Name Stamp Here Partner Lecture Instructor Date

CHEM& 151 Winter 2009 EQUIPMENT, MEASUREMENT, DENSITY, AND GRAPHING Prelab attached (p. 17-18) Fill-in - Refer to your Laboratory Procedures handout for how to do your fill-in lab reports. Name Stamp Here Partner Lecture Instructor Date _ Have you attached the graphs and the conclusion? INTRODUCTION Any comprehensive course in chemistry must include a certain amount of laboratory time. In a chemistry laboratory, you will learn how to develop proper lab techniques, carefully observe experimental results, and accurately interpret data to arrive at a desired solution to a chemical problem. The laboratory also allows you to observe how the chemical principles and theories presented in lecture apply to real life situations. The development of good laboratory techniques is essential in obtaining precise, accurate experimental results. It is, therefore, important to develop these skills early in the quarter. The measurement of the physical properties of pure substances is a very important technique as a part of the larger scheme of identifying elements and compounds. This first experiment will introduce you to: A. Significant Figures B. Finding Equipment in the lab C. Proper methods for performing volume and mass measurements. D. Methods of measuring and calculating density of an unknown solid by volume displacement. E. Density and graphing F. Good graphing techniques (important for all lab reports) SECTION A: SIGNIFICANT FIGURES Each time you make a measurement, you must pay attention to the markings (divisions) on the measuring device to determine how many digits (significant figures) to record in your answer. Correct use of significant figures is important throughout this remainder of this experiment and all subsequent experiments. Significant figures in your measurements: Digital instruments (example balance): record every digit given. For example, if the balance readout looks like this, record 1.70g, not 1.7g. 1.70 Manual instruments: always include an estimated digit. For example, using the centimeter ruler in Figure 1, the pencil might be recorded as having a length of 1.87cm. In this number, the 7 is the estimated digit. Another acceptable reading would be 1.88cm, but any other number of significant figures (or number of decimal places) would be incorrect. For example, 1.9cm would be an incorrect reading. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 1 of 18

0 1 2 3 4 5 Figure 1. Pencil image from the Yale University Picture Dictionary. http://berlin.cls.yale.edu/picturedictionary/pub/word.asp, accessed 2-21-07. Significant figures in measurements that someone else has made: All non-zero numbers are significant 4.56cm includes 3 s.f. Zeroes between non-zero numbers are significant 10.77mL includes 4 s.f. Leading zeroes are never significant 0.01077L includes 4 s.f. Trailing zeroes are significant in the presence of a decimal place 123.70g includes 5 s.f. 120.0mL includes 4 s.f. Trailing zeroes in the absence of a decimal place are ambiguous, and are generally assumed to be non-significant unless more information is available. It is best, in this situation, to write the number in scientific notation, this ensures no ambiguity regarding the number of significant digits in the number. 2300g might have 2, 3, or 4 s.f. To correctly indicate the number of sig figs in this number, put it in scientific notation: 2.300x10 3 g includes 4 s.f. 2.30x10 3 g includes 3 s.f. 2.3 x 10 3 g includes 2 s.f. Significant figures in calculations: Multiplication and Division: the result is rounded to the same number of significant figures as the least precise number in the calculation: 5.67 ml 0.70g = 3.969g round to 4.0g (2s.f.) ml Addition and Subtraction: the result is rounded to the same number of decimal places as the least precise number in the calculation: 121.0g - 4.34g = 116.66g round to 116.7g (round to tenths place): the least precise number is only known to the tenths place, so the answer can only be reported to the tenths place. When you perform a series of calculations, round after each different operation, perform addition and subtraction: get the answer to the correct number of significant figures. Then perform multiplication and division. It is important to remember, that you can gain or lose significant digits when you add and/or subtract numbers together! #2 Basic Equipment Rev W09 AEM Winter 2009 Page 2 of 18

