Chemistry 155 Introduction to Instrumental Analytical Chemistry

Chem 155 Unit 1 Page 32 of 3131.9.1 Linear Least Squares CalibrationThe most common method for determining theconcentration of an unknown analyte is the simplecalibration curve.In the calibration curve method, one measures theinstrument signal for a range of analyteconcentrations (called standards) and develops anapproximate relationship (mathematically orgraphically) between some signal ‘S’ and analyteconcentration ‘C’.If the signal-concentration relationship is linear, then:S = S B + mC y = a + bxBut, one can not just draw the line between any twopoints because all the points have some error. So,one mathematically attempts to minimize theresiduals.χ 2 = Σ(y i – (a + bx i )) 21.51.5Instrument Signal (S)S iS iF i10.5F i10000 2 4 6 8 10Page 32 of 3130 C iAnalyte Concentration (C)