Data Analysis and Presentation

1. Data Analysis and Presentation • Chapter 5- Calibration Methods and Quality Assurance EXCEL – How To Do 1- least squares and linear calibration curve/function (chapter 4) 2- standard addition (chapter 5) 3-internal standard (addition) (chapter 5)

2. CHAPTER 05:Opener B

3. CHAPTER 05:Unnumbered Figure 5.1

4. CHAPTER 05:Table 5.1

5. Calibration function Q: How the selected instrument responds to the change in quantity (concentration, M ppm ) of the measured analyte? A: Measure the instrument responses (peak hights, peak areas etc.) from known but different concentrations of the analyte (say 0, 5,10, 15 20 ppm standards). Then construct the response diagram figure (response vs. concentration) with the response or calibration function through the points.

6. OLD SLIDE: Caffeine again: first step calibration If points are out of line: error If one assumes that the calibration curve is linear – there are physical reasons for that. There is a linear function that can best represent the response of the instrument. There are methods based on the propagation of error that can help us calculate the best fit: linear regression of the straight-line calibration curves

7. Liner vs. nonlinear

8. CALIBRATION: Instrument used to measure signals must be calibrated, must have the calibration relation. Example (linear): y = m [x ]+ b (general algebraic form for linear equation) Often given in other similar forms: Smeasured(total signal) =k nA (concentration) + Sreag ( signal from reagents, from blank) Calibration is the determination of that relation: it is used for the determination of analyte by using standards and blanks to determine a relationship (function) between concentrations and assay responses.   Validationimplies that other labs have approved the analytical method of analysis and produced similar results. Standardsare materials containing accurately known concentrations of the desired analyte. Standardization is the process of determining relationship between the measured signal and the amount of analyte (fittting for k in linear relations). Blanksare solutions containing all added reagents except the sample analyte.(method, reagent and field blanks) Controlscan be an alternate sample, in which the contents are well known. Primary and Secondary reagents

9. similar expressions that you could find: SA(signal due to analyte) =k nA (moles of analyte) Smeasured(total signal) =k nA +Sreag ( signal from reagents, from blank) Smeasured(total signal) =k nA +Sreag + SI( signal from interferents) Total analysis technique & Concentration techniques SA(signal due to analyte) =k CA (concentration of analyte) Calibration Language: -Accuracy, precision, sensitivity, selectivity, detection limits, noise -Robust and rugged method -Scale of operation (analytes classification )

10. Concentration of Standard '=' Signal of Standard Concentration of sample Signal of sample OK , if physics of the response process for that instrument is linear, that is the more analyte you have the higher the signal, how can we get that calibration function: Answer 1: One point standard: Answer 2: Rather than do a one point determination, we run a series of standards (of known concentration) and then relate their signals to the signal of the unknown sample to find its concentration. Example: We have an analytical instrument available for a chemical analysis. We prepare a blank and a series of external analyte standards (solutions of known analyte concentration). We monitor and record their instrumental signal response. From this information, we prepare a calibration curve plot. Next, we run the unknown sample and record its signal response. Finally we use the calibration curve to find the analyte's concentration Note: External standards are not added to our unknown samples!!!

11. Calibration Answer 1: Function from single point standardization -and its domain: not the best !!!

12. Calibration Data: Answer 2

13. FYI: Uncertainty: Finding the best calibration function from the data: linear regression

14. If one assumes that the calibration curve is linear – there are physical reasons for that- there is linear function that can best represent the response of the instrument. If points are out of line: error There are methods how to calculate the best fit: linear regression of straight-line calibration curves

15. (1) EXTERNAL STANDARD (standard is not added to the sample) We can run a series of standards (of known concentration) and then find the relationship We can use that relationship to relate the signal of an unknown sample to find its concentration. We can use EXCEL program for that. Example 1 We are trying to determine the concentration of an unknown Fe+2 solution. We have prepared several Fe+2 solutions of known concentration to be used as known standards. We record and plot the concentration and absorbance data for all Fe+2 solutions and unknown solution. We zeroed the standards with the blank to get the net absorbance. # Absorbtion S measured(units) Concentration C (ppm) 1 0.016 1.00 2 0.056 2.00 3 0.110 3.50 4 0.160 7.50 5 0.430 10.00 unknown reading = 0.119 (What is the concentration of this solution??)

16. MFYI: Method of Least Squares/Linear regression The method of least squares assumes that the errors in the y values are substantially greater than the errors in the x values. A second assumption is that the uncertainties in all of the y values are similar. Derivation of the Least Squares Method (Equation for a straight line) y = mx + b Vvertical deviation = dii = yi–y = yi–(mxi+b) SSome of the deviations are positive and some are negative. To minimize the magnitude of the deviations irrespective of their signs, we square the deviations to create positive numbers.

18. We will see that the error behavior of individual points is also important!

19. Back to the example 1 NOTE : There is an “outliner” this is due to the systematic error, maybe the dilution of the standard stock solution was not prepared well in this flask—TAKE IT OUT!!! How to get the correlation function using least square based linear regression: Use Excel!