Precision: A measurement with a greater number of significant figures is more precise than a measurement with fewer significant figures. (For example, 5.0g is more precise than 5g) Accuracy: Accurate measurements are correct measurements. A digital watch, for example, might have a high degree of precision and measure hundredths of seconds, but if it s running ten minutes late, it is not accurate. B. FINDING EQUIPMENT IN THE LAB: A SCAVENGER HUNT While we encourage everyone to have a lab partner, this section will serve you better if it is completed independently. If you do have a partner, make sure that each person looks around the lab and participates in finding the items in the scavenger hunt. You need to find the items listed below (they will be located in a variety of places around the lab!), and place them on the bench-top in front of you in the order listed. After you have found all of the items, ask the lab instructor to check off on your items. Once the instructor has given his/her approval, you should return the items back to the appropriate place in the lab (note: some of the items you will need for the next section, so read that and keep those items at your bench-top. Those can be returned after you finish the rest of the experiment!) By instructor Instructor Initials: Item Utility clamp Buret Clamp Buret 50-mL beaker 125-mL Erlenmeyer flask Thermometer Tongs Ring stand Test tube Spatula/scoopula Graduated pipet Graduated cylinder C. VOLUME AND MASS MEASUREMENTS (Refer to the appropriate sections in the in the Laboratory Handbook for information about using measuring devices.) Discussion of Volume Measurements Almost all chemical experimentation requires accurate measurement of some physical or chemical property. In this section of the experiment you will learn to use the buret, the graduated cylinder, the graduated pipet, and the beaker as a means of measuring the volume of a liquid. The precision and accuracy of the three methods of measurement will be compared using water as the liquid. Water is attracted to glass, so instead of forming a flat surface, it forms a concave surface (curves upward at the outer edges) so all volume measurements should be made at the bottom of the curved surface when using glass devices. This curvature is called the meniscus. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 3 of 18

Figure 2 shows the correct eye position to use when reading the volume. Incorrect positioning (called parallax) can result in a volume measurement that is either too large or too small. The correct reading of this volume would be 82.0 ml. Typically, precision is defined as the reproducibility of the results, or how many decimal places you can measure with a particular device. If your answers are grouped together and you can get the same reading each time, your results are precise. Accuracy is how close your value is to some true value. In some cases we need to use an average instead of a true value. The following is a set of data collected by one student of the length of a particular object: 42.56 cm, 42.55 cm, 42.58 cm. The class average when 10 students took 3 measurements each using the same type of measuring device was 42.12 cm. This person made very precise measurements, but the results were not very accurate when compared to the class average. Beakers Beakers are designed to give an approximate volume measurement. They come in a variety of sizes ranging from those which will hold only a few ml to others which hold many liters. You will use many of these sizes in lab. The precision and accuracy of the measurement depends on the size of the beaker, but the measurement is never more precise than a whole number value (i.e., 40 or 45 ml, never 45.3 ml). Beakers have a large width as compared to height (see Figure 3) which adds to the difficulty in precisely and accurately reading the volume measurement. Beaker volumes are always whole number readings. Graduated Cylinders Graduated cylinders are designed to deliver a volume of liquid. While graduated cylinders also come in a variety of sizes, you will use primarily the 10 ml and 50 ml sizes in lab. The precision of the volume measurement is estimated to one tenth of the smallest division shown on the cylinder. This will give you an additional estimated decimal place (example 45.3 ml, never 45 ml). Most graduated cylinders in the lab can be read to the tenths place ( + 0.1 ml) Graduate cylinders are considerably smaller in width than in length (see Figure 3) so the meniscus can be more easily seen and the spacing between marks on the scale is larger. Figure 3: a typical beaker 1-2 cm in width, 15-30 cm in length Graduated Cylinder Figure 4 #2 Basic Equipment Rev W09 AEM Winter 2009 Page 4 of 18

