LABORATORY MANUAL
GENERAL CHEMISTRY - CHM 152L
INTRODUCTION
CHM 152L is the laboratory course that should be taken concurrently with CHM 152, the second semester of general chemistry. It is assumed that the key techniques, concepts, and calculations covered in CHM 151L have been mastered. CHM 152L will explore more complex chemical concepts and problem solving. The topics of thermodynamics, kinetics, equilibrium, spectroscopy, and redox chemistry will be explored using various chemical reactions. Each student will do laboratory work, data collection and record keeping in a lab notebook, calculations, error analysis, and pre and post lab questions for each experiment. Chemical analysis, data interpretation, and the keeping of a laboratory notebook will be the focus of CHM 152L.
This course will be tied together by a cooperative project conducted by a team of students. The project will focus on the synthesis, purification, and characterization of emerald green crystals (iron salt). The synthesis and purification of the iron salt will be done in experiment C and then analyzed during subsequent experiments. The analysis or characterization will be done as extensions or applications of concepts and techniques introduced in later experiments. Student teams will have to coordinate individual analysis work to discover the empirical formula of the emerald green iron salt crystals and then write individual reports on their results.
Table of Contents: page
Course Objectives (“I” in the page number stands for introduction) I-2
Grading I-2
The Laboratory Notebook I-3
Safety in the Chemistry Laboratory I-8
Handling Reagents and Standard Procedures I-13
Data Recording, Significant Figures, and Error Analysis I-14
Experiments
A. Enthalpy of Formation of MgO – Calorimetry A-1
B. Enzyme Kinetics of Papain B-1
C. Synthesis of a Complex Iron Salt C-1
D. Spectrophotometric Determination of an D-1
Equilibrium Constant
E. Acid-Base Chemistry E-1
F. Redox Chemistry F-1
Periodic
Table Back
Cover
COURSE OBJECTIVES:
Laboratory manipulations and operations including the use of a computer interfaced spectrophotometer, pH electrode, and temperature probe.
Chemical concepts and calculations
Including chemical synthesis, thermodynamics, kinetics, equilibrium, acids/bases, and redox chemistry
Computer data collection and analysis
Construction of graphs and plots
Record keeping with emphasis placed on correct data collection and recording in a permanent notebook
Critical analysis and interpretation of data
GRADING:
Grades will be assigned based on the grading scale and point assignments listed in the course syllabus. The point distribution is based primarily upon evaluation of the laboratory notebook, pre-lab work and quizzes, post-lab work, reported values for unknowns, and a final examination. In addition, two short scientific reports will be required one for experiment B and another for the synthesis and analysis of the iron salt.
The recording of procedures, data, observations, and calculations in a laboratory notebook in the proper format is a key aspect of this course. The details on how the notebook is kept and graded are provided starting on the next page. The laboratory notebook will be checked each lab period and it must be signed and dated after the last entry at the end of each lab period by the TA or instructor. Error analysis will be an important theme of post lab work done in the lab notebook. The notebook will be formally evaluated twice during the semester.
Pre-lab work begins by reading the experiment in the lab manual and concisely outlining key aspects of the experimental procedure. Pre-lab questions must then be completed and a pre-lab quiz taken before starting the experiment. Many of the questions on the pre-lab quiz will be similar to the pre-lab questions. The post-lab work will involve calculation and analysis of data and completing post lab work.
Students will also submit results for unknowns that must be within given tolerance limits to receive full credit. Points for unknowns will be assigned on how close the student’s answer is to the correct answer. Students may repeat any unknown (using a new unknown sample checked out from the chemistry stockroom) with the best score contributing to their course points for that unknown.
Be aware that the CHM 152 lecture and CHM 152L are different courses with separate grades assigned for each. Each course must be added or dropped separately. The grade of incomplete may be given only when a course is unfinished because of illness or other conditions beyond the control of the student. The deadline to drop is published in the Class Schedule.
THE LABORATORY NOTEBOOK
Introduction:
The laboratory notebook serves several purposes; the most important of which is to be the permanent, understandable record of data and observations taken during an experiment. You should be able to look at your notebook a year from now and be able repeat the experiment or calculations. Calculations should also be shown in the lab notebook using dimensional analysis or unit cancellation. If the same calculation is repeated several times, the calculation can be shown once, and the rest of the results can be listed in a table. If a spreadsheet is used to do the calculations, a copy of it can be taped into the lab notebook.
