### Lab Report on Capillary Electrophoresis

The lab report below was submitted as part of the coursework for CM3292 Advanced Experiements in Analytical and Physical Chemistry. Please do not plagiarise from it as plagiarism might land you into trouble with your university. Do note that my report is well-circulated online and many of my juniors have received soft copies of it. Hence, please exercise prudence while referring to it and, if necessary, cite this webpage.

Aim
The aims are to determine the concentration of chloride in an unknown sample using capillary electrophoresis with indirect UV detection using a calibration plot, to identify the peak of chloride, nitrate and bromate anions in the anion mixtures, to calculate the percent relative standard deviation of the migration time and the number of theoretical plates.
Results and calculations
Quantitative Analysis of Chloride in an Unknown Sample
Sample calculation of concentration of chloride:
C1V1 =C2V2
0.2 x 500 = 10 C2
[Cl-] in S1= (0.2 x 500) / 10 L =10 ppm

Table 1: concentration and corrected area
 Standard Solution Volume of stock solution taken (mL) Concentration of [Cl-]/ ppm Migration time (min) Area (10-4 mV/min) Corrected area (10-5mV) S1 0.20 10 3.730 0.936 2.51 S2 1.00 50 3.855 4.37 11.3 S3 2.00 100 3.918 6.20 15.8 S4 4.00 200 4.001 9.64 24.1 U1 - - 3.867 3.80 9.84
Figure 1: calibration curve of area against concentration of Cl-
From the calibration curve, y = 0.106 x + 3.820
9.94  = 0.106 x + 3.820
concentration of Cl- in U1, x = 56.79 ppm

Since the concentration was diluted by 10 fold, the original Cl- concentration in the bulk unknown sample = 567.9 ppm

Qualitative Analysis of Anions
Table 2: identification of anions based on area
 Anion Mixture Anion Concentration (ppm) Area (10-5 mV/min) Migration time (min) Half-width (min) M1 Cl- 10 3.76 3.727 0.0667 NO3- 10 2.88 4.010 0.0450 BrO3- 10 1.65 5.323 0.0608 M2 Cl- 20 8.90 3.777 0.0917 NO3- 10 2.87 4.042 0.0500 BrO3- 20 4.35 5.388 0.0825 M3 Cl- 10 4.97 3.695 0.0792 NO3- 20 6.10 3.995 0.0642 BrO3- 20 4.93 5.282 0.1033

Since Cl- has smallest ionic radius and the highest charge density, it experiences the least resistance in the capillary column and thus, has the shortest migration time. Because BrO3- is the biggest anion, it will experience greatest friction and has a longer retention time. As such, peak 1 can be deduced to be Cl-, peak 2 is NO3- while peak 3 is BrO3-.
Calculation of Percent Relative Standard Deviation of the Migration times
Using Cl- ions for sample calculations,
Mean migration time = 3.727+3.777+3.6953 = 3.733 mins
Standard deviation = [ (3.727-3.733)2+ (3.777-3.733)2+ (3.695-3.733)23-1 ]1/2 = 0.04133
% relative standard deviation = 0.041333.733 X 100% = 1.107%
Similarly, the Percent Relative Standard Deviation of the Migration Times were calculated and tabulated in table 3 as shown below.

Table 3: percent relative standard deviation of the migration times
 Anion Migration time tm (min) tmean (min) s % RSD Cl- 3.727 3.733 0.04133 1.107 3.777 3.695 NO3- 4.010 4.016 0.02401 0.598 4.042 3.995 BrO3- 5.323 5.331 0.05345 1.00 5.388 5.282

Calculation of the Total Mobilities & Number of Theoretical Plates
Apparent mobility, μapp = μep + μeo = LDtV/Lt = LDLtVt
where µeo = electroosmotic mobility, µep = electrophoretic mobility, V = -20000 V, Ld = effective length = 68 cm and Lt = total length = 73 cm.

Number of theoretical plates = 5.54 [tmw1/2]2
where N = Number of Theoretical Plates, tm = Migration Time (min) and w1/2= Peak Width (min).

