Chemical Analysis Measurement Techniques

2.4.2 Purpose of Replicate Measurement in Chemical Analysis

  • Replicates Defined:

    • Samples of similar size analyzed in nearly identical conditions.

  • Purpose of Replicates:

    • Improve reliability of measurements.

    • Provide information regarding variability of results.

  • Measurement Terms:

    • Accuracy: Closeness to true value, expressed in terms of error.

    • Precision: Reproducibility of measurements.

  • Carrying Out Replicates:

    • Typically, 2 to 5 portions of a sample are analyzed through the same procedure.

Central Value in Measurements

  • Mean and Median:

    • Individual results are often different; the best estimate is the central value.

    • Mean:

    • Also called the arithmetic mean or average.

    • Calculated as:
      T = \frac{\Sigma X_i}{N}

      • Where:

      • \Sigma x_i signifies the sum of all values.

      • N is the number of replicate measurements.

    • Median:

    • Middle value when data is ordered numerically.

    • Advantageous in the presence of outliers (results differing significantly from others).

    • Outliers affect the mean but not the median.

Understanding Precision and Accuracy

  • Precision:

    • Agreement among results obtained using the same measurement process.

    • Demonstrated through repeated measurements on replicate samples.

    • Quantified as standard deviation, variance, or coefficient of variation.

  • Accuracy:

    • Closeness of measurement to true value, expressed by the error.

    • Measures agreement between result and accepted value; harder to determine as true value is typically unknown.

    • Expressed in absolute or relative terms.

  • Targets Illustration:

    • Targets demonstrate the relationship of precision and accuracy:

    • Target A: Neither precise nor accurate.

    • Target B: Precise but not accurate.

    • Target C: Accurate but not precise.

    • Target D: Both precise and accurate (ideal case).

  • Error and Uncertainty:

    • Experiments have inherent uncertainty; it is critical to identify and evaluate errors in measurements.

2.4.3 Types of Error in Chemical Analysis

  • Three Main Types of Error:

    1. Random error (Indeterminate error)

    2. Systematic error (Determinate error)

    3. Gross error

1. Determinate (Systematic) Errors

  • Definition:

    • Errors that consistently displace measured mean value \bar{x} from true mean \mu in a specific direction.

    • Influenced by significant mistakes, reproducible.

2. Indeterminate (Random) Errors

  • Definition:

    • Causes individual measurement values to scatter randomly around the mean \mu .

    • Results from uncontrollable variables; cannot be defined/eliminated.

3. Gross Errors

  • Definition:

    • Occasional, large errors that can cause results to differ significantly (outliers).

    • Often due to human errors; difficult to predict.

Detection and Elimination of Errors

Systematic or Determinate Errors

  • Types of Systematic Errors:

    1. Instrumental errors.

    2. Method errors.

    3. Personal errors.

1. Instrumental Errors

  • Caused by non-ideal instrument behavior, faulty calibrations, or inappropriate conditions.

  • Affected by external factors like noise, temperature, pH.

2. Method Errors

  • Result from non-ideal behavior of reagents and reactions, including:

    • Reaction slowness or incompleteness.

    • Instability of chemical species.

3. Personal Errors

  • Result from carelessness or limitations of the experimenter, often requiring personal judgment.

Minimizing Systematic Errors:

  1. Periodic calibration of equipment.

  2. Careful, disciplined laboratory practices.

  3. Systematic checking of instrument readings and calculations.

  4. Use of automated procedures when feasible.

Error Correction Techniques

  1. Blank Determination:

    • Analysis done under identical conditions without the sample to reduce reagent impurities.

  2. Independent Method of Analysis:

    • Parallel evaluations using different methods to minimize common error effects.

  3. Control Determination:

    • Use standard materials in experiments under identical conditions to reduce errors.

  4. Dilution Method:

    • Diluting samples to lower interference errors, ensuring analyte measurements remain consistent.

  5. Standard Addition:

    • Addition of known analyte amount to calculate concentration based on response changes.

  6. Internal Standard Method:

    • Adding reference species to all samples to compare analyte responses.

  7. Parallel Determination:

    • Conducting duplicate or triple analyses to reduce the likelihood of unintentional errors.

Performance Characteristics of Instruments

  • Figure of Merit:

    • A numerical evaluation derived from measurements to assess instrument performance.

    • Include criteria such as:

    • Accuracy

    • Precision

    • Bias

    • Sensitivity

    • Detection limit

    • Dynamic range