Before you start an experiment you may wish to note key aspects of the laboratory procedure in the notebook. Any procedures not in the lab manual including changes to procedures listed in the manual must be noted in the lab notebook. The laboratory notebook used for this course should be bound and have at least 50 pages (not spiral).
At the end of each class period the TA will put a line across the notebook page under the last entry, initial by the line and put the date and time. They will do a quick check of the notebook at this time and give you suggestions on how to improve your notebook. Points will be taken off if the notebook is not checked and initialed by a TA or instructor at the end of each lab period.
The notebook will be graded twice during the course of the semester. One grading will be done at random during the course of the semester and the second will be done after the last experiment has been completed. The notebook will be evaluated based on adherence to proper format as explained below and will include observations, data, calculations, and post lab work for experiments completed. Computer generated graphs should be trimmed to size and taped into the lab notebook. A copy of the grading sheet for the notebook can be found later in the notebook information.
Format of the Notebook:
Write your name, class number and section letter, and the semester on the front of the notebook. For example:
Joe Smith CHM 152L-J Fall 2012
Also be sure to reserve the first two pages in the lab notebook for a Table of Contents. All pages used in the notebook must be numbered. Numbering the first 50 pages before you start using the notebook would be a good idea. Certain rules need to be followed when keeping a scientific laboratory notebook:
1. Record all data and observations directly into the notebook. This is by far the most important rule in keeping a good laboratory notebook. Do not transcribe from other pieces of paper, i.e., DO NOT record data on scraps of paper or in this manual and then recopy the data into the notebook! Write down exactly what you are doing and your observations as you are doing it. Errors in your procedure can be caught this way. In addition all computer generated graphs must be printed and taped into the notebook on the same day the data is collected. Points may be taken off for writing data outside the lab notebook or not taping graphs into your notebook on the same day they are collected.
2. Clearly identify all data, graphs, and axes, and use correct units.
3. Use a black or blue ball point pen for all entries. Do not white out, erase, or obliterate any entry; simply cross out mistakes with a single line (the mistake should still be readable) and give a short note to explain the nature of the mistake, e.g., “misread.” (Sometimes you will find later that the entry was not a mistake after all and you may want to retrieve the data!)
4. All the work in the notebook should be sequential going from oldest to newest entries (don’t skip spaces). You may, however, start a new lab period or a new experiment on a new, unused page. If blank spaces are left in the notebook put an X through them.
5. Begin each page and new section of work with the date and title of the experiment (i.e., sections or parts of an experiment). If, when you stop work for the day, there is space left on the page for more entries enter the new date at that place when you resume work unless you are starting a new experiment.
6. As mentioned above, reserve the first two pages in the lab notebook for a Table of Contents. One convenient form for the Table of Contents is:
Experiment A – Calorimetry pp. 4-11 9/6/12
Changes to Experimental Procedure pp. 4-5 9/6/12
Data and Observations pp. 5-6, 9 9/6/12
Calculations pp. 7, 8, 10 9/9/12
Data and Calculations pp. 11 9/13/12
Note how the data and observations are intermingled with the calculations. This student was completing the calculations each week instead of waiting to finish the whole experiment. This will be important since some of the experiments may take up to three weeks to complete.
7. Before an experiment is started, the entire experimental write up must be read. As you read, it would be a good idea to note the objectives and key points of the experimental procedure in your laboratory notebook. This will prepare you for the experiment before you come to lab.
8. Another important facet of scientific experiments involves the propagation of uncertainty in measurements and calculations. Use the correct number of significant figures, as outlined later in the introduction, in collection of data and calculations, to communicate the uncertainty or precision of your final results.
An
example notebook page showing data collection and calculations can be found on
page I-5. Note how data at the bottom of the page was lined through and not
obliterated. Also note how unit cancellation was used when doing the
calculation in the middle of the page. Be sure to use unit cancellation
whenever possible!
Example Page from Laboratory Notebook
CHM 152L NOTEBOOK GRADING SHEET
Name______________________________ Dana ID____________ Section Letter____
Locker #_____ Instructor_____________________ TA_________________________
Note: Each section will be worth a certain amount of points. TAs will provide exact point distributions. For certain experiments the point distribution may be changed or other requirements added.