Using the above formulae for sample calculations on the Cl- anions in M1,
Total mobility =  68 ×73-20000 ×3.727 = -0.06660 cm2 V-1min-1
Number of theoretical plates = 5.54 [3.7270.06667]2 = 47073 plates (rounded off to nearest integer)
Calculations were repeated for the other samples, and their results are as shown:
Table 4: Total mobilities and number of theoretical plates for S1, S2, S3 and S4
 Sample Migration time, t / min Half peak width / min Total mobilities / cm2V-1min-1 Number of theoretical plates S1 3.730 0.09167 -0.06654 9172 S2 3.855 0.1542 -0.06438 3463 S3 3.918 0.1817 -0.06335 2576 S4 4.001 0.2225 -0.06203 1791

Table 5: Total mobilities and number of theoretical plates for M1, M2 and M3
 Sample Anions present Migration time, t / min Half peak width / min Total mobilities / cm2V-1min-1 Number of theoretical plates M1 Cl- 3.727 0.06667 -0.06660 17310 NO3- 3.777 0.04500 -0.06571 39030 BrO3- 3.695 0.06083 -0.06717 20440 M2 Cl- 4.010 0.09167 -0.06190 10600 NO3- 4.042 0.05000 -0.06141 36200 BrO3- 3.995 0.08250 -0.06213 12990 M3 Cl- 5.323 0.07917 -0.04663 25040 NO3- 5.388 0.06417 -0.04607 39060 BrO3- 5.282 0.1033 -0.04699 14480
The migration order of anions and the significance of the theoretical plates shall be discussed in the “Discussion” section.
Discussion
Capillary electrophoresis separates analytes according to their different mobilities. Typically, the solutes being analysed are charged ions and are separated based on their differing charges and sizes.
On introduction of the sample into the capillary, all the ions will move in the same direction due to osmotic flow. However, each ionic species would have different rates of migration due to their different electrophoretic mobility. A detector – a UV/VIS detector in this experiment – is placed at the end of the capillary. A UV/VIS detector is appropriate only if the analyte has chromophores which are able to absorb UV/VIS light. Although the anions used in this experiment are colourless, the addition of a buffer solution containing K2Cr2O7 into the solution creates a high UV background. When the analyte of interest is moved pass the detector, a drop in the absorbance (in the form of an inverted peak) would be observed, as the analyte would prevent the absorbance of UV light by the buffer solution.
The data is obtained in the form of an eletrophoregram, in which the separated compounds are displayed as peaks with different migration times. The area of each peak indicates the amount of the particular ion being analysed.
The unknown concentration of Cl- ions in U1 was determined by comparing its peak area to the equation of the calibration curve plotted using the values from the standard solutions prepared. It was assumed that the concentrations of the standard solutions used to plot the calibration curve lie well within the linear dynamic range. Since the graph of best fit suggests a linear relationship with a good R2 value, then this assumption is taken to be valid. Using this comparison with the calibration curve, it was determined that the Cl- concentration of the unknown sample measured was 56.79ppm, and the Cl- concentration in the stock solution was 567.9ppm.
In the quantitative analysis of anions, all three anions (Cl-, NO3- and BrO3-) have the same magnitude of charge. Thus, their mobility would only be differentiated by their relative sizes. It is expected that Cl- would move fastest, followed by NO3- and lastly by BrO3-. This expectation is reasonable, and is found to agree with experimental results. By comparing the concentrations of the anions used in the three solutions, and their peak areas observed, the peaks could be identified to the anion. The experimental results confirm that Cl- had a mean retention time of 3.733min, NO3- had a mean retention time of 4.016min and BrO3- had a mean retention time of 5.331min.
Statistical calculations and precision of experiment
Accuracy is a description of how close the measured value is to the true value of the measured quantity. Precision refers to the reproducibility of the measured result. The difference between them is that precision is more concerned about getting the measurements close to each other, while they may not necessarily be centred about the true value of the item. Accuracy requires the measurements to have the average value of the measurements to be as close as possible to the true value. The precision of a set of readings is usually expressed in terms of its standard deviation from the mean of the set of readings.
In this experiment, the standard deviations and relative standard deviations were calculated for the three anion species. Comparing the standard deviation values for the anions, it was observed to be the largest for BrO3- and Cl- ions. This can be explained by the size of the anions. BrO3- ions are the largest anions analysed in this experiment. As BrO3- ions are heavier, they require more time to travel across the capillary and are more spread out in the capillary, causing a greater variation in the retention times.
All the RSD values were below 2%, suggesting good reproducibility of the migration times for these anions. The precision can be better determined if more replicates were obtained.
Migration order of anions
The mean migration time for Cl- ions was the fastest at 3.733mins, followed by NO3- ions at 4.016mins and lastly by BrO3- ions at 5.331mins. The comparison using total mobilities also showed the same order, with Cl- having the fastest mobility, and BrO3- the slowest.
The mobilities of the anions were affected by both the electrophoretic mobility and electroosmotic mobility. The electrophoretic mobility is mainly dependent on the charge of the analyte, since the frictional force is the same for all the analytes. The electroosmotic mobility is dependent on the charge density of the silanol layer of the capillary, as well as the ionic strength in the solution. As such, it is important to maintain the pH level in the capillary so as to ensure constant electroosmotic mobility.
Calculations on theoretical plates
The number of theoretical plates were calculated to be the highest for NO3-, followed by BrO3- and lastly by Cl- for the same concentration of 10ppm in all three solutions. The number of theoretical plates is determined by N = Ld2 / σ2, and σ is affected by the standard deviation. Since Cl- has the highest standard deviation, it was expected that it will have the lowest number of theoretical plates.
A large number of theoretical plates is desirable as this would give a better resolution of the peaks. A small plate height is also desirable to obtain a narrower bandwidth. According to the Van Deemter’s equation, H = A + B/u + Cu. In capillary electrophoresis, the “A” term is negligible since it is an open tubular column. As the mobile phase used is a gas, the mass transfer term “C” is also negligible. Thus peak broadening will occur mainly due to longitudinal diffusion term “B”.
Comparing with HPLC / ion chromatography, the columns used are packed with the stationary phase, and this will result in large value for the multiple path term, “A”. Also, time would be required to achieve equilibration between the stationary phase and the mobile liquid phase, thus having a large value for “C”. All in all, the plate height will be large for HPLC / ion chromatography compared to CE. Plate height is also given by H = σ2 / x, where σ represents the standard deviation and x is the longitudinal distance travelled. From this equation, it can be deduced that HPLC / ion chromatography will have a large standard deviation. Using the equation N = Ld2 / σ2, the number of plates on a HPLC / ion chromatography experiment is expected to be lower than that in CE given the same length of the column, since N is inversely proportional to standard deviation.
The broader band observed in HPLC than CE can also be explained by the hydrodynamic flow of the mobile phase in HPLC, compared to uniformed flow in electroosmosis. Their differences are illustrated in the following diagram (Figure 1).
 Figure 1: Illustration of electrosmotic flow and laminar flow [1]