20. Excel: this works!! Using Exel trend line

21. A spreadsheet for Least Squares: A more detailed analysis in Excel • Example LSQ fit

22. CHAPTER 04:Unnumbered Table 4.3

23. CHAPTER 04:Unnumbered Table 4.4

24. CHAPTER 04:Figure 4.12

25. CHAPTER 04:Table 4.7

26. CHAPTER 04:Figure 4.13

27. CHAPTER 04:Figure 4.14

28. CHAPTER 04:Equation 4.27

29. CHAPTER 04:Figure 4.15

30. CHAPTER 04:Figure 4.16

31. CHAPTER 04:Unnumbered Table 4.5

32. CHAPTER 04:Unnumbered Table 4.6

33. Is such external standardization the only way to calibrate and acquire the accurate and precise values? • No, there are also other methods that include addition of analyte or some other material into the sample (aliquot)

34. Possible problems with external standardization

35. Spike • Sometimes (often) the response to analyte is affected by something else in the sample, which we call MATRIX. • SPIKE is a known quantity of analyte added directly to the sample to verify if the response to analyte is the same as that expected from pure sample observed in the calibration curve.

36. 2. Standard addition SStandard addition: Known quantities of analyte are added to the unknown, and the increased signal lets us deduce how much analyte was in the original unknown. Typically we use the method of standard addition when unknown sample matrixis sufficiently complex. The blank and standards are not representative of the unknown sample and lead to analysis error. This method requires a linear response to analyte. For a single spike, one trial [X]i / [X]f + [S]f = Ix / I s+x [X]i = unknown initial concentration of analyte Ix = signal from first solution [S]f = concentration of standard in second solution [X]f = diluted concentration of analyte I s+x = signal from second solution

37. CHAPTER 05:Equation 5.7

38. EExample 2 A blood serum sample containing sodium ion gives a signal of 4.27 mV on a light intensity meter in an atomic emission experiment. The Na+ concentration in the serum is then increased by 0.104 M by a standard addition, without significantly diluting the sample. This "spiked" serum sample gives a signal of 7.98 mV in atomic emission. Find the original concentration of Na+ in the serum.  [X]i = unknown initial concentration of Na+ Ix = 4.27 mV [S]f = 0.104 M [X]f = diluted concentration of analyte = [X]i I s+x = 7.98 mV [X]i = 0.120 M

39. FYI: (2) Sampledirect addition S sample = S spike a b a b

40. FYI: Accurate description (1)Sampleseparate aliquots (portions) S sample = S spike a b Ssample = signal sample CS= concentration spiked CA= concentration analyte a b

41. Example 3. WWe use standard addition methods when our sample has matrix effects which are hard to duplicate in a blank. Let's again find the amount of Pb+2 in a blood sample. A 5.00 mL blood sample containing lead yielded a signal of 0.712 units. Afterwards, the sample was spiked with 5.00 L of 1560 ppb Pb+2 standard. (note: a small addition) This spiked solution gave a reading of 1.546 units. Find the concentration of Pb+2. [X]i / [X]f + [S]f = Ix / I s+x or [C]i / [C]f + [Cs]f = Sx / S s+x Be careful with volume! CA=1.33ppb

42. CHAPTER 05:Figure 5.7

43. FYI: Standard addition: How to work with many points: FIT -EXCEL from previous multipoint figure : many points  fit Graphic treatment (standard additions plot), alternatively we can perform a series of additions and plot the signal response verses spiked concentration and extrapolate to find the initial concentration. Note, we can plot the x-axis as concentration of spike or as the concentration of spike with dilution.

44. CHAPTER 05:Figure 5.8

45. FYI: Similar: multipont, For standard addition(s)

46. Volume of spike added, mLs Signal , units 0.0 0.119 0.10 0.231 0.20 0.339 0.30 0.442 FYI: Standard addition - Example 4 A 5.00 mL sample solution containing an unknown amount of analyte was analyzed and then a series of spikes was added to the sample. The unknown solution was analyzed after each addition. The concentration of the standard used for the spikes was 400.0 ppm. The readings and respective spikes are shown: so for y=0, x=.1212/1.077=0.1125mL (x axis is volume in mL) By using, Conc of unknown => (0.1125mL)X(400 ppm) = (5.00 mL)(Conc?) answer = 9.003 ppm

47. Conc(Cfinal) Absunits mLs added Vfinal ppm(added) ppmadded / Vf 0.00 0.105 0.00 0 0.04 0.212 0.100 50.1 2 0.0399 0.08 0.409 0.200 50.2 4 0.0797 0.12 0.671 0.300 50.3 6 0.119 0.20 0.890 0.500 50.5 10 0.198 x = 0.021 ppm in unkn conc of std = 20ppm ( all same conc) FYI: Standard additions example –5 : (the x-axis as the concentration of spike with dilution) This time we have enough sample solution to make several standard addition solutions. We remove five 50 mL aliquots, we read one without a spike. Then we add successive amounts of 20.0 ppm standard to the rest and determine their signal. We plot signal verses the final concentration of standard solutions.

48. X=.0903/4.201 Solve for X intercept! X= 0.021 ppm

49. 3. Internal Standard • In addition to the analyte you measure add another similar compound (not analyte ) that has similar response ( sensitivity ) as the analyte.

50. Internal Standard is sometimes added to an unknown sample. The reason may be to verify the signal response in situations where instrument response varies slightly from run to run. For example, an analysis is preformed on different days or different instruments or under different operating conditions. Typically, the internal standard resembles the analyte. Let's say we are separating isomers of octane and determining their concentration on a gas chromatograph (GC). To verify how much is present we might add a known amount of cyclohexane as an internal standard