1. Lecture 3 Calibration and Standards

2. The points (1,2) and (6,5) do not fall exactly on the solid line, but they are too close to the line to show their deviations. The Gaussian curve drawn over the point (3,3) is a schematic indication of the fact that each value of y is normally distributed about the straight line. That is, the most probable value of y will fall on the line, but there is a finite probability of measuring y some distance from the line. Least-squares curve fitting Carl Friedrich Gauss in 1795

3. Least squares:

4. y=kx+b straight line equation

5. k = Slope =  y /  x b - blank! Let us subtract blank: y-b = Y = kx y=kx+b straight line equation Y 1 =kx 1 Y 2 =kx 2 One standard

6. Procedure: 1.Measure blank. 2.Measure standard. 3.Measure unknown. 4.Subtract blank from standard and from unknown. 5.Calculate concentration of unknown If you have several (N) standards, do it several (N) times

7. Standard addition: Why and when? Matrix (interfering components) can affect the slope In equation Y=kx you do not know k any more !

8. Use your sample as a new “blank”: Add a known amount to your sample XX + standard IxIx I x+standard Increase in intensity: because of this addition I x+standard – I x

9. Procedure: 1.Measure unknown. 2.Add a known amount to the unknown and measure this sample. 3. Subtract (2) from (1). 4. Calculate concentration of unknown If you have several (N) standard additions, do it several (N) times

11. Internal Standard Why and when? All intensities vary from sample to sample Sample 1 x s Sample 2 0.6x 0.6s Sample 3 1.2x 1.2s No reproducibility! Let us divide intensity in the first column by the intensity in the second: Sample 1 x s x/s Sample 2 0.6x 0.6s x/s Sample 3 1.2x 1.2s x/s Now they are the same!

12. Restriction: you need to measure 2 values simultaneously You may prefer to have the same amount of internal standard in all your samples Procedure: 1. Add equal amounts of the internal standard to all your standards and analytes. 2. Measure intensities of your target compound (atom) and your internal standard in your solutions. 3. For each pair of measurements, divide the intensity coming from your target compound by the intensity of the internal standard. 4. Process these new “normalized” intensities like you did before.

13. Good Plot! Bad plot! One VERY BAD point: Y = 1.5 x + 1 Least squares does not work?

14. b= 0.3; 1; 1 k = 2.33, 1.5; 1.50 Median: Y = 1.5 x + 1 A possible solution: “robust”

15. Straight line Any function Weighed least squares