Calibration Curve

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Calibration Curve

• Purpose To determine specific analyte
  concentration (amount) from signal, detector
  response, intensity, A, etc.
• Step 1 Measure response to a set of known
  concentrations ? equation or plot
• Step 2 Measure response to sample ?
  concentration (amount) from plot or eqn

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Calibration Process

• Standards prepared by serial dilution
• For each analyte of interest
• Multiple measurements (either a different
  concentration or at selected concentrations)
• Blank (typically reagents alone) can give a
  blank correction

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Characteristics

• Range lowest concentration to highest
  concentration (validity)
• Linear Range data fit by y mx b

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Objective

• To obtain sample(s) concentration from measured
  signal
• 1. Analyte value
• 2. Uncertainty in analyte value

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Absorbance Signal

• Transmittance T I/I0

?
? ?      
I0
I
Light Source h?
Sample cuvet
Monochromator
Detector
? b ?
A log10 (I0/I) - log T A ebc (Beers
Law) e molar absorptivity c M
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Least Squares Fit

• Set of n yi and xi values
• di yi mxi b
• D

?(xi2 ) ?xiyi ?xi n
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• Because average di 0 (?di 0),
• sy (di d)2
• deg of freedom
• (di)2 / (n-2)
• sm2 nsy2 / D and sb2 sy2
  (xi2)
• 
  D
• (y sy) (m sm) x (b sb)

½
S

_________

½
S
S
_________
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Linear Equation

• S signal (corrected for blank)
• M molarity x 106
• S 37.0 (13.997 0.031)M (112.34 20.02)
• or
• M S - (112.34 20.02)/ (13.997 .031)

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Uncertainty in Sample M

• If sample is measured and signal is 8888, what is
  sample M and uncertainty?
• x (y - b)/m
• (8465 37) (112 20)/(14.00 0.03)
• so M 567 x 10-6
• and sM 0.549 or sM 3 x 10-6

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Correction m and b dependent

• sx sy 1 x2n (xi2) - 2x xi
  
• m k D
• (k is the number of unknown
  replicates)
• 1.2 x 10-6 (compared with 3 x 10-6 before)

S
S
½

___
_
____________________
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Summary of Process

• Prepare standard solutions and blank
• Measure response to standards (corrected for
  blank)
• Prepare/calculate graph/equation
• Measure response to sample(s)
• Calculate analyte value and uncertainty