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Unformatted text preview: Calibrating Instruments I. Calibration Curves: A. determine the response of an instrument to some measured property 1. Measure the response of instrument when one varies the concentrations of species of interest 2. Hopefully the response will be linear with regards to concentration of species being looked out. 3. Finding the best fit line to represent the instrumental response a. eye balling the best fit line - generally not too bad a response b. mathematically determining the best fit line - method of least squares fitting 1) assumptions of method x values are very good with no uncertainties y values - the uncertainties are about the same in all values 2) best fit line is determined when (y calc- y exp ) 2 is minimum c. derivation: let Q = (y calc- y exp ) 2 is minimum y = a + bx; so Q = [y - (a + bx)] 2 is minimum to find minimum Q/ a + Q/ b = 0 Q / a = -2 [y - (a + bx)] = 0 Q / b = -2 x [y - (a + bx)] = 0 Q / a = -2 [y - (a + bx)] = 0 y = na + b x a = 1/n( y - b x) Q / b = -2 x [y - (a + bx)] = 0 xy = a x + b x 2 b = ( xy - n xbarybar)/( x 2-nxbar 2 ) or m =(n (xy) - x y)/(n (x...
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- Spring '08