POINTS AREA
EARNED GRADED – check indicates area is ok.
_____PTS – General Mechanics of Notebook Entry
____ data was recorded directly into notebook (very important)
____ chronological order was use from older to new work (no blank areas)
____ student’s name, class #, and section letter appears on outside of notebook
____ all pages of notebook currently in use are numbered
____ current and complete table of contents
____ notebook understandable, each page and each day’s lab work started with title and date, also each new section of work, readable
____ did not obliterate, use pencil, or white out but “X” or line out blank space
____ all data, calculations, and graphs are identified and have correct units
____ reasonable significant figures were used
____ notebook initialed and dated after each lab period’s work
_____PTS – All data, observations, procedures, and calculation present in notebook
Experiment Letter A B C D E F
Procedure Outline/Changes ____ ____ ____ ____ ____ ____
Risk Assessment ____ ____ ____ ____ ____ ____
Data & Graphs ____ ____ ____ ____ ____ ____
Observations ____ ____ ____ ____ ____ ____
Calculations ____ ____ ____ ____ ____ ____
_____TOTAL POINTS FOR THIS GRADING
Special Notebook Instructions for Individual Experiments:
Experiment A
Experimental Data: Record all masses, volumes, and concentrations used.
Calculations: All time-temperature data will be collected and plotted on a computer. Tape computer generated graphs into your notebook. Record the initial and final temperatures and the temperature change determined from each graph or trial in your lab notebook by or on the graphs.
Experiment B
Experimental data: You will be doing the experimental work in groups, but each of you should maintain a copy of the data in your notebook and tape all graphs generated into your notebook before leaving lab. Make copies if needed.
Calculations: All calculations are to be done individually.
Experiment C
Student teams formed from each lab bench will acquire the data. The observations and data for the synthesis of the iron salt should be copied into each student's notebook.
Experiment D and E
Calculations: Plot graphs on a computer. Tape all graphs into your lab notebook during the lab period they are made. Record key information such as slope and correlation coefficients for Exp. D and buret readings, equivalence point, etc. for Exp. E close to or on the graphs taped into the notebook.
Experiments F (No separate instructions)
Scientific Integrity:
Scientific advances are based firmly on experimental observations and depend on the accuracy and honesty of the experimental data. The laboratory notebook must preserve the "sanctity" of data and observations--once the measurement is taken and recorded, it cannot be changed. "Dry-labbing” (using fake data) or using data from past semesters is totally unacceptable because it negates the very basis of the scientific method and is considered academic dishonesty. Proven cases will result in serious consequences such as failing the course.
SAFETY IN THE CHEMISTRY LABORATORY
Laboratory safety involves the prevention of, and response to, laboratory emergencies. Good prevention is far better than someone getting hurt. This begins with always being aware of chemical and laboratory hazards. Hazard codes, chemical labels, and material safety data sheets are the first sources of information that help us prepare to work safely in a laboratory. This information can be used to do risk assessment before starting an experiment. Certain rules need to be followed to keep you safe and you must know what to do in case of an emergency. Chemical waste management is another important aspect of a safe laboratory and a key regulatory compliance issue.
Chemical Labels, Hazard Codes, And Material Safety Data Sheets:
The first source of information is the label on a chemical bottle. Read the label carefully before using a chemical. A commercial chemical bottle will have extensive information on the label such as the chemical name and formula, physical properties, purity, molar mass, hazards, safety precautions, suggested protective equipment, and other information. A hazard code may also be included on the label.
The chemistry department has adopted the “Baker” hazard code classification system to inform users of potentially hazardous chemicals. This system is designed to provide information to people who handle chemicals in laboratories. Hazards are classified according to four types: health (toxic), flammability (fire), reactivity (explosive or reactive), and contact (corrosive). The intensity of the hazard is indicated by using a number from "0" (no hazard) to "4" (extreme hazard). This information is conveyed using either a four-colored label found on "J.T.Baker" chemical products or as a series of four digits. The label on chemical bottles may look like this:
The four-digit hazard code used in the lab manual would look like this:
1321
For example, the code listed above for acetone indicates a slight health hazard (1), a high flammability hazard (3), a moderate reactivity hazard (2), and a slight contact hazard (1). Hazard codes will be listed after the chemical inside parentheses: (1321)
The "Baker Codes" for each of the four hazards are defined according to the following scheme:
HEALTH (BLUE): Toxic effects of a substance if inhaled, ingested or absorbed.
