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CE4501 Environmental Engineering Chemical Processes Laboratory Manual

Fall 2008

Instructors: N.R. Urban Graduate Teaching Assistant: Brandon Ellefson

Dept. Civil & Environmental Engineering Michigan Technological University

Prepared by:

J.A.Perlinger, N.R. Urban

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TABLE OF CONTENTS

I. OVERVIEW: TERM-SPECIFIC INFORMATION .................................................................................... 3

II. LABORATORY SAFETY RULES: ............................................................................................................. 4

III. LABORATORY NOTEBOOKS AND REPORTS .................................................................................... 7 A. NOTEBOOKS .............................................................................................................................................. 7 B. REPORTS ..................................................................................................................................................... 7

B1. ORGANIZATION ..................................................................................................................................... 7 B2. VOICE, TENSE, AND NUMBER ............................................................................................................ 9 B3. CONCISENESS ..................................................................................................................................... 10 B4. REFERENCES ...................................................................................................................................... 11 B5. FIGURES .............................................................................................................................................. 13 B6. TABLES ................................................................................................................................................. 13 B7. SUMMARY ............................................................................................................................................ 13

IV. GRADING: .................................................................................................................................................. 13

V. LABORATORY TECHNIQUES ................................................................................................................ 14 A. SIGNIFICANT FIGURES .................................................................................................................................. 14 B. BLANKS ....................................................................................................................................................... 15 C. CALIBRATION CURVES ................................................................................................................................. 16 D. ERROR QUANTIFICATION ............................................................................................................................. 18

D1. Statistical tools: Distributions, means and variances ........................................................................... 18 D2. Propagation of Errors ........................................................................................................................... 19

E. QUALITY ASSURANCE .................................................................................................................................. 22 VI. EXPERIMENTS .......................................................................................................................................... 23

A. LAB 1. SAMPLE COLLECTION AND FIELD MEASUREMENTS ........................................................ 23 B. LAB 2. ANALYSIS OF MAJOR IONS ....................................................................................................... 33 C. LAB 3. MINEQL LABORATORY ............................................................................................................. 42 D. LAB 4. ACID-BASE TITRATIONS, ALKALINITY, AND BUFFER CAPACITY .................................. 68

PREPARATION AND MEASUREMENT OF FE STANDARDS ................................................................ 87

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I. OVERVIEW: Term-specific information You will not become expert analytical chemists through taking this lab, but you will learn information and skills that will be useful to you for a career in environmental engineering. You will learn about: 1. Techniques of water analysis, and some common pitfalls in the chemical analyses; 2. The chemical composition of natural and “engineered” waters; 3. Quality Assurance and Quality Control; 4. Computerized calculation of equilibrium conditions; 5. Technical Writing. You will learn about these five areas by measuring the chemical composition of water samples that we will collect in and around Houghton/Hancock, by comparing the composition of the different samples, and by analyzing the data. You will also model the composition of the water using a chemical equilibrium program, and write lab reports and make an oral presentation that describes what you did in lab and how to interpret the results. The lab activities this term will relate to the composition of water from lakes, rivers, and aquifers in the Houghton/Hancock area. The dissolved constituents found in the water samples depend on biological processes as well as on the minerals to which the water was exposed. Some of the water samples will have undergone treatment to inactivate pathogens or remove undesirable components. The treatment processes to which these samples have been exposed will also affect their chemical composition.

In week 1, you will prepare containers needed to collect the samples as well as containers needed to store aliquots of the samples for analyses to be done in later labs. In the second week, you will collect the water samples and measure in the field several properties including temperature, pH, dissolved oxygen, conductivity, and turbidity. Upon return to the lab, the samples will be filtered immediately and put into the prepared containers for later analyses. The subsequent analyses of the samples are designed to teach you about the composition of natural waters and the chemical processes that determine chemical composition, as well as about aspects of analysis that are essential to produce reliable results. At the end of the term, you should have an increased knowledge of the effects of natural and engineering processes on the chemical composition of water, and you will be able to assess the reliability of analytical results, a capability that many of you will use in your future jobs. You will perform analyses in the lab every 2-3 weeks. Prior to the lab session the following week, you will be expected to hand in the raw data and preliminary analysis of your measurements. We will then discuss the reliability of the results, compare your results with those of other groups, discuss reasons for differences among water samples, and you may model your results using a chemical equilibrium computer program. Following this discussion, each lab group will write a lab report that summarizes the laboratory procedures and analytical results, that evaluates the quality of the data, and that interprets the results. Reports will be graded on (1) comprehension of the material, (2) quality of analytical results, and (3) quality of the written report. Guidelines on report writing are given in section III.B of this handout. Four lab reports will be collected and graded. In week 14 you will summarize the results determined by all lab groups. About 40 % of your course grade will be based on the lab.

