Class Notes (808,548)
Chemistry (260)
ENCH 213 (25)
Lecture

7leastsquares.pdf

5 Pages
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School
Queen's University
Department
Chemistry
Course
ENCH 213
Professor
Diane Beauchemin
Semester
Fall

Description
The Method of Least Squares • used to find the best straight line through a set of experimental points • appropriate for most analytical techniques Finding the slope Assumptions • linear relationship between y (signal) and x (analyte concentration): y = mx + b ◦ where b=intercept and m=slope of calibration curve (aka sensitivity) • any deviation of individual points from the straight line results from error in the measurement ◦ i.e. negligible error in x values of the points ◦ usually true if standards are prepared with care: their concentration is known exactly Origin of the method of least squares • the vertical deviation of each point from the straight line = residual d = y – y i i = y i (mx +bi ◦ where y=ordinate of the calculated straight line corresponding to x=x • d'i can be positive and/or negative ◦ to minimize their magnitude irrespective of their sign → use di = (y - y) = (y2- mx -i) 2 i i 2 • minimizing the squares of the residuals = Method of Least squares “Best” straight line • Slope = m = = sensitivity • intercept = b = • standard deviation of the vertical deviations: • standard deviation of the slope = s = m • standard deviation of the intercept: = s = b Calculations Blanks • Reagent blank: contains all the reagents and solvents used in the analysis • Method blank: contains all the reagents and solvents used in the analysis and is taken through all steps of the analytical procedure • Field blank: method blank that has also been exposed to the sampling site Q: Which of the following is untrue regarding a blank solution? a) Solutions containing known concentrations of analyte are called blank solutions. b) A solution containing all of the reagents and solvents used in the analysis and no deliberately added analyte is called a blank solution. c) Ablank solution measures the response of the analytical procedure to impurities or interfering species in the reagents. Which of the following is true regarding a blank in an analysis? a) Amethod blank is a sample containing all components except the analyte and is taken through all steps of the analytical procedure. b) Afield blank is a sample containing all components except the analyte and is taken through all steps of the analytical procedure. c) Areagent blank is the same as a method blank; that is, it has been taken through all of the steps of the analytical procedure. Building and using calibration curves • Analyse blank solutions. • Analyse a series of standard solutions whose concentrations encompass those expected in the samples. → 0.5-1.5 x expected analyte concentration • Analyse the sample solutions (with calibration check). • Subtract the blank signal from that of all samples and standards. • Apply the method of least squares to find the equation of the best straight line for the standards. • Apply the equation to the samples. Propagation of uncertain
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