Chapter 5. Errors in Chemical Analysis 熊同銘.

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1 Chapter 5 Errors in Chemical Analysis 熊同銘 tmhsiung@gmail.com Slide 1 of 19 Contents in Chapter Accuracy, Precision and Bias 5.2 Types of Errors in Experimental Data 5.3 Systematic Error Slide 2 of 19 1

2 5.1 Accuracy, Precision and Bias Precise Imprecise Unbiased Biased Accurate = Precise + Unbias Slide 3 of 19 Which one is accurate? (A) (B) μ μ (C) μ (D) μ μ: true value Slide 4 of 19 2

3 Bias: A measure of how far the analytical result is from the true value caused by systematic error(s). Precision: A measure of how similar the replicate measurements to each other caused by random error(s), NOT how close to the true value. Accuracy: A combination of precision and bias, which describe the degree of agreement between the analytical result and the true value. Slide 5 of The mean and Median Mean x N i 1 N x i Median: The central value in a set of replicate measurements. (for even number of data points, the median is the average of central pair) * The median is used advantageously when a set of data contain an outlier, a result that differs significantly from others in the set. Slide 6 of 19 3

4 5.1.2 Evaluation of Precision Standard deviation (s) s N i 1 ( x x) i N 1 2 Relative standard deviation (RSD) (also called coefficient of variation, CV): s RSD 100% x Variance (v) v = s 2 Slide 7 of Evaluation of Accuracy Absolute error E x i x t x t : true or accepted value Relative error E r x i x x t t 100% Slide 8 of 19 4

5 5.2 Types of Errors in Experimental Data Systematic (Determinate) error: Errors that have a known source, they affect accuracy, measurements in only one way(either positive or negative). It can be avoided, detected, and corrected. (Section 5.3) Random (Indeterminate or Statistic) error: Uncertainties resulting from fluctuation of uncontrolled variables and it can not be attributed to any cause. (Chapter 6) Gross error: An occasional error, neither random nor systematic, that results in occurrence of a questionable outlier result. Slide 9 of Systematic Error Sources of Systematic Errors (1) Instrumental errors: caused by nonideal instrument behavior, by faulty calibrations, or by use under inappropriate conditions. For example: A 100 ml volumetric flask, which exact volume is ml.. Slide 10 of 19 5

6 (2) Personal errors: result from the carelessness, inattention, or personal limitations of the experimenter. For example: The ability to see a change in the color of an indicator at the end point of a titration. Consistently overestimating or underestimating the value on an instrument s readout scale. Failing to calibrate glassware and instrumentation. Misinterpreting procedural directions. Slide 11 of 19 (3) Method errors: arise from nonideal chemical or physical behavior of analytical systems. Classical analytical method for example: More or less excess of titrant required for color change in titrimetry by indicator (titration error). Instrumental analytical method for example: S meas = kc A + S blank - Sensitivity (proportionality constant), k, may be incorrect because of the matrix interferences. - Reagents impurities and contamination may introduce the signal of blank (S blank ). Slide 12 of 19 6

7 5.3.2 The Effect of Systematic Errors on Analytical Results Constant (systematic) error: Those systematic errors they are independent of the size of the sample being analyzed. Proportional (systematic) error: Those systematic errors they decrease or increase in proportion to the size of the sample being analyzed. Slide 13 of 19 (1) Method errors on Instrumental analytical method for example: S meas = kc A + S blank - the blank signal, S blank, is an example of a constant determinate error. - The proportionality constant k may be affected by proportional errors. * Blank determination: The process of performing all steps of an analysis in the absence of analyte. Blank determinations reveal errors due to interfering contaminants from the reagents and vessels employed in the analysis. * Sample matrix: The whole constituents of the sample other than analyte. Difference in sample matrix may affect the proportionality constant. Slide 14 of 19 7

8 (2) A simulation of constant error and proportional error Theoretical estimation of constant error Theoretical estimation of proportional error Slide 15 of Detecting and Minimizing Systematic Errors (1) For Instrumental Errors: Periodic calibration of the equipment (2) For Personal Errors: check instrument readings, notebook entries, and calculations systematically. carefully choosing the analytical method or using an automated procedure. self discipline with the assistance of duplicate analysis and interlaboratory comparison. Slide 16 of 19 8

9 (3) For Method Errors: Analysis of standard reference materials (SRMs) Independent analysis with another reliable method Analysis with the variation in sample size Blank determination Spike analysis Slide 17 of 19 Homework (Due 2018/10/4) 1. Explain the difference between (a) precision and accuracy (b) random error and systematic error (c) constant error and proportional error (d) absolute error and relative error (e) mean and median 2. Name three types of systematic error. 3. Describe at least three examples of systematic errors that might occur while weighing a solid chemical on an analytical balance. 4. Describe at least three examples of systematic errors that might occur while using a pipet to transfer a known volume of liquid. 5. The color change of a chemical indicator requires an overtitration of 0.03 ml. What is the smallest volume of titrant such that the relative error is less than 0.1%? Slide 18 of 19 9

10 End of Chapter 5 Slide 19 of 19 10