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II. LABORATORY SAFETY RULES: 1. MIOSHA approved eye protection must be worn at all times when you are in the laboratory. Wearing contact lenses while doing lab work may not be advisable because some lenses are permeable to gases, and certain gases can be trapped next to the eye by contact lenses. Check with a physician to determine if your lenses are suitable for laboratory work. 2. Never work alone in the laboratory. Another adult must be in verbal contact with you whenever you are doing laboratory work. Children are not permitted in the laboratory. 3. Never carry out unauthorized, unplanned, nonscheduled experiments. Discuss any unusual work with your instructor prior to doing it. 4. Do not handle any lab equipment from on-going experiments unless specifically authorized by the laboratory instructor. 5. Report all accidents and/or injuries to your instructor, even seemingly minor ones. Medical consultation/treatment may be required (Student Health Center - MTU Campus during Student Health Center’s regular hours). Your instructor will arrange for you to be brought to the health center for treatment. Give her/him your student I.D. number so that the Health Service can be called prior to your arrival. 6. Never eat, drink, or taste anything (food or chemicals) in the laboratory. Do not place fingers, pencils, pipettes, etc., in your mouth. Wash hands and arms when you finish working in the laboratory. 7. Always use a suction bulb, never your mouth, when filling a pipette with a chemical reagent or sample. 8. Attire: confine long hair and sleeves when working. Wear closed shoes, not sandals, in the lab. Leather shoes are recommended. Wear clothing that offers the most protection - a lab coat or apron is required when working in the laboratory. In spite of precautions, accidents do happen. Do not wear your favorite clothing to lab. 9. Always avoid unnecessary hazards. Keep working surfaces clean at all times. Do not sit or lean on bench surfaces. Keep the floor clear of tripping hazards. Jackets and bookbags should be left in rm. 111 DESEB. Only carry your notebook into the laboratory. In the lab, keep drawers closed except when removing equipment. 10. Wear appropriate gloves and face protection when working with hazardous liquids, solids, or solutions. 11. Do not force glass tubing and/or thermometers into rubber stoppers - always lubricate the hole in the stopper and protect your hand with a towel when inserting the glass. 12. Never use an open flame (Bunsen burner) in the vicinity of flammable solvents.

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13. Clean up all chemical spills immediately. Consult your instructor for the proper chemical waste disposal procedure. 14. Do not throw chemical waste in the sink or in the waste baskets. Always consult your instructor for the proper chemical waste disposal procedure. 15. Broken glass is to be put in receptacles marked “Broken Glass Only”. If you break glass make sure all of the pieces are swept up. 16. Do not test odors by direct inhalation from the container. 17. For chemical contact with skin or eyes, wash affected area with water for 15 minutes. 18. Handle all electronic equipment with care. Do not allow equipment to get wet. 19. Read all labels on reagent bottles to make sure you have the right reagents. Report empty reagent bottles to your instructor. 20. Always add concentrated acid to water and acids to bases. Pour slowly while stirring the mixture constantly. 21. Do not insert pipettes directly into reagent bottles. Transfer an approximate amount into a beaker or other container. 22. During the first day of lab: locate all emergency and safety equipment that you may need to use at some time. This includes: shower, eye wash, fire extinguisher, fire blanket. Locate the nearest emergency exit and emergency telephone. 23. Material Safety Data Sheets (MSDS) are located in a bin to the right of the entry to Room 110 of DESEB. This information is made available to you as part of the Michigan “Right to Know” law. These sheets provide information on hazards of materials used in the lab. 24. Use good judgement and care while working in the laboratory. 25. Extreme Emergency: From a phone dial 911 for fire, ambulance, medical assistance or police. From the lab intercom, dial 123-911 26. Campus Security for non-emergencies: 487-2216. 27. Hazard Communication Standard: I am aware that I have a “right to know” all safety information contained in the Manufacturers Material Safety Data Sheet (MSDS) for any chemical used by me or to which I am exposed. I can obtain this information by requesting a copy of the MSDS from room 110 DESEB. After reading the paragraph below, complete the section below and return it to your lab instructor. ------------------------------------------------------------------------------------------------------------

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Laboratory Safety Agreement I understand that I am responsible for conducting myself in a safe manner and for studying and making myself aware of special hazards of techniques, apparatus, or chemicals in the environmental engineering laboratory. I will conform to any safety instructions presented orally or in writing by the instructor or contained in posted instructions or safety memoranda that are distributed or any other informational material. I have read the environmental engineering safety rules 1-27 above and I will observe and adhere to them. Signature:_________________________________ Date:___________________ Print Name:________________________________ MTU Student I.D. No._______________________ Course No.__________________

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III. LABORATORY NOTEBOOKS AND REPORTS A. NOTEBOOKS Laboratory notebooks are an essential part of research. In our litigious society it is necessary to maintain lab notebooks such that other people may follow the methods that are used and see the results obtained. Because you will be involved in a long-term research project over the duration of this term, each group of 3-4 students will be expected to maintain a notebook. These notebooks will allow you to view the results of previous analyses performed on the same samples. The notebooks will be collected throughout the term and may constitute part of the lab grade. For each lab you should enter in the notebook the date, the lab title, the objective of the lab, any changes in procedure that are discussed in class but not in the lab handout, all of the raw data that you collect, and any observations or facts that will help you to interpret the results. Entries should be clearly labeled such that a person with no familiarity with the lab could read and understand them. Important information to enter in the notebook from, for example, the first lab includes the site characteristics, the water temperature at sample time, the pH measurements, the labels applied to the samples and the type of filtration that was done for each sample bottle. B. REPORTS The purpose of technical writing is to convey information as efficiently as possible. Technical reports generally are not read for the sake of entertainment, but for the purpose of obtaining information. Technical writing is not colorful and does not use exaggeration. Technical writing is well organized; significant findings are not hidden at the end as a surprise to the reader. It is best to give the reader the important conclusions as soon as the reader has learned enough to appreciate them. The rest of the report should be written to justify and amplify the conclusions. An efficient way to begin organizing a report is to write down the important conclusions of the report. Next, fill in the other information that the reader will have to be told to understand the conclusions. Written and oral communication abilities are some of the most important skills that you should obtain at MTU; honing those skills is the primary objective of the lab reports in this class.