0 - No Hazard
1 - Slight hazard
2 - Moderate hazard
3 - Severe danger
4 - Deadly, life threatening
FLAMMABILITY (RED): Tendency of a substance to burn based on flash point or the temperature a substance will burn when exposed to a spark or flame.
0 - Will not burn
1 - Flash point above 200°F
2 - Flash point from 100-200°F
3 - Flash point from 73-100°F
4 - Flash point below 73°F
REACTIVITY (YELLOW): Potential of a substance to react violently with air, water or other substances.
0 - Stable.
1 - Reacts under elevated temperature or when in contact with other substances
under other than normal working conditions.
2 - Reacts violently but will probably not explode under normal working
conditions.
3 - Reacts violently or explodes under normal working conditions when in
contact with air, water or other substances.
4 - May react violently or detonate spontaneously under normal working
conditions.
CONTACT (WHITE): The danger a substance presents when it comes in contact with skin, eyes, or mucous membranes.
0 - No contact hazard to normal, healthy tissues.
1 - Slight hazard; irritant to sensitive tissues, avoid contact with eyes and
mucous membranes.
2 - Moderate hazard; irritant to sensitive tissues, damages tissues.
3 - Severe danger; destroys tissues, including skin.
4 - Extreme danger; life threatening.
The National Fire Protection Association (NFPA) has a hazard code system that was adopted in 1975 to communicate hazards to emergency responders. This system uses a label that you may be familiar with since it appears on entrances to stores containing hazardous chemicals and on chemical containers. The NFPA may differ from the “Baker” code since it provides information to firefighters while the “Baker” code provides hazard information in a laboratory situation. The codes are very similar except the white section in the NFPA code refers to special or specific hazards of importance to firefighters such as “ox” for oxidizing agent.
There are other hazard communication systems that are in use or being developed. The American Coatings Association uses the Hazardous Materials Identification System (HMIS) that is similar to the Baker and NFPA systems but includes a code for precautions to take for using a product or chemical. The Federal Government is in the process of adopting the new Global Harmonized System (GHS) using a more in depth hazard coding system that will be implemented nationally over the next few years.
The hazard codes are given only as a guide to warn the user of probable hazards and to approximate the degree of hazard under normal use. The user must not be lulled into a false sense of security by a low number on the label, but must take full responsibility for safe use of the chemicals. Avoid over-reliance on hazard codes. Refer to the Material Safety Data Sheets (MSDS) and other safety information whenever you are working with chemicals that are unfamiliar to you. This is especially important when mixing chemicals. Chemicals with relatively safe hazard codes can become dangerous when mixed with other chemicals.
The MSDS should be read to obtain additional safety information before more a hazardous chemical is used or in the future the Safety Data Sheet (SDS) for the new GHS. These sheets are available for all chemicals used in the chemistry department in room 212 of building 17 and in lab. They must not be removed from these locations. The internet is a great resource for MSDS and general safety information. To get an MSDS, search the internet using the chemical name and MSDS.
Risk Assessment:
A risk assessment determines what hazards will be encountered during an experiment or lab procedure, how to mitigate them (precautions such as goggles or gloves), and what should be done if something goes wrong. There may be physical or chemical hazards present that will be discussed in the experiment write up. Chemical hazards will be expressed using hazard codes and/or special warning stickers on bottle labels. If you observe a 3 or 4 in the hazard code you may want to obtain more information by referring to the material safety data sheet (MSDS) and note hazards and how to respond to them. For every experiment you must write a risk assessment and outline the experimental procedure before you start lab work.
How to Protect Yourself:
What To Do In Case Of An Accident:
Hazardous Waste Disposal:
The Resource Conservation and Recovery Act (RCRA) mandates the proper disposal of hazardous waste. Disposal of many waste chemicals by putting them down the sink is now illegal. Regardless of regulations, the proper management of hazardous waste is of particular importance to the people of Arizona where the contamination of groundwater by hazardous waste could have grave consequences. Please carefully follow the instructions below to protect our groundwater and keep your lab safe. Hazardous waste is determined by four properties:
TOXIC: A poisonous substance, potentially harmful to human health, can cause cancer or birth defects, or can contaminate, harm or kill wildlife.
FLAMMABLE: Substances, which can explode, ignite, or emit toxic gases or fumes if exposed to a source of ignition.
REACTIVE: An unstable substance which can react spontaneously if exposed to heat, shock, air, or water. Reactions may include fires or explosions. The research director or instructor for the lab must neutralize any reactive substance before it can be accepted for disposal.
CORROSIVE: A substance that could corrode storage containers or damage human tissue upon contact. (For example, acids and bases, pH <4 or >10)
Chemical waste that does not fit into the above categories may be flushed down the drain with large amounts of water. The instructor or TA must be consulted if there is uncertainty with regard to the collection of a chemical waste.
All waste bottles are labeled and color-coded with tape. The label will include an experiment number and a hazardous waste description that will help you decide which bottles to put your waste into. Find the correct waste bottle for your experiment number and for the type of chemical waste you have; make sure the description of the composition fits the waste you are adding to the bottle. Using the wrong waste bottle could create a safety hazard and will be treated as a safety violation. The following table should help. Some nonhazardous chemical waste from experiments you do may be put down the drain. Avoid using cup sinks or water troughs to dispose of chemicals, instead use large sinks in the lab.
Class Exp. Colors Description of Waste Comment
152L C red Waste Acetone Trace potassium oxalate
152L A,D,E,F white Corrosive Liquids Neutralize
152L C,D,E,F blue Iron Salt Crystals Waste Dehydrated or Extra
Acidic or basic used chemicals (pH <4 or >10) will be disposed of by neutralization in a fume hood. Waste bottles are also color-coded using the following scheme:
Blue - health hazard, poison
Red - flammable hazard, organic liquid
Yellow - reactivity hazard (strong oxidizers, etc.)
White - contact hazard, corrosive
Green - low hazard materials with hazard codes of 1 or less
HANDLING REAGENTS AND STANDARD PROCEDURES:
The liquids, solids, and solutions used in a laboratory are called reagents. You must become well acquainted with these reagents, their containers, and their proper use. The reagents are kept on a separate bench away from your work area. Some reagents, such as concentrated NH3 must be kept in the fume hood because it generates toxic fumes. The reagents are grouped according to experiment, starting with Experiment A and ending with Experiment F. When you need a reagent please follow these rules:
DATA RECORDING, SIGNIFICANT FIGURES, AND ERROR ANALYSIS
Recording Experimental Data Using Correct Significant Figures:
It is important to take data and report answers such that both the one doing the experiment and the reader of the reported results know how precise the results are. The simplest, way of expressing this precision is by using the concept of significant figures where a significant figure is any digit that contributes to the accuracy of an experimentally measured number or to a number calculated from experimentally measured numbers. Please refer to the chemistry lecture textbook for a discussion of the use of significant figures.
In this laboratory course mass, volume, time, and temperature are experimentally measured and used to calculate density, concentration, percent by mass, and other values of interest. In CHM152L mass in grams (g) is measured using a top loading electronic balance with a precision of ±0.001g or with an analytical balance if greater precision (±0.0001g) is needed. All mass measurement taken on a top loading electronic balance should be recorded to ±0.001g even though the last digit may vary somewhat. For example if the mass of an object on a balance reads 25.001, 25.000, 24.999 and moves between these values, 25.000 should be recorded. Recording 25, 25.0, or 25.00 would be wrong since these would not communicate the true precision of the number. If values on the balance read 25.000, 25.001, and 25.002 then 25.001g should be recorded.
Time in seconds (s) is measured using a computer. Temperature will be measured using an alcohol thermometer that can be read to a precision of ±0.2°C that is used to calibrate the temperature probe connected to the computer. You need to estimate the tenths of a degree.
Measuring volume is a tradeoff between speed and the precision of the measurement and requires skill in choosing the right glassware for the task. Recognizing when to make an accurate measurement and when to be satisfied with an approximate measurement can save much time. Frequently, the written directions will give clues to the needed precision by using the words "approximately" or "about" when the precision is not important and "exactly" or "precisely" when the precision is important. Another clue would be the number of significant figures used to write a number. For example if a procedure says transfer 5.00 mL this must be done with great precision and a 5 mL pipettor or volumetric pipet should be used, but instructions that say transfer about 5 mL or 5.0 mL would indicate a measurement requiring much less precision so that it can be done faster using a graduated cylinder. A larger number of significant figures can and should be carried when you are using a volumetric pipet or flask, pipettor, or buret than when you are using a beaker, erlenmeyer flask, or graduated cylinder. Different equipment in the laboratory is used to achieve different levels of precision. This is shown in the table below. It is also important to note that glassware used for accurate measurements is calibrated at a specific temperature, which is noted on the glassware.
When a measurement is made, the question arises: "How many digits or figures should be recorded?" The answer is straightforward: For a measured number record all digits, which are known with certainty, and the last digit, which is estimated. Many of the measurements in this course involve the estimation to the nearest one-fifth or one-tenth of a scale marking. For example, a 25mL graduated cylinder, which has scale markings every 0.5 mL, should be read to the nearest 0.1 mL, estimation to the nearest one-fifth of a division. Whenever estimation between markings is being done and the reading is "on the mark," the last digit should be included to convey the idea of accuracy to the reader. For example, with a buret, which has markings every 0.1 mL, a reading on the mark of 11.3 mL would be recorded as 11.30 mL; otherwise, the reader will not know that the buret was really read to the nearest 0.01 mL. The graduated cylinder does not always need to be used to the precision listed below; for example, if the instruction say “add about 25mL of water” being within about 1 mL of 25 would be ok.
Generally speaking all the glassware in the following table is for transferring known volumes of liquid from one container to another except for the beaker and volumetric flask. Beakers along with Erlenmeyer flasks are generally used for conducting chemical reactions or other lab manipulations. The volumetric flask is used for doing precise dilutions.
Precision of Glassware
Equipment |
Precision |
Purpose of Glassware/Equipment |
250 mL Beaker |
±10 mL |
Solution preparation, storage, reactions |
125 mL Erlenmeyer flask |
±6 mL |
Solution preparation, storage, reactions |
250 mL graduated cylinder |
±1 mL |
Volume transfer – moderate precision |
25 mL graduated cylinder |
±0.2 mL |
Volume transfer – moderate precision |
5 mL bottle top dispenser |
±0.1 mL |
Volume transfer – moderate precision |
100 mL volumetric flask (class A) |
±0.08 mL |
Precise final volume for dilutions |
10 mL measuring pipet (Mohr) |
±0.05 mL |
Volume transfer – good precision |
5 mL pipettor |
±0.025 mL |
Volume transfer – very precise |
25 mL buret |
±0.02 mL |
Precise volume delivery for titration |
5 mL, 10 mL volumetric pipet |
±0.01 mL |
Volume transfer – very precise |
Another factor to take into account when measuring volume is the level of hazard for the chemical being measured. Bottle top dispensers will often be used to dispense more hazardous liquids. Pump dispensers reduce the amount of transfers from one container to another and can be used with good precision. Be sure to familiarize yourself with the use of each type of pump dispenser. Slow deliberate use of the dispenser will help insure that the right volume is delivered. Sometimes approximate small amounts of liquid are needed. In this case instructions may indicate measuring out drops from a dropper bottle or eye dropper. One drop of water or a dilute solution on average is about 0.05 mL. This can also be a safer method because it does not involve pouring the liquid from one container to another.
Calculated Values and Tracking Uncertainty Using Significant Figures:
Recorded data is then used to calculate some value of interest in one or more steps. You will need to know how precise or how many significant figures an answer should have depending on the precision of the data or calculated values used in the calculation and the type of math operation done. If you are unsure how many significant figures to use for calculated values it is better to use too many than too few. Using too few significant figures will introduce rounding errors into final answers!
Reporting Answers in Addition and Subtraction:
When experimental data have been recorded correctly, the uncertain or estimated digit is the last digit. The calculated sum or difference of experimental measurements must be carried out only to the place where the first digit of uncertainty enters the calculation.
Example: Add 14.75, 1.475, and .001475 (all of which are experimental numbers). The digits of uncertainty are underlined.
14.75
1.475
0.001475
--------------
16.226475
Since the answer may include only the first digit of uncertainty, it should be rounded off to that digit and reported as 16.23. It helps to line the numbers up by the decimal point.
Reporting Answers in Multiplication and/or Division:
1. All measurements should be recorded to the appropriate number of digits as discussed in the section on recording experimental data.
2. The position of the decimal point is ignored in counting the number of significant figures.
3. All digits except zero are always significant.
4. Zeros may or may not be significant. Any zero to the left of the first non-zero digit is never significant (0.0256 has 3 significant figures because neither zero is significant).
a. Any zero to the right of the first non-zero digit is always significant if there is a decimal point (2.5070 has 5 significant figures since both zeros are significant).
b. If there is no decimal point, zeros to the right of non-zero digits are significant unless it is stated otherwise (the number 25000 has 5 significant figures unless some other precision is stated, such as 25000 ± 100). Numbers with "trailing" zeros (zeros to the right of all other digits) should be written in standard exponential form to remove questions (2.50 x 104 has 3 significant figures; 2.5000 x 104 has 5 significant figures).
In multiplication and/or division, the answer should be reported to the same number of significant figures as the value in the computation with the least number of significant figures. Example: Find the answer to the following multiplication/division problem to the correct number of significant figures.
0.085 has 2 significant figures; 0.08206 has 4; 366 has 3; and 0.782 has 3. A calculator shows the answer to be 22.989865, so the answer should be reported as 23.
Interpretation of Data:
Significant figures are excellent to express the precision of raw data but not always so good to express the precision of calculated values. As a general rule in this laboratory course you should always use at least four significant figures for calculated values to avoid rounding errors. Once the final answer is calculated, it can be expressed using correct significant figures. In order to interpret how good your results are, certain terms need to be understood. You will need to understand the following definitions.
1. Accuracy: The term "accuracy" describes the nearness of a measurement to its accepted or true value. In CHM 152L, the accuracy of your work becomes known when your unknown is graded. Full credit indicates good accuracy while a low grade indicates that your results had poor accuracy.
2. Precision: The term "precision" describes the "reproducibility" of results. It can be defined as the agreement between the numerical values of two or more measurements that have been made in an identical fashion. Good precision does not necessarily mean that a result is accurate.
3. Range: The "range" is one of several ways of describing the precision of a series of measurements. The range is simply the difference between the lowest (or lower) and the highest (or higher) of the values reported. As the range becomes smaller, the precision becomes better.
Example: Find the range of 10.06, 10.38, 10.08, and 10.12.
Range = 10.38 – 10.06 = 0.32
4. Mean: The "mean" or "average" is the numerical value obtained by dividing the sum of a set of repeated measurements by the # of individual results in the set.
Example: Find the mean of 10.06, 10.38, 10.08, 10.12
(Note that the value 10.38, which is far greater than the other values, has a large influence on the mean, which is larger than three out of the 4 individual values.)
5. Median: The "median" of a set is that value about which all others are equally distributed, half being numerically greater and half being numerically smaller. If the set has an odd number of measurements, selection of the median may be made directly. (Example: the median of 7.9, 8.6, 7.7, 8.0 and 7.8 is 7.9, the "middle" of the five). For an even number, the average of the central pair is taken as the median (Example: the median of 10.06, 10.38, 10.08, and 10.12 is 10.10--the average of the middle pair of 10.08 and 10.12). Notice in the example that the median is not influenced much by the value 10.38, which differs greatly from the other three values. For this reason, the median is usually better to use in reporting results than the mean for small data sets.
6. Error: The absolute error of an experimental value is the difference between it and the true value. For example if the experimental value is 30.9 and the true value is 26.5, the error would be 30.9–26.5 or 4.4.
7. Relative percent error would be the error divided by the true value times 100: (4.4/26.5)x100%=16.6% or 17%.
8. Relative percent range is one way to estimate the relative percent error when we don't know what the true value is. To calculate this value divide the range by the median value and multiply by 100%. Using 10.06, 10.38, 10.08, and 10.12 from the previous items 3 and 5:
You will also be graphing data using a program called Graphical Analysis and doing a linear fit or regression to examine the linearity of data sets. The correlation coefficient from doing the linear regression indicates how linear the data is where 1.0000 would indicate perfectly linear data and smaller numbers such as 0.6000 a much poorer fit. Your TA will provide instructions for using this program. In some cases you may use excel or other software to graph data.