Analytical Chemistry - Errors in Chemical Analysis

ANALYTICAL CHEMISTRY QUANT. ANALYSIS: ERRORS IN CHEMICAL ANALYSIS INTRODUCTION CHARACTER AND SKILL BUILDING IN ANALYZING Striving for Accuracy One of the core values of CEU is Excellence in All Endeavors. If this guiding principle is instilled in us, we will always be reminded to strive for accuracy and excellence in all the things that we engaged in. We do not aim for perfection, because perfection means that we are never finished and can never have an error. If we aim for perfection, we will keep on checking our work to ensure that there are no errors. This cannot be done in analytical chemistry where analytical processes are quite long and tedious. We recognize that error can never be eliminated but somehow can be reduced. How? Perhaps, by being more cautious of how we do things but foremost, we must first recognize the nature of errors. If we know the sources of these errors and how they will affect analytical results then, we can take steps to avoid and reduce their occurrence. Aspiring for accuracy requires diligence and thinking of ways to ensure that procedures are properly executed and materials are selected. Analytical determinations are usually done in replicates. You can carry out the processes more confidently the second time around. As you build confidence, you gain excellence. It is hoped that this introduction will somehow help build one's character and the lessons that will be presented will help develop skills through the following objectives. If this will be so, then we recognize the significance of CEU's philosophy of Science and Virtue. LESSON 1-SYSTEMATIC/DETERMINATE AND RANDOM/INDETERMINATE ERROR ACCURACY OF MEASUREMENT Accuracy of measurement as defined by The International Vocabulary of Basic and General Terms in Metrology (VIM) is the "closeness of the agreement between the result of a measurement and a true value." True value can only be obtained by perfect measurement but since there is no perfect measurement in analytical chemistry, true value can never be known, and by nature it is indeterminate. We cannot do perfect measurement because analytical processes are always subject to error. This error can be quantified relative to the true value. ERRORS IN MEASUREMENT Errors in measurement can either be systematic or random. Systematic errors may be due to the following. Instrumental error-malfunctioning instrument Personal error-eye strained Methodical Error - limitation of the procedure used in the analysis The systematic error is present when the mean result of the experiment is biased high or low in relation to the true value. Since systematic error can be determined and be avoided, analyst sometimes refer to it as "determinate error Unlike systematic errors, random errors are unavoidable no matter how careful an analyst is in doing measurement and no matter how many times replicate determinations are done. Here are some terms in relation to errors in analysis. Precision is commonly interpreted as the degree of agreement among experimental results or measurements taken under the same conditions. This is usually expressed as mean and standard deviation. The VIM uses repeatability and reproducibility instead of precision. Repeatability as defined by VIM is the closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement. Reproducibility on the other hand is the closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement. ACCURACY, PRECISION, AND ERROR TYPES being right is actually being accurate precisely technically means you got it reproducibly wrong means inaccurate correct is accurate precise is reproducible Precision: Measure of spread Precise Imprecise (reproducibility error) Accuracy: Nearness to the "truth" Accurate Inaccurate (systematic emor) so accuracy and precision are usually covered with the dartboard bullseye is your target it is the truth the correct value here and so to be accurate means you've got nearness to the truth you're right so on average you've got an accurate situation so here which is also precise because reproducibly you're able to hit the bull's eye with very low spread but you're also right around here okay so that one's accurate as well but its imprecise on average I hit the bull's eye it doesn't really fly right if you want both accurate and precise you want to be in the top-left comer here but there's also the other condition the other two plots here are when you do not have accuracy okay here and not averaging to hit the bull's eye and so yes precisely could mean this graph as well okay where you keep the hit the same place over and over again but you're not hitting the bull's eye I like to call that when I'm playing darts be admire the grouping effect okay that's cute that's funny not what you want from an analytical chemistry analysis now what you really really don't want like super super bad is if your data is both imprecise meaning it's very scattered and it's inaccurate all right hopefully that error is a measurement of accuracy Accuracy Absolute error E = obtained result- expected result Percent error %e = obtained result-expected result x 100 expected result there's absolute error which is just the difference between the obtained results this is the one that you actually measure right here percent error where you're taking the difference between obtained result in the expected result and hopefully that would be small you want to minimize that difference and then you're dividing it as a proportion of the expected true result multiplied by 100%, low values for error are desirable but how do we know what is true accepted or expected certified reference material which an agency like the National Institute standards NIST has been lending measurements on different techniques basic physical principles and tells you this is true you need to have true value enough to know all right so percent error and absolute error from gives you a measure of accuracy precision because it's a measurement of spread we rely on standard deviation standard deviation is the individual sample so that little marking right there is Xi for individual measurements, X bar difference from the mean which is your typical average square all those differences in addemup okay and then a note minus 1 remember that the number of minus one Σχ X = individual measurements X bar = mean n = number of measurements percent relative standard deviation (%RSD) or coefficient of variation or CV %RSD = (s/X) x 100 sstandard deviation X = average Variance 82 s = standard deviation TWO TYPES OF ERROR Systematic Error Determinate error Affects accuracy Flaw in equipment or experimental design Reproducibly positive or reproducibly negative With care, error can be found and eliminated Eg: mis-calibrated equipment, failure to use a blank, bad standards Sampling error - sampling plan doesn't give a representative sample Method error - inappropriate blank, assumptions that aren't true (assuming a ppt is pure) Measurement error-tolerances on equipment flasks or balances Personal error failing to calibrate instruments, bias in a reading scale Random Error Indeterminate error Affects precision From uncontrolled variables in the measurement Equally likely to be positive or negative Cannot be fully eliminated Eg: electronic noise, thermal variations, inconsistency in reading a scale, etc Repeatability -precision for a single analyst and session, same solutions, equipment, and instrumentation Reproducibility-precision for other conditions Inconsistency in reading a scale, in sample preparation (cleaning, etc.) Also includes electronic noise, and thermal variation There is always some random error Accuracy D D Nearness to the truth Governed by determinate (systematic) errors that could in theory be fixed, eg. By calibrating equipment Describe by measure a known sample and calculating % error What is true? Someone ahs to measure true value True and Correct Precision Measure of spread Governed by indeterminate (random) errors Described by std dev, %RSD, etc. Every measurement always has some random error, which we can minimize by taking more samples Reproducible