B1. ORGANIZATION Organization is an essential element of good writing that contributes to readability. Four levels of organization must be considered in every written report: the whole-report level, the section level, the paragraph level, and the sentence level. You will have no options on the whole-report organization; there is a required format that you are to follow (either the memo format or the lab report format) as is explained below in this handout. Each section of your report has a function; you must organize the material in that section such that it achieves that function, reads smoothly, and is as short as practicable. Each section is likely to consist of one or more paragraphs; in cases of multiple paragraphs, these must be strung together such that there is a logical sequence of topics. Paragraph structure is, perhaps, the most often neglected element of organization. However, paragraph structure is as important as sentence structure. A paragraph typically has one theme; generally, this theme is identified in the opening sentence of the paragraph. Often, the final sentence of a paragraph gives the conclusion or the message that the reader is intended to remember about that topic. The sentences in between the opening and closing lines must develop the theme (identified in the first sentence) and lead the readers to the

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conclusion. Paragraphs should consist of at least three sentences, but should not be so long that the reader cannot remember the beginning or the sequence of ideas. Sentence structure in technical writing can become very awkward unless care is used. Sometimes sentences become too long. Usually a long sentence can be broken into two or more short sentences. One way of insuring that your writing is readable is to read aloud what you have written. This technique often will reveal grammatical errors and the need for punctuation as well. Another common problem in sentence formation is the sentence fragment. Every sentence must have a subject and a verb within the body. The technique of reading out loud also will help to locate incomplete sentences. In this and some subsequent classes, you will use either a "short" or a "long" report format. The short format is that of a memo; the primary purpose of the memo is to convey the results and conclusions. Memos are the common, every-day method of communication of factual information in the work place. The longer report format typically is used at the conclusion of an engineering or scientific project. You will be told for which lab exercises you are to use the memo and the long format. Report Format There are several slight variations on the standard format for a lab report, but all are similar. A lab report may vary from two to fifty or more pages in length. The tight organization of the report allows the reader to easily find all information that is necessary to interpret the results. The format that you will follow is summarized below. 1. Title page - Every report should have a title page, which gives the title, the author(s)'s

name, the date, the report title, and signatures of group members. The title should be short and descriptive. Each author should sign the report.

2. Abstract – The abstract (sometimes replaced by an executive summary) is the single most important part of the report. This section is short (always less than 1 page in this class), and it states briefly what is the topic of the lab, why it is important, what was done, what results were obtained, and what conclusions were drawn. It summarizes the most important information in the report.

3. Introduction - This may be from one to several paragraphs long. In the introduction identify the subject of the lab and discuss its importance in the field of environmental chemistry. Include a brief discussion of the fundamental chemical principles being explored in this lab and any important reactions and equations. You may identify any open questions that exist concerning the topic of the lab. The objectives should be stated very clearly and concisely. Complete sentences rather than a tabulation of partial sentences are required. Do not copy the lab handout or merely paraphrase it.

4. Methods - In this section you should describe very briefly the specific methods and materials that were used in the lab.

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5. Results - In this section you will present the specific results of the measurements that were made. Ordinarily these will be graphed or tabulated, but complete sentences and paragraphs are to accompany the graphics. The text should explain the contents of each table or graph. In this section also comes the statistical analysis of the data. All raw data and sample calculations should be placed in an appendix at the end of the report. Number and title all sample calculations and reference them in your results section. You should briefly refer to and explain, not discuss, your results.

6. Interpretation & Discussion - Here you have great liberty to evaluate the scientific, sociological, metaphysical, philosophical or diabolical implications of the results that you obtained. In this section you must demonstrate that you understand the results. Reference tables and figures where pertinent. Discuss sources of error encountered during the experiment.

7. Appendix - Insert raw data and sample calculations. Without sample calculations, no partial credit can be given for errors in data analysis!

B2. VOICE, TENSE, AND NUMBER Reports should be written in the active voice, or on occasion in the passive voice. The imperative voice should be avoided. It may be acceptable in cookbooks (e.g., “Mix one cup of sugar with the flour and blend.”) or in operating instructions (e.g., “Turn the knob counterclockwise until the pilot light glows.”), but it is not acceptable in technical reports. For example:

1. Active Voice (BEST)— “The dissolved lead concentration was 10 nanomolar.”, or “The vapor pressure of benzene was 93 mm Hg.” 2. Passive Voice (OK)—

“The water was frozen in plastic trays.”, or “The solution was analyzed for total metal content.”

3. Imperative Voice (WORST)— “Dissolve 3 grams of iron in 100 ml of HNO3.”, or “Use the refractive index to determine the concentration of isopropanol.”

The past or the perfect tenses are usually the most natural. Occasionally the present tense can be used, particularly for stating enduring truths. Frequent shifting of tenses can leave the reader confused. Almost all technical writing is done in the third person. The pronouns you, I, we, etc. are avoided. While a few people feel they make technical writing less stilted, most people regard their use as pompous. One thesis advisor suggested that her student avoid using I and we in writing until he had won a Nobel prize. One common mistake is the use of pronouns like it, they or them when it is not clear to what they refer. Also the over-generalized references like “It is known that....”, “They believe the reason....” (when they isn’t clear) should be avoided. Even “Most engineers regard...” is not good unless the statement is documented.

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B3. CONCISENESS Reports should be as concise as is consistent with being complete and unambiguous. Most readers are busy people. They don’t want to be burdened with thicker reports than necessary. Concise writing requires some assumption about the level of the reader. For the purposes of this course, the reader is the graduate student in charge of the lab or the instructor. Imagine these people to be your bosses in an environmental engineering consulting firm. In describing laboratory procedures, it is not necessary to go into detail about every step unless nonstandard techniques were used. Avoiding excessive verbiage requires practice and usually revision of the first draft. Some examples of how writing can be condensed follow.