In the hydrodynamic flow, the analyte moves at the fastest speed, while those at the wall of the column moves the slowest. This in turn gives a broad band. However, for electroosmosis, the uniformed movement of the analyte would mean that all the analyte would be eluted out at the same time, thus giving a sharper peak. Thus, the number of theoretical plates for CE would be higher than that of HPLC / ion chromatography.
Capillary electrophoresis is a very efficient method of analysing charged compounds. Only a small amount of analyte is required for analysis. Other advantages that CE has over ion chromotrography or Liquid Chromatography (IC or LC) include lower detection levels, ambient temperature to reduce sample degradation, shorter separation time and higher separation efficiency, make it an outstanding instrument for quantitative studies. However, it is unable to analyse neutral compounds, which must be analysed with HPLC.
Conclusion
The concentration of chloride in the unknown sample solution was determined using capillary electrophoresis to be 567.9ppm Cl-. The migration time of the anions in the anion mixtures was determined to be Cl- < NO3-< BrO3- . The % RSD for the anions were very small indicating that the results obtained were precise.

References
[1] IUPAC Compendium of Chemical Terminology, website:http://www.iupac.org/goldbook/H02723.pdf (Accessed 3rd September 2009)
[2] Whatley and Chapman,
Precision in Capillary Electrophoresis, Beckman Coulter Inc.
pg.1, website:
http://www.beckman.com/Literature/BioResearch/t1860a.pdf (Accessed 3rd September 2009)
[3] Skoog et. al., Fundamentals of Analytical Chemistry, 8th Edition, 2004 Brooks/Cole,
Glossary pg. G-1