Calibration Methods

1
Chapter 5

• Calibration Methods

2
Calibration Methods

• Calibration Curve
• Standard Addition
• Internal Standards

3
Calibration Curve

• Graphs the instrumental response to
• Standard Solutions
• Analyte solutions of known concentrations
• Blank Solution
• Solution that contains all reagents and solvents
  except the analyte
• Negates effects caused by impurities and
  interfering species

4
Calibration Curve Construction and Use

• Prepare the standard solutions
• Varying concentrations of analyte
• Ideally incorporates the concentration of unknown
• Collect data for each of the standards
• 3 or more recommended
• discovery of inconsistent measurements
• Calculate the Corrected Absorbance value for each
  standard concentration
• Corrected Absorbance standard solutions average
  absorbance - blank solutions average absorbance

5
Calibration Curve Construction and Use

• Plot a graph of corrected absorbance values
  versus analyte concentration
• Obtain Calibration Curve
• Method of Least Squares
• Determinants

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Obtain Calibration Curve

• Method of Least Squares
• di2 (yi - y)2 (yi - mxi -b)2
• Determinants

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Calibration Curve Construction and Use

• Find the Uncertainties associated with the slope,
  y-intercept, and y (corrected absorbance)
• d(bar) - 0 for best straight line
• 2 degrees of freedom are lost in determination of
  slope and y-intercept

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Calibration Curve Construction and Use

• Find the Uncertainties associated with the slope,
  y-intercept, and y (corrected absorbance)

9
Calibration Curve Construction and Use

• Calculate the Uncertainty associated with the
  x-value
• Analyze the unknown

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Calibration Curve Example
Amount of Protein (?g)
Absorbance of Independent Samples
Range
Corrected Absorbance
m 0.01630 sm 0.00022 sy 0.0059
b 0.0047 sb 0.0026
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Standard Addition Method

• Unknown concentrations of analyte are determined
  via deduction obtained from the calibration curve
  resulting from adding quantities of known
  standards to unknown concentrations of analyte.
• Important when the sample composition is unknown
  or complex

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Standard Addition Curve Construction and Use

• Procedure 1
• Prepare samples to be analyzed
• Add the same quantity of unknown to each of
  several volumetric flasks
• Add varying quantities of known standard to all
  but one of the volumetric flasks
• Dilute all volumetric flasks to their mark

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Standard Addition Curve Construction and Use

• Analyze the samples
• Construct a graph using the data obtained

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Standard Addition Curve Construction and Use

• Construct a graph using the data obtained
• x-intercept of the extrapolated line is the
  concentration of the unknown Xf after it has
  been diluted to the final volume
• Method of Least Squares - construct the line
• uncertainty in x-intercept

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Standard Addition Curve Construction and Use

• Procedure - 2
• Sample 1
• Add a quantity of unknown to a volumetric flask
• Analyze the sample
• Sample 2
• Add a quantity of known standard to sample 1
• Analyze the sample
• Sample 3
• Add a quantity of known standard to sample 2
• Analyze the sample
• Additional Samples - repeat procedure for Sample
  3

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Standard Addition Curve Construction and Use

• Calculation of the standard solutions and the
  unknown are completed using

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Internal Standard

• Compares the intensity of the absorbance of an
  internal standard compared to that of the analyte
• Important when instrument response may vary
  slightly from one run to the next

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Internal Standard

• Preparation Procedure
• Prepare a sample of unknown analyte concentration
• Add an amount of known standard to the solution
• Analyze the sample
• Compare the area under each signal - Response
  Factor

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Chapter 5 - Homework

• Problems - 2, 7, 18, 21, 22