Henry Su December 12, 2001Errors in Chemical Analyses: Assessing the Quality of Results5A—Defining Terms5B—Systematic ErrorsHenry Su December 12, 2001Chapter Notes Chemistry 221Chapter 5 Dr. RahniErrors in Chemical Analyses: Assessing the Quality of Results-It is impossible to perform a chemical analysis in such a way that the results are totally free of errors or uncertainties. We can only hope to minimize these errors and estimate their size with acceptable accuracy.-Every measurement is influenced by many uncertainties that combine to produce a scatter of results-Measurement uncertainties can never be completely eliminated, so the true value for anyquantity is always unknown. However, the probable magnitude of the error in a measurement can often be evaluated. It is then possible to define limits within which the true value of a measured quantity lies at a given probability.-It is seldom easy to estimate the reliability of experimental data. Nevertheless, we must make such estimates whenever we collect laboratory results because data of unknown quality are worthless!5A—Defining Terms-5A-1 The Mean and the Median-Mean, arithmetic mean, and average are synonyms for the quantity obtained by dividing the sum of replicate measurements by the number of measurements in the set.-The median is the middle result when replicated data are arranged in order of sizeExample: Calculate the mean and the median for this set of data [(19.4) , (19.6) , (19.5) , (19.8) , (20.1) , (20.3)]mean = (19.4+19.5+19.6+19.8+20.1+20.3) = 19.78 6median = (19.6+19.8) = 19.7 6-5A-2 What is Precision?-Precision describes the reproducibility of measurements, or the closeness of the results that have been obtained in exactly the same way.-Three terms are widely used to describe the precision of a set of replicate data-Standard Deviation, Variance, and Coefficient of Variation-All above terms are a function of the deviation from the meandI = | xi – x |-5A-3 What About Accuracy?-Accuracy indicates the closeness of the measurement to its true or accepted value and is expressed by the error.-Note that the basic difference between accuracy and precision is that accuracy measures agreement between a result and its true value, while precision describes the agreement among several results that have been obtained in the same way.-We may determine precision just by replicating or repeating a measurement, but we can never determine accuracy exactly because a true value of a measured quantity can never be known exactly.-Accuracy is expressed in terms of either absolute or relative error.-Absolute error-The difference between the accepted and experimental resultsE = Xi - Xt-Relative Error-Absolute error divided by the accepted valueEr = Xi - Xt x 100 Xt-5A-4 Classifying Experimental Errors-Random, or indeterminate error, causes data to be scattered more or less symmetrically around a mean value, and affect the precision of measurement.-Systematic, or determinate error causes the mean of a set of data to differ from the accepted value.-Gross error usually only occur occasionally, are often large, and may cause a result to be either high or low-Lead to outliers, results that appear to differ markedly from all other data5B—Systematic Errors-Systematic errors have a definite value, an assignable cause, and are of about the same magnitude for replicate measurements made in the same way-Lead to bias in measurement technique-Affects all the data in a set in approximately the same way and bears a sign-5B-1 How Do Systematic Errors Arise?1-Instrument errors are caused by imperfections in measuring devices and instabilities in their components-differences in calibration, distortion in container walls, etc.2-Method errors arise from nonideal chemical or physical behavior of analytical systems-slowness or incompletion of reactions, instability of certain species, etc.3-Personal errors result from the carelessness, inattention, or personal limitations of the experimenter-estimation errors, observation errors, etc.-5B-2 What Effects Do Systematic Errors Have on Analytical Results?-Systematic errors may either be constant or proportional-The magnitude of a constant error does not depend on the size of the quantity measured-Proportional errors increase or decrease in proportion to the size of the sample taken for analysis-A common source of proportional errors is the presence of interfering contaminants in the sample.Example: Suppose that 0.50 mg of precipitate is lost as a result of being washed with 200 mL of wash liquid. If the precipitate weighs 500 mg, the relative error due to solubility loss is –(0.50/500) x 100% = -0.1%. Loss of the same quantity from 50 mg of precipitate results in a relative error of –0.1%.-5B-3 Detecting Systematic Instrument and Person Errors-Systematic errors are usually found and corrected by calibration-Most personal errors can be minimized by care and self-discipline-5B-4 Detecting Systematic Method Errors-Bias in method is particularly difficult to detect. Use the following steps to help.1-Analyzing Standard Samples-The best way to estimate the bias of an analytical method is by analyzing standard reference materials, materials that contain one or more analytes atwell-known or certified concentration levels2-Using an Independent Analytical Method-The independent method should differ as much as possible from the one under study to minimize the possibility that some common factor in the sample has the same effect on both methods3-Performing Blank Determinations-Blank determinations are useful in detecting certain types of constant errors-In a blank, all steps of the analysis are performed in the absence of a sample. The results from the blank are then applied as a correction to the sample measurements.-Reveal errors due to interfering contaminants from the reagents and vessels employed in analysis4-Varying the Sample Size-As the size of a measurement increases, the effect of a constant error decreases. Thus, constant errors can often be detected by varying the sample