request
If you are the original writer of this essay and no longer wish to have your work published on UKEssays.com then please: