CHAPTER 2

• Analyte


  Substance measured
• Determination


  Process of measuring the analyte - identity, concentration, properties of analyte
• Matrix


  All other constituents in a sample except for the analytes
• The general analytical problem

  1. Select sample

  2. Extract analyte(s) from the matrix

  3. Separate the analytes

  4. Detect, identify and quantify analytes

  5. Determine reliability & significance of results
• Impossible to eliminate errors. Data of unknown quality are useless!
• Replicate


  • Every measurement is influenced by many uncertainties which can reflect the experiment
  • Carry more than 1 (replicate) sample through an entire analytical procedure to provide more reliable data
  • Replicates are samples of about the same size that are carried through an analysis in exactly the same way
• Accuracy


  Degree of agreement between the measured value and the true value, μ
• Precision


  • Degree of agreement between replicate measurements of the same quantity
  • An indication of reproducibility of a measurement/result
• Good precision does not assure/imply good accuracy because there might be systematic error in analysis
• It is nearly impossible to have accuracy without good precision
• Absolute error


  Measured value - True value
• Relative error


  Absolute error / True value x 100%
• Relative accuracy

  Measured value / True value
• Mean (X)


  Numerical average for a data set
• Median (M)


  Estimation of the central value when the data was ordered from the smallest to the largest value
• Standard Deviation (S)


  Indication of precision of analysis, describes the spread of a data set's individual values about its mean
• Variance (S^2)


  The square of the standard deviation
• Relative Standard Deviation (RSD) or Coefficient of Variation (CV)


  Standard deviation / mean x 100%
• Repeatability


  The precision for an analysis in which the only source of variability is the analysis of replicates samples
• Reproducibility


  The precision when comparing results for several samples, for several analysts or several methods
• Types of errors


  • Systematic errors
  • Random errors
• To determine error of a method

  1. Analysis of standard sample

  2. Independent analysis
• Significant figures


  The minimum number of digits needed to write a given value in scientific notation without loss of accuracy
• Random errors are errors that are unpredictable and can only be avoided when method condition is altered. For example incomplete reaction, impurity in reagent.
• Instrumental uncertainty


  • Changes in the environment during the experiment (such as change in the room temperature/humidity)
• Personal uncertainty


  • Observer misinterpreting the volume of a pipette or burette
• Method uncertainty


  • Insufficient data (not conducting repeat trials)
• Random errors cannot be eliminated but can be reduced by conducting repeat trials. (e.g. using volumetric pipette rather than a beaker to measure volume)
• To determine error of a method

  • Analysis of standard sample
  • Independent Analysis
• Significant figure


  The minimum number of digits needed to write a given value in scientific notation without loss of accuracy
• Significant figure


  The number of digits necessary to express the results of a measurement consistent with the measured precision
• Rules for counting significant figures

  • All non-zero digits are significant
  • All zeros between non-zero digits are significant
  • All zeros at the left of the number are not significant
  • When zeros are at the right of the number: if there is no decimal, the zeros are NOT significant; if there is a decimal, the zeros are significant
• Significant figures


  • 92067 µm, 9.2067 cm, 0.92067 dm & 0.092067 m
• Rules for multiplication and division

  • Find out the operator with the least significant figure ~ key number
  • If > 1 operator with same low significant figure, find the one with the greatest uncertainty ~ key number
  • If the operator with the least significant figure without decimal point, one additional figure may be carried in the answer written as subscript to express the minimum degree of uncertainty (to indicate doubtful)
• Multiplication and division


  • 42.67 & 0.0967 (3 significant figure)
  • 100.0 (greater uncertainty) & 0.4570
  • 42.68 x 891 / (132.6 x 0.5247) = 546.6
  • 22.91 x 0.152 (3 significant number) = 16.302 = 0.21361 = 0.214
• Rules for addition and subtraction


  • The answer is known to the same number of decimal place as the number containing the least significant unit
• Addition and subtraction


  • [97.7 x 100.0 / 32.42] + 36.04 = 687 = 301.4 + 36.04 = 337.4 = 0.49118 = 0.491
• Logarithms: Keep the result as many digits to the right of the decimal point as there are SF in the original number
• Antilogarithms: Keep the result as many digits as there are digits to the right of the decimal point in the original number
• Rounding off rules


  • If the last significant figure >5, the number is rounded up to the next higher digit
  • If the last significant figure <5, the number is rounded up to the present value of the last significant figure
  • Always round to the even number if the last digit is a "5"