Buret The buret is also designed to accurately deliver a volume of liquid. In other words, you are measuring the amount of liquid removed from the buret. You will be using a 50 ml buret in lab. The buret has a very small width compared to length (see Figure 5a and b) allowing for easy reading of the meniscus, and therefore, the volume. The buret volume can be measured to the hundredths place ( + 0.01 ml). Liquid is drained from the bottom of the buret. Numbering of the buret, therefore, starts at the top of the buret. Volume readings are made by (1) filling the buret to the 0.00 ml mark (first reading located at the top of the buret) or some initial volume, (2) drawing off the desired volume of liquid, (3) measuring the new volume reading on the buret and, (4) subtracting the initial buret reading from the final reading to obtain the delivered amount of liquid. Pipets Figure 5a and 5b: typical burets Pipets (Figure 6) come in many sizes and many shapes, but if they are used for precise and accurate measurement, they are made out of glass. Plastic pipets are disposable and are used only when exact volumes of liquids are not required. The pipet is designed to deliver a volume of liquid by gravity. Liquid is sucked into the pipet using a pipet bulb. The pipet is immersed in the liquid. The bulb is squeezed to expel air, then gently, but firmly placed over the top of the pipet (the pipet is never inserted into the bulb). By slowly and carefully releasing the pressure on the bulb, liquid will be sucked into the pipet. The appropriate amount of liquid is obtained and a finger (thumb or forefinger) is placed over the top of the pipet to hold the liquid at a certain volume, then the liquid is dispensed by gravity into the appropriate receptacle. The last bit of liquid is never blown out of the pipet by the bulb. The pipets are all calibrated to leave a small amount of liquid behind. Pipets, just like burets, must be read to the hundredths place. Figure 6: Volumetric and graduated glass pipets #2 Basic Equipment Rev W09 AEM Winter 2009 Page 5 of 18

Procedure: This section should be completed with a partner meet someone new and partner up! Obtain two 100 ml beakers. Fill one of the beakers (called the stock beaker) with ~ 50 ml of water. Set the other beaker aside. Obtain a 10.00 ml pipet, a 10.0 or 25.0 ml graduated cylinder, and a buret. You will perform the same procedure 4 times, using a different piece of measuring equipment. Review the glassware section of this laboratory handout to remind yourself about significant figures and measuring using these pieces of glassware. Many times it is also necessary to measure the mass of a liquid or solid. You will use an electronic top-loading balance to perform these measurements. These balances can be read to + 0.01 grams. When you use any balance be sure to record your data to the appropriate number of significant figures, even if they are zero (20.00 g not 20 g). Part 1: The beaker Mass the dry beaker, record this mass under the starting mass of the beaker for the beaker portion of the experiment. Using the stock beaker, which you previously filled with ~ 50 ml of water, pour 20-30 ml of that into your pre-weighed dry beaker.(note: you do not need to measure exactly twenty milliliters, but you do need to record the exact volume.) Record the volume of the water in the beaker exactly (with the correct number of significant figures see your prelab!) in the table below. Mass the beaker and the water. Record the mass of the beaker and water in the data table in the beaker portion of the experiment. Pour the water out of the beaker, and dry the beaker with a paper towel. Repeat for trial 2. Part 2: The pipet Re-mass the dry beaker, record the mass of the beaker in the table below. Pipet 10 ml of water from the stock beaker. Again, you need not get exactly 10 ml but you should record the actual volume of water you placed in the pipet with the correct number of significant figures. Drain the water from the pipet into the dry beaker (remember not to blow out the last little bit!). Mass the beaker with the water and record the mass in the data table below. Pour out the water and dry the beaker with a paper towel. Repeat for trial 2. Part 3: The graduated cylinder Re-mass the dry beaker, record the mass of the beaker in the table below. Fill your graduated cylinder with 20-30 ml of water. Again, you need not get exactly 20 ml of water but you should record the exact volume of water in your graduated cylinder with the correct number of significant figures (see the pre-lab!). Pour the water from the graduated cylinder into the dry beaker. Mass the beaker with the water and record the mass in the data table. Repeat for trial 2. Part 4: the buret Re-mass the dry beaker, record the mass of the beaker in the table below. Fill your buret with water. You need not fill the buret all the way to the 0.00 ml mark, but fill it with a substantial amount of water. Open the stop-cock to drain out some of the water which will fill the tip of the buret. Close the stop-cock. Record the starting amount of water in the buret (simply read the location of the meniscus) with appropriate significant figures. Record the starting volume in the data table. Open the buret to dispense 15-30 ml of water directly into the dried, pre-weighed beaker. Again, you need not get exactly 15 ml of water but you should record the final volume of water with the correct number of significant figures. The amount of water dispensed by the buret = final volume measurement initial volume measurement. (example: if you filled the buret and read the initial volume at the meniscus it reads 0.55 ml. You dispense a volume of water you want it to be around 15 ml. You open and then close the stop-cock. Your final volume reading of water at the meniscus is 18.12 ml. The total volume dispensed by the buret = 18.12 0.55 ml = 17.57 ml) Don t forget each piece of glassware is used twice record data in the table on the next page. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 6 of 18