1. Original “First 7.9 pounds of copper were weighed out and transferred into a

crucible. Then 2.1 pounds of aluminum were weighed and added to the crucible. Next the crucible was placed into the furnace and heated until it was determined that the metal was molten. The metal was then stirred and superheated to 1150°C. Finally the molten alloy was poured into an ingot mold...”

Rewritten “A 10 pound ingot of a copper-21% aluminum alloy was prepared

from metal by melting in a clay-graphite crucible in a gas-fired furnace. Stirring and superheating to 1150°C insured homogeneity and sufficient fluidity for casting...”

2. Original

“Exactly 9.8 grams of potassium thiocyanate were weighed out and put into a 1 liter flask. Then, distilled water was added to the mark. The solution was mixed until all of the potassium thiocyanate was dissolved. Three 25 ml samples of a known silver nitrate solution were measured and placed into conical shaped flasks. To each, 100 ml of distilled water was added. About 5 ml of concentrated nitric acid and 5 ml of iron (III) ammonium sulfate indicator were then added. Small amounts of the potassium thiocyanate solution were added to each until a red-brown color was observed. The amount of the potassium thiocyanate in the solution was then calculated from the amount of silver nitrate that reacted to achieve the color. The concentration of potassium thiocyanate was determined to be 0.1 M with a standard deviation of +0.025.”

Rewritten “One liter of 0.1 M (+0.025) solution of potassium thiocyanate (KSCN) was prepared and titrated against a silver nitrate (AgNO3) standard in an acidic medium with ferric ammonium sulfate indicator. To determine the endpoint, AgNO3 was added until the red-brown color was permanent for 1 minute. The pH was adjusted with concentrated nitric acid.”

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Note that the rewritten versions are shorter and actually give more information. The reader will assume the weighing steps from the body of text. The reader will also assume the placing of metal in the crucible, and the dissolution of KSCN in water. The reader should also know standard titration techniques (if not, refer the reader to an appendix which goes through step-by-step instructions). Furthermore, neither example hides what is being done (preparation of an ingot, determination of a solution concentration).

B4. REFERENCES Statements of fact as well as descriptions of past work should be referenced so that the reader can, if she/he wishes, check these. This is done by inserting a number in the text at the appropriate place. The number corresponds to the number of the reference in a separate reference section. The number may be in parentheses (1) or brackets [2] or it may be superscripted3, but is placed in the text where it will be clear to the reader what statement is being referenced. The numbers of the reference should be sequential, (1) referring to the first citation in the text, (2) to the second, etc. An alternative style is to have the authors and date in parentheses in the text of the report following the information that has been cited rather than using numbers for each citation. In the reference section, the authors, the source, the date, and the pages should be given. A reference section is not a bibliography. Only those references specifically cited in the text should be listed. Below is an example of a portion of text and the corresponding reference section.

Research report excerpt: “In a recent study, Nesbitt et al. (1) investigated the effect of thiourea as a sulfide donor in the removal of metal contaminants from water by precipitation as sulfides. The results of this investigation were the development of two processes that have direct industrial application. The study showed that copper, zinc, lead, cadmium, and mercury would be removed as metal sulfides. The results give credence to Pearson’s Hard-Soft Acid-Base Theory (2) which predicts that each of these metals would combine with sulfur over any other species. Many analytical procedures were used in this study. The atomic absorption spectrophotometer (see Ref. 3 for details of the analytical technique and flame conditions) was used for metal ion determination. Electron microscopic techniques (4) were employed for determining precipitate composition and structure.” References 1. C.C. Nesbitt, J.L. Hendrix, and J.H. Nelson, “Use of Thiourea for Precipitation of Heavy Metals in Metallurgical Operations Effluent”, Extraction Metallurgy ’85, Institute of Mining and Metallurgy, London, 1985. 2. R.G. Pearson, “Hard and Soft Acids and Bases”, Journal of the American Chemical Society, 85(22), 1963, pg. 3533.

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3. D. A. Skoog, and D.M. West, “Fundamentals of Analytical Chemistry”, 3rd Ed., pp. 268-273, Holt, Rhinehart and Winston, New York, 1976. 4. M. Von Heimdahl, “Electron Microscopy of Materials”, Academic Press, New York, 1980.

Table 1. Reference format of AIME (other periodicals differ slightly)

Journal: J.B. Tucker, “Biotechnology Goes to Sea”, High Technology, 5(2), (1985) pg. 34.

Book: A.F. Taggert, “Handbook of Mineral Dressing”, pg. 12-32, John Wiley & Sons, Inc., New York, 1940.

Paper in an anthology: B.L. Bramfitt, A.R. Marder, and R.J. Dotton, “Continuous Deformation of Austenite to Develop Tough High-strength Steels”, pp. 537-555 in The Hot Deformation of Austenite, John Ballance, ed., AIME New York, 1977.

Paper at a meeting: J.J.C. Jansz, “Thermodynamics of Aqueous Chloride Solutions: Calculations of Ionic Activities and Distribution Data for Chloro Complexes”, Presented at the Winter AIME conference, Los Angeles, February, 1985.

Private conversation: Private communication, J.L. Hendrix, University of Nevada—Reno, January, 1985.

A reference to a book should include the title in capital letters, the publisher, city, and pages referenced (unless it is the whole book), e.g.,

20. R.B. Fischer and D.G. Peters, A Brief Introduction to Quantitative Chemical Analysis, W.B. Saunders Company, Philadelphia, 1969, pp. 135-137.

If the reference is to an article in a conference proceedings or book which is a compendium, the editors should also be cited, e.g.,

30. D.M. Muir and A.J. Parker, in “Hydrometallurgy: Research and Development and Plant Practice”, Eds. J.D. Miller and K. Osseo-Assare, pp. 341-356, AIME, New York, 1983.

If the author is unknown, the citation should start with the title of the work, e.g.

1. ASM Metals Handbook, Vol. 8, 8th ed., 1973, p. 259, A.S.M., Metals Park, Ohio.

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A reference may be cited several times. It should not appear more than once in the list of references. All citations should be to the same number.

B5. FIGURES Figures include photographs, graphs, schematic drawings and other visual material. A Table is not a Figure!!! Figures should be numbered in the order to which they are referred in the text. They should appear either at the end of the paper (in a Figures section) or as soon after they are cited as convenient. All figures should be cited somewhere in the text. Every figure should have a caption written below the figure, which is a title and as much of a description as can be concisely given. (A little redundancy with the text does not hurt.) As a general rule, one should put enough information in the title and description so that if the figure is viewed without the report it can be understood. In other words, it should be able to stand on its own. For a graph, one should try to avoid using the axes labels in the description. For example rather than title a plot of pH versus concentration for a titration “Concentration as a Function of pH for Silver Nitrate”, it would be better to use “Titration Curve of Silver Nitrate”. With the software that is readily available to all of us there is little excuse for producing anything but high quality graphs and figures. Some simple rules include:

• Axes must be clearly labeled as to the parameter and the units of measurement of that parameter;

• Data points (i.e., the actual measured values) should be clearly visible and not obscured by lines;

• Data points should NOT be connected by lines unless there is a specific reason for doing so;

• Regression lines should be clearly labeled as such; • The type size and style (font) should be easily readable, not fancy; • For photographs, some measure of scale or magnification should be given.

B6. TABLES Frequently the best way to present data is in the form of a table. Like figures, tables should be sequentially numbered (usually with Roman numerals) in the order that they are used in the text, and titles should be included above the table. The title should appear at the top of the table. Tables should appear at the end of the paper or as soon after the reference to them as is convenient.

B7. SUMMARY Reports should be written with the reader in mind. The writing should be concise, but unambiguous and complete. IV. GRADING: Your laboratory grade counts for 40% of the course grade. See the lab syllabus for details on how the lab portion of the grade will be determined. Lab reports are due by 5 p.m. in the TA’s mailbox on due dates without lab sessions.

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V. LABORATORY TECHNIQUES There are several procedures that will be used repeatedly in the weeks ahead. This section alerts you to the correct procedures that are to be followed. Failure to adhere to these procedures will affect your grade. Many of the procedures outlined below are applicable not only to this course, but also to other courses as well as to your future jobs. A. Significant Figures It is very important to keep track of significant figures in numbers reported in the text of the report, and in tables and figures, in order to ensure that calculations involving the data reflect the precision of the measurements. In general, it is fairly easy to determine how many significant figures are present in a number by following these rules (from Chemistry, R. Chang, 1994, McGraw-Hill, Inc., NY): • Any digit that is not zero is significant. Thus 834 cm has three significant figures, 1.345 kg has four significant figures, etc. • Zeros between nonzero digits are significant. Thus, 606 m contains three significant figures, 46,503 kg contains five significant figures, etc. • Zeros to the left of the first nonzero digit are not significant. Their purpose is to indicate the placement of the decimal point. Thus, 0.08 m contains one significant figure, 0.0000468 g contains three significant figures, and so on. • If a number is greater than 1, then all the zeros written to the right of the decimal point count as significant figures. For example, 2.0 mg has two significant figures, 30.053 mL has five significant figures, and 2.050 cL has four significant figures. If a number is less than 1, then only the zeros that are at the end of the number and the zeros that are between nonzero digits are significant. For example, 0.090 kg has two significant figures, 0.3005 L has four significant figures, 0.00420 min has three significant figures, etc. •For numbers that do not contain decimal points, the trailing zeros (that is, zeros after the last nonzero digit) may or may not be significant. Thus 400 cm may have one significant figure (the digit 4), two significant figures (4 and 0), or three significant figures (400). We cannot know which is correct without more information. By using scientific notation, however, we avoid this ambiguity. In the previous example, we can express the number as 4 × 102 for one significant figure, 4.0 × 102 for two significant figures, or 4.00 × 102 for three significant figures. •Addition and Subtraction The sum or difference should contain the same number of places to the right of the decimal point as there are in the value that contains the fewest places to the right of the decimal point. Examples:

266.31 5.203 0.1223 (4 sig. figs., 4 places) + 823.1 - 0.00420 (3 sig. figs., 5 places) 1094.6 0.1181 (4 sig. figs., 4 places) (one sig. fig. after the decimal point) •Multiplication and Division

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The product or quotient should contain the same number of significant figures as the value that contains the fewest number of significant figures. Examples: 250.0/50.000 = 5.000 50.00 x 5.00 = 250. (2.50 × 102) Once you have determined the correct number of significant figures that your result should contain, the rounding off procedure is as follows: If the digit to the right of the significant figure is less than 5, the preceding number is left unchanged. If the digit is greater than 5, round up. If the digit is 5, round up 1 digit if the number preceding it is odd, and leave it unchanged if the number preceding the 5 is even. Example: 415.0/9.29 = 44.7 (44.671689 rounded off is 44.7) If you use your calculator to perform a series of calculations, all digits can be entered and the rounding off done at the end. Example: 12.3350 x 3.0045 = 13.828547 = 13.8 2.68 Do not round off at every step of a series of calculations because error is introduced at each step. This discussion of significant figures refers to measured quantities such as those obtained in a laboratory setting. Exact numbers are those that are defined (such as 1 gram = 1000 mg) or are counted (such as 2 hydrogen atoms in a water molecule). These exact numbers are considered to have an infinite number of significant figures in calculations involving them. B. Blanks Two types of blanks should be utilized in analyses of environmental samples: field blanks and analytical or reagent blanks. Field blanks consist of pure water (e.g., Milli-Q™, double distilled, deionized, etc.) that is subjected to all of the handling procedures that the samples receive. The field blank should be stored in the same type of container under the same conditions for the same period of time as the samples. The field blank should be filtered or preserved in exactly the same fashion as are the samples. Concentrations of analytes found in the field blank are presumed to have been caused by contamination during sample handling. It is further assumed that all samples would be contaminated to the same extent because they were handled identically to the field blank. Hence, analyte concentrations in the field blanks are subtracted from the concentrations found in the samples. As for any single sample, there is some uncertainty in the concentration measured in the field blank. Analysis of the field blank should be performed identically to that for the samples such that the analytical uncertainty is equal for both; if samples are analyzed in duplicate or triplicate, so also should the field blanks be analyzed. The larger the number of samples being handled, the more variable is the contamination of the samples likely to be. Hence, to assess this variability, the number of field blanks is increased in proportion to the number of samples. One example of a protocol would be to have one field blank for each ten samples. The exact protocol will depend on many factors such as the regulations, the cost of analysis, the probability of contamination, the variability in the extent of contamination.

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Analytical blanks, in contrast to field blanks, are prepared at the time of analysis. These blanks are identical to the standards to be used for calibration with the important difference that they have no analyte added to them. Analytical blanks are used to correct the standards for any background contamination. Correction can be done in one of two ways: either (1) the analytical response (e.g., absorbance, peak height, detector response) for the blanks is subtracted from the response for the standards, or (2) the blanks are included in the standard regression (response vs. concentration). Method 1 is used when the contamination in the standards will not be present in the samples. This often is the case when the source of contamination is the water used to dilute the standards (assuming that the samples are not also diluted), or when the standards are made using totally different containers, solvents or reagents than are used with the samples. Negative concentrations calculated for field blanks (equivalent to higher detector responses for the analytical compared to field blanks) are one indication that Method 1 rather than Method 2 should be applied. Method 2 is used whenever the contamination present in the standards also is likely to be present in the samples. Contamination from glassware, from lab air, from reagents, or other substances common to samples and standards should be addressed with Method 2. C. Calibration Curves Frequently one analyzes a series of standards with increasing concentrations and uses the instrument responses to construct a calibration curve. The standard concentrations are chosen to span the range of concentrations in the samples. The calibration curve in turn is used to estimate the concentrations in the samples. Although the basic procedures are straightforward, several aspects warrant discussion. The analytical blanks are an important constituent of the calibration curve. If the standards are corrected for blanks according to Method 1, the instrument response to the blanks (an average of all blanks) is substracted from the responses to the standards before the calibration curve is made. In this case, the regression for the standards should be forced through the origin. The regression equation will take the form:

Response = K•Concentration and concentrations of samples are calculated simply by dividing the instrument response for each sample by the slope, K. This scenario is illustrated in the figure below.

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25 30 35

Inst

rum

ent R

espo

nse

Concentration (mmoles/L)

Standards before blank subtraction

Regression line forced through the origin

Standards after subtraction of blank

Figure 1. Calibration curve demonstrating the effects of analytical blanks. The regression line has been forced through the origin after subtraction of the analytical blanks.

17

There are instances in which analytical instruments are not expected to give zero response to analytical blanks; in these cases the regression is not forced through the origin. More frequently in this class, Method 2 will be used to correct for the analytical blank. In this case, the blank(s) are not subtracted from the standards, and the regression is not forced through the origin. The regression then has the form: Response = b + m•Concentration where b is the y-intercept and m the slope. Concentrations for samples (and field blanks) then are calculated as Conc. = (Response - b)/m The concentrations for the field blanks then may be subtracted from the concentrations for the samples. The discussion above ignores the fact that there is some uncertainty (error) in all measurements, including the measurements of standards. It often is necessary to quantify this uncertainty by determining the error in the slope and intercept of the calibration curve. This uncertainty, calculated automatically with many software packages, may be presented graphically as shown in the figure below where the dotted lines represent the 95% confidence intervals for the regression equation. One interprets such a diagram to mean that there is a 95% probability that the instrument response will lie between the dotted lines on a vertical line above the standard concentration. Errors are minimized when analyses are performed over a concentration range in which the instrument response varies linearly with analyte concentration. With the software available today, it generally is possible to fit even nonlinear calibration curves to an equation. However, a decrease in sensitivity with increasing concentration implies that small changes (or uncertainties) in instrument response correspond to increasingly large changes (or uncertainty) in concentration. In other words, the confidence interval becomes wider in nonlinear regions. Clearly, it is inappropriate to fit a nonlinear calibration curve to a straight line using a linear regression. The effect of such a mistake is an erroneously high y-intercept and a low correlation coefficient (r2) for the regression. Conversely, non-zero values for the

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 5 10 15 20 25 30 35

Inst

rum

ent r

espo

nse

Concentration (mmoles/L) Figure 2. Calibration curve for a putative analysis showing the confidence intervals (dashed lines) for the linear regression line (solid line) performed on the measured data (solid circles).

18

y-intercept combined with low r2 values may be an indication that the instrument response did not vary linearly with concentration. In such a case, one should either use a nonlinear regression or perform the linear regression only over the linear portion of the calibration curve. D. Error Quantification There is some level of uncertainty or error in all analytical measurements. Often it is important to quantify that uncertainty in order to know if a result is within regulatory limits, to know if two results are significantly different from one another, or to know how representative a value is of other measurements that could be made, or to know if a result is correct. There are two major sources of uncertainty: (1) the variability among samples, and (2) the analytical errors or uncertainties. Both sources of uncertainty may be either random or systematic. Random errors may be revealed by repeated sampling or measurement, while systematic errors will not be discovered in this fashion. One must employ different strategies to account for these two types of errors. Systematic errors often determine the accuracy of an analysis and are the most difficult to detect. By accuracy is meant correctness or truth of the measurement. An example of a systematic error or source of variation would be a repeating, temporal or spatial pattern to the parameter to be measured. For instance, one could not measure an average daily rate of photosynthesis by always making measurements in the afternoon because rates in the morning and evening are different than in the afternoon. Field sampling techniques must be designed to sample across all gradients that may influence the property of interest. That is easily stated, but we do not always know what gradients exist nor what environmental parameters influence the property of interest. Examples of systematic analytical errors include contamination in standards or reagents, and under- or overestimation due to poorly calibrated instruments (e.g., balances). The best method to detect systematic analytical errors is to measure "samples" of known concentration; such standards can be purchased from the EPA and NIST. Random errors affect the precision or replicability and can be quantified by performing an adequate number of analyses. This implies that enough samples must be collected to characterize the "population" (by population is meant the total possible number of samples that could be taken), and enough analyses must be performed of each sample (or of a representative set of samples) to characterize the random variation in analytical results. A number of statistical tools are used to quantify random errors. The following discussion is not a substitute for a statistics book, but merely summarizes some commonly used tools.

D1. Statistical tools: Distributions, means and variances Analytical results and the environmental parameters that we wish to measure are characterized by a distribution of values. By distribution we mean the frequency of occurrence of all values. It frequently is assumed that if enough analyses were made or if enough samples were collected, the results would be normally distributed; this means that they would be distributed symmetrically about the mean with 67% of the values lying with + 1 S.D. of the mean. When fewer samples are collected the results frequently are log-normally distributed. Alternatively, a t-distribution (the width is a function of the number of samples) often describes small numbers of samples. The statistical descriptors that are used to describe a population and, more importantly, the statistical tests used to compare results

19

depend on the type of distribution. Because environmental samples often follow log-normal distributions, they are first log-transformed before statistical analysis. The mean generally is used as the "best estimate" of the parameter of interest. If we have N measurements of parameter x, the mean is defined as

x =1N

(x1 + x2...xn) =1N

⋅ xii∑ (1)

This equation defines the arithmetic mean; if the data have been log-transformed the result will be the geometric mean.

The spread of the values about the mean is characterized by several possible terms. The standard deviation (σ or S.D.) is one common descriptor:

σ =1

N −1(xi − x)2

i∑ (2)

Many calculators use N rather than (N-1) in the denominator to calculate the standard deviation. One uses N for very large numbers of samples, and (N-1) for all other situations. In this class you should always use (N-1). Another descriptor is the relative standard deviation which is simply the standard deviation divided by the mean. Yet another descriptor is the standard error, which is defined as:

SE =σN

(3)

As for the standard deviation, the relative error is the standard error divided by the mean. Based on the standard error we may define a confidence interval (CI) as the range

within which there exists a stated probability that the true value exists. An assumption has to be made about the type of distribution that exists in order to calculate a confidence interval; a t-distribution commonly is assumed. Based on the t-distribution, the CI is defined as:

CI = tνα ⋅ SE (4)

where t is the t-statistic (from a statistics table) for ν degrees of freedom, and α is related to the level of confidence (100(1-2α)). For instance, if we wanted the 95% confidence interval for 5 measurements whose mean was 125.0 and whose S.D. was 3.8, we would look up the t-statistic for (N-1) or 4 degrees of freedom and α equal to 0.025. The t-value is 2.776, and thus the 95% C.I. is 125 + 2.776•(3.8/√5) or 125.0 + 4.7 (i.e., 120.3-129.7). We could state that, based on the five measurements, there is a 95% probability that the true value lies between 120.3 and 129.7. (Note that if the mean was given only as 125, then the confidence interval would be 120-130. Rules for significant digits must be followed in reporting statistical descriptors.)

D2. Propagation of Errors Often we use analytical results for further calculations and then must determine the uncertainty about the final calculated number. The uncertainty about the final calculated result depends on the uncertainties of all of the numbers used in the calculation. There are set rules for determining the error about the final calculation. The process of determining this error is called propagation of errors. 1. General Case

20

First, let us consider the general case in which w is a function of the variables x, y, and z (w = f(x,y,z)). As long as the errors for each variable are independent we may write a generalized expression for the uncertainty in w:

εw2 =

∂f∂x

⎛ ⎝

⎞ ⎠

2εx

2 +∂f∂y

⎛ ⎝ ⎜ ⎞

⎠ ⎟

2εy

2 +∂f∂z

⎛ ⎝

⎞ ⎠

2εz

2 (5)

For the error terms, either S.D. or S.E. may be used. In equation 5, f may represent any simple or complex function involving x, y and z. From this generalized equation, simpler and more specialized equations may be derived for specific types of functions (f). Two such special cases are illustrated below. 2. Addition and Subtraction If x,y, and z are measured values with random errors of εx, εy, and εz (the errors also have to be independent of one another), then we may calculate the uncertainty about w (w=x+y-z) as:

εw = ε x2 + εy

2 + εz2 (6)

