Chapter 5 Errors In Chemical Analyses

Chapter 5 Errors In Chemical Analyses We will use eight criteria to define a good method: 1. Precision 2. Accuracy 3. Selectivity 4. Sensitivity 5. Range 6. Robustness 7. Cost 8. Safety Precision Precision is the closeness of results to others that have been obtained in exactly the same way. Precision describes the reproducibility of measurements. Precision of a measurement is determined by simply repeating the measurement on replicate samples. Three terms are widely used to describe the precision of a set of replicate data: standard deviation, variance, and coefficient of variation. All these terms are functions of the deviation from the mean di or just the deviation. di = | xi – x | Sample set 1 is more precise than sample set 2. Accuracy Accuracy is the closeness of a measurement to the true or accepted value and is expressed by the error. Accuracy measures agreement between a result and its true value (precision describe the agreement among several measurements). We can never determine accuracy exactly because the true value of a measured quantity can never be known exactly. We need to use an accepted value. Accuracy is expressed in terms of either absolute or relative error. • Accuracy is more difficult to quantify than precision. • Most methods claim to give the true value! Illustration of accuracy and precision Accuracy, cont., Absolute Error The absolute error of a measurement is the difference between the measured value and the true value. The absolute error E in the measurement of a quantity xi is given by the equation, E = xi - xt where, xt is the true or accepted value of the quantity. The negative sign indicates that the experimental result is smaller than the accepted value and the positive sign indicates that the result is larger than the accepted value. Relative Error Relative error of a measurement is the absolute error divided by the true value. The percent relative error is given by the expression, xi  xt Er   100% xt Relative error also expressed in parts per thousand (ppt). Analytical Errors In analytical measurements of a given system, the total variability is the sum of the true variability of the system and any introduced error during the analysis. • Our goal as analysts is to minimize the amount of error in the measurement so that we can understand our samples. • There are three types of error that can be present in any measurement: 1. Random (indeterminate) 2. Systematic (determinate) 3. Gross error Types of Errors in Experimental Data Absolute error in nitrogen determination Systematic error Systematic (or determinate) error: The errors that affect the accuracy of a result. This type of error causes the mean of a set of data to differ from the accepted value. A systematic error caused the results in a series of replicate measurements to be all high or all low. • causes a measurement to be systematically too large or too small. • reproducible. • the result of an experimental flaw (e.g. inaccurate standards, experimental design, personal bias, etc.) • can be corrected (in almost all cases). e.g. ** 10.00 mL pipette that delivers 10.02 mL **The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared throughout your experiment). How do Systematic Errors Arise? There are three types of systematic errors: 1. Instrumental errors are caused by the imperfections in measuring devices and instabilities in their components. – pipets, burets, and volumetric flasks may hold or deliver volumes slightly different from those indicated by their graduations. – the voltage of a battery operated power supply decreases with use. – noise induced from the alternating current (ac) power lines 2. Method errors arise from nonideal chemical or physical behavior of analytical systems. – the slowness of some reactions, the incompleteness of others, the instability of some species, the nonspecificity of most reagents, and the possible occurrence of side reactions that interfere with the measurement process. 3. Personal errors results from the carelessness, inattention, or personal limitations of the experimenter. – one person may read a pointer consistently high, another may be slightly slow in activating a timer, and a third may be less sensitive to color changes. Effects of Systematic Errors I. Constant Errors: Constant Errors does not depend on the size of the quantity measured II. Proportional Errors: Proportional errors decrease or increase in proportion to the size of the sample taken for analysis. A common cause of proportional errors is the presence of interfering contaminants in the sample. Detecting Systematic Errors • Systematic instrument errors are usually corrected by calibration. Periodic calibration of equipment is always desirable. • Personal errors can be minimized by care and self-discipline. – Errors that result from a known physical disability can usually be avoided by carefully choosing the method. • Method errors or bias of an analytical method is estimated by analyzing standard reference materials. Standard reference materials (SRM) are substances sold by the National Institute of Standard and Technology (NIST) and Certified to contain specified concentrations of one or more analytes. The concentration of the components in these materials has been determined in one of three ways: 1. By analysis with a previously validated reference method. 2. By analysis by two or more independent, reliable measurement methods. 3. By analysis by a network of cooperating laboratories. Blank Determinations A blank solution contains the solvent and all of the reagents in an analysis. Whenever feasible, blanks may also contain added constituents to simulate the sample matrix. Blank determinations are useful for detecting certain types of constant errors. In blank determination all steps of the analysis are performed in the absence of a sample. Blank are applied as a correction to the sample measurements. In which it can reveal errors due to interfering contaminants from the reagents and vessels employed in analysis. Bias measures the systematic error associated with an analysis. It has a negative sign if it causes the result to be low and a positive sign otherwise. Bias has a definite value, an assignable cause and are about the same magnitude for replicate measurements. Bias affects all the data in a set in the same way. Bias =μ- xt Random error Random (or indeterminate) error: The errors that affect the precision of measurement. This type of error causes data to be scattered more or less symmetrically around a mean value. Random error in a measurement is reflected by its precision. • Is always present. • Has an equal chance of being positive or negative. • Is the result of uncontrollable variables in an experiment. • Cannot be entirely eliminated. e.g. electrical noise on an instrument You measure the mass of a compound three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g Gross errors  Occur only occasionally, are often large, and many cause a result to be either high or low.  Product of human errors.  Lead to outliers (is an occasional result in replicate measurements that differs significantly from the rest of the results). Homework (5-13) Richards and Willard determined the atomic mass of lithium and collected the following data. a) Find the mean of atomic mass determined by these workers. b) Find the median of atomic mass. c) Find the standard deviation and relative standard deviation for atomic mass result. d) Assuming that the currently accepted value for the atomic mass of lithium is the true value, calculate the absolute error and the percent relative error of the mean value determined by Richards and Willard. e) Discuss your answers based on term of precision and accuracy for the result data. Note: use MS-Exel to solve this problem and submit it on printed paper. Experiment Molar Mass, g/mol 1 2 3 4 5 6 7 6.9391 6.9407 6.9409 6.9399 6.9407 6.9391 6.9406