1 1 Chapters 0, 1, 3 Analytical chemistry is chemical measurement science. Qualitative analysis what is it? Quantitative analysis how much of it is there? This class covers the following: 1. Measurement science basics 2. Gravimetric analysis (by mass), 1 st lab of semester 3. Volumetric analysis (by volume, titrations) too many labs 4. Spectrophotometric analysis (by light absorption), lab 3 5. Potentiometry (by voltage) near the end of the semester Read Chapter 0, pages 1 8. Know definitions of terms in bold, glossary in back. Review Chapter 1, pages 9 17, mostly on units and unit conversions. Stoichiometry problems must be mastered to pass this class. For practice I have included additional problems on the web site. Of utmost importance: 1. How to prepare solutions from the solid 2. How to prepare a dilute solution from a more concentrated solution. Chapter 1 problems from book: Excercises A, C + Problems 8, 15, 17, 23, 28, 31, 32a, 34. Chapter 2 is for the laboratory, read it before we first meet. You may not understand it all, you will understand some.
2 2 Chapter 3 Experimental Error We will be covering pages in this chapter. Vocabulary/jargon to know: Absolute uncertainty, accuracy, determinate error, indeterminate error, precision, random error, relative uncertainty, significant figure, systematic error.
3 3 A statement of fact every quantitative measurement has error (uncertainty) associated with it. Corollary quantitative measurements are meaningless without knowledge of the error (uncertainty) of the measurement(s). So how is this uncertainty determined? In great part the answer to this question is the subject of Chapters 3 & 4. A short discussion of significant figures see page 46. Systematic (determinate) error is basically a reproducible screw up that gives an experimental bias such that the result is always too high (positive bias) or too low (negative bias). In principle at least this can be corrected. Random (indeterminate) error is from the natural limitations of the ability to make a measurement. This cannot be corrected. It
4 4 is random because it may give a result that is either too high or too low; i.e., positive or negative bias. This random or indeterminate error is what is possible to address statistically. Precision describes the measurement reproducibility arising from random or indeterminate error. Accuracy describes the agreement between a result and its true or accepted value. Accuracy can affected by both indeterminate and determinate errors. Delete measurements with systematic error if you know they exist, so only random error is present. The measurement of random error (precision) is discussed in Chapter 4 when standard deviation, variance, and confidence interval are introduced. The accurate or true value of a measurement is the average of a large number of measurements, mathematically an infinite number but practically a hundred or more, in the absence of systematic error.
5 5 Two more definitions of immediate importance: The absolute error of a buret measurement is ± 0.02 ml The relative error is: Absolute error/measurement value 1) Consider a buret with ± 0.02 ml of liquid: 2) Consider a buret with ± 0.02 ml of liquid: Or if multiple measurements are made as is almost always done: The following, Section 3.4, is mostly helpful in lab. People find this possibly the most difficult stuff in quant. You still have to be able to do it, or you will pay for it by at least 1 grade reduction per lab. Error (uncertainty) is usually expressed as a standard deviation (s), variance (s 2 ), and usually ultimately as a confidence interval. These are introduced in Chapter 4. For now error is just given the symbol e, but we will use the standard deviation (s) once it is defined.
6 6 Almost invariably a quantitative measurement results from a series of measurements, each measurement with its own inherent uncertainty. You then do math on these measurements to obtain the final result. How does the uncertainty propagate through the calculation? (Can t just add them up since some may have + bias and others bias). 2 rules: 1 for adding/subtracting numbers derived from measurements, and 1 for multiplying and dividing numbers derived from measurements. 1. Addition/subtraction. If 2 numbers each with its own uncertainty must be added or subtracted, the answer s absolute uncertainty is obtained from the absolute uncertainties of the individual measurements. If e is the absolute uncertainty (it will be s later) Example: An analytical balance can measure a mass to ± 0.2 mg or g. Normally one obtains a mass by difference, meaning 2 measurements are made for each mass obtained. The value of the 2 measurements are subtracted one from the other.
7 7 The following illustrates the real rule of significant figures. Similarly for 2 buret readings in a volumetric analysis, each measurement can be done to ± 0.02 ml. Doing the same math shows that the error from a single titration, comprising 2 readings one before titration and one when it is done, is ± 0.03 ml. This won t be used much unless we go all out. However the following rule will be used a lot. 2. Multiplication/division. If 2 numbers each with its own uncertainty must be multiplied or divided, the answer s absolute uncertainty is obtained from the relative uncertainties of the individual measurements. Note that we are always ultimately interested in the absolute uncertainty of the final value. Example: If you have a ± M HCl solution and deliver 100 ± 0.02 ml of solution to another flask, how many mmoles have you delivered? What is the (absolute) uncertainty?
8 8 Additional notes: 1. In Labs 2 & 3, to propagate uncertainty you will do the equivalent of the mixed operations example on page Read the real rule for significant figures also on page 46. Think about it. 3. Skip section Remember what we just did is really for working up uncertainties in lab data. 5. If you want to know why uncertainties propagate in the way just discussed, see Appendix C (calculus required). Chapter 3 problems: 9 13