It will always be the case that εw < (εx+εy+εz). It should be readily apparent that one would arrive at eqn 6 by applying the general case (eqn. 5) to the function: f= x + y - z The partial derivatives (squared) of each term in this function are equal to unity. 3. Multiplication and Division Given x,y, and z with their respective errors as above, let us now define w as:

w = xy/z Again assuming that the errors in each term are independent, the uncertainty for w is given by:

ε ww

=ε xx

⎛ ⎝

⎞ ⎠

2+

ε y

y⎛

⎝ ⎜ ⎞

⎠ ⎟

2+

ε zz

⎛ ⎝

⎞ ⎠

2 (7)

You may wish to test your skills and see if you can derive eqn. 7 from application of eqn. 5 to the function w. 4. Linear Regression It was discussed above that linear regressions often are used to compute the coefficients for calibration curves. (There also are numerous other cases where linear regressions are used to calculate coefficients for linear relationships between two variables.) It was further stated that there often is uncertainty in the variables, and, consequently, there is uncertainty in the calculated regression coefficients. Since the coefficients in calibration curves are used to calculate the sample concentrations, the uncertainties in the coefficients in turn determine the uncertainties (errors) in the calculated sample concentrations. Below we illustrate how the uncertainties in coefficients and sample concentrations are calculated. Let us define a linear relationship where dependent variable y is a function of the independent variable x: y = A + Bx

21

In the case of a calibration curve, multiple standards with concentrations xi would have been measured and found to yield instrument responses of yi. Using the least squares method, the coefficients A and B are calculated as follows:

A =xi

2∑( ) yi∑( )− xi∑( ) xiyi∑( )Δ

(8)

B =N xiyi∑( )− xi∑( ) yi∑( )

Δ (9)

where Δ = N xi2∑( )− xi∑( )2 (10)

Because we are assuming that there is a linear relationship between x and y, we may define the error in y to be related to the discrepancies between the actual measurements of yi and the predicted values of yi for the corresponding values of xi. Specifically, we can take the average discrepancy:

σ y =1

N − 2⎛ ⎝

⎞ ⎠ yi − A − Bxi( )2i=1

N∑ (11)

This definition allows us to calculate the uncertainties in A and B by using the general formula for propagating errors. The results are:

ε A2 =

σ y2

Δxi

2∑ (12)

and εB2 =

Nσ y2

Δ (13)

What we really desire, however, is the uncertainty in calculated concentrations of our samples. We use the calibration equation to calculate sample concentrations (xi) from measured values of yi. If we assume that the measured values of yi have the uncertainty (σy) as defined above, we are then in a position to calculate the uncertainty in xi.

xi =yi − A

B (14)

As a first approximation, we could simply propagate the errors through equation 14 using the errors for y, A and B as defined above. One additional complexity arises because A and B (and hence the errors in A and B) are not independent variables. Hence we must add a term to account for the covariance in A and B. The equation for the propagated errors thus becomes:

σ x2 =

∂x∂y

⎛ ⎝ ⎜ ⎞

⎠ ⎟

2σ y

2 +∂x∂B

⎛ ⎝

⎞ ⎠

2σ B

2 +∂x∂A

⎛ ⎝

⎞ ⎠

2σ A

2 + 2σ AB∂x∂A

⎛ ⎝

⎞ ⎠

∂x∂B

⎛ ⎝

⎞ ⎠ (15)

We have replaced ε with σ for all of the error terms in eqn 15, and the final term in this equation accounts for the covariance in A and B. The new error term (σAB) is defined as:

σ AB =−σ y

2

Δxi∑ (16)

where the summed x terms refer to the values of x used in the regression. After the appropriate substitutions for the partial derivatives are made equation 15 becomes:

σx2 =

1B2 σ y

2 +σ A2( )+

A − yB2

⎛ ⎝

⎞ ⎠

2σ B

2 +2σ y

2

BΔA − yB2

⎛ ⎝

⎞ ⎠ xi∑ (17)

22

Although cumbersome, this equation allows us to estimate the uncertainty in the calculated sample concentrations. E. Quality Assurance Quality Control or Quality Assurance refers to protocols that are followed in order to insure that accurate results with a quantifiable uncertainty are obtained. The development of quality control is one of the rare examples of a useful synergism between science and jurisprudence. Without quality control there is no way of knowing how reliable analytical results are. Those of you who end up working for consulting firms or governmental agencies that have anything to do with "hazardous wastes" will be expected to evaluate the reliability of laboratory measurements; in other words, you will be expected to evaluate the quality control procedures and results of contract labs.

There are several components of Quality Assurance protocols including the following: (1) Design of sampling schemes to avoid systematic errors; (2) Design of sampling schemes to allow quantification of random errors; (3) Design of analytical procedures to avoid or to quantify systematic errors (procedures include measurement of samples of known concentrations and determination of the detection limits and the magnitude of analytical and field blanks); (4) Design of analytical procedures to allow quantification of random errors. All of the components of Quality Assurance have been discussed above with the exception of the detection limits. For any instrument, there is a lower limit to the concentration at which it is able to measure accurately; this limit is called the detection limit. The detection limit depends on the type of instrument, the laboratory procedures, the specific analyte, and the skill of the analyst. The detection limit is defined mathematically in terms of the background noise. Specifically, the detection limit is equal to twice the standard deviation recorded in non-zero analytical blanks or low level standards. (Some agencies and statisticians define it as three rather than two times the S.D. of blanks or low level standards.) Clearly, it must be documented that sample concentrations are above the detection limits for any analytical procedure that is employed. Samples whose concentrations are below the detection limits should be labeled as "less than the detection limit". The method of calculating the detection limit should also be stated, as this method varies, as discussed above.