Data include units with each number mass of dry beaker volume of water mass of beaker + water mass of water (calculation) density of water (calculation) Beaker: Trial 1 Beaker: Trial 2 Pipet: Trial 1 Pipet: Trial 2 Graduated Cylinder: Trial 1 Graduated Cylinder: Trial 2 Buret: Trial 1 Starting volume: Ending volume: Total volume: Buret: Trial 2 Starting volume: Ending volume: Total volume: Calculations: For each step, calculate the mass of the water that you added. Then use the mass of the water and the volume of the water to compute the density, given that density = mass/volume. Show your calculations in the table above where needed Before going any further obtain instructor initials #2 Basic Equipment Rev W09 AEM Winter 2009 Page 7 of 18

Questions: a. Which volume-measuring device was easiest to use? b. For each piece of glassware, calculate the average density. Show all your work: (don t forget units!) **hint: perform addition first to determine correct number of sig figs Beaker: average density of water = Pipet: average density of water = Graduated cylinder: average density of water = Buret: average density of water = c. A reasonable assumption given the water s temperature is that the density of water is 0.998 g/ml. For each of your devices, compute the percent difference between your average density value for each piece of glassware and the true density. Show your work and pay careful attention to the significant figures when you perform the subtraction! Beaker: your value - "true"value x 100 = % difference "true" value Pipet: Graduated cylinder: Buret: d. Which device was most accurate? Which was most precise? Explain. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 8 of 18

D. DETERMINATION OF THE DENISTY OF AN UNKNOWN Discussion of Density Determinations Density is defined as mass per unit volume. In this experiment you will use three different methods for determining density. In Part I the two methods will be for solids. Be sure to record object identification codes and shapes for the solids. Part II will be used for a liquid. Solids It is possible to determine the density of a solid that fits the category of having a regular geometric shape such as: cylinder, sphere, rectangle, and cube. Two techniques will be used to measure the volume of each solid object. The first method will involve using a Vernier caliper to determine the dimensions of the object in units of centimeters, calculating the volume from the appropriate equation. V sph 4 = π r 3 3 V cyl = π r 2 h V rect = l w h The second method requires the use of a graduated cylinder filled to a calibrated level with water to measure volume by the displacement of water. The difference in the volume of water originally and the volume with the solid is the volume of the solid alone. Liquids In Part II you will employ the techniques of graphing to determine the density of water. You will collect at least five sets of volume and mass data, record this data as shown in Part E, and then graph this data using the graphing techniques of Part F to find the density of water. EXPERIMENTAL SECTION I. Density of a Solid Do all your mass measurements on only one Electronic balance use the same balance for all mass measurements. Obtain one solid sample from the reagent bench and determine its density using both Methods. Procedure, Method 1: Record the data in the table below/next pg. 1. Using the Electronic balance, determine the mass of the solid. 2. Using your Vernier caliper, measure the dimensions of your solid and determine its volume. 3. Calculate the density of your solid. Method 1- Solid Density Object Identification (letter tapes on the solid sample) Object shape Mass, Electronic balance g #2 Basic Equipment Rev W09 AEM Winter 2009 Page 9 of 18

Volume via dimensions (Label values with units and appropriate number of significant figures. Formulas for volume are on pg. 9.) You must get instructor initials for your measurements before you perform your calculations diameter of the cylinder = height of the cylinder = Instructor initials for measurements Calculations for volume of the cylinder: Calculations for density of the cylinder: Volume of object ml Density of object g/ml Procedure, Method 2: Record the data in the table on the next pg. 1. Add roughly 30 ml of water to your 50 ml graduate cylinder and then carefully record the volume to the proper precision. 2. Add the solid to the graduate cylinder. This should be done by tilting the graduated cylinder at an angle and allowing the solid to slide down into the cylinder. If you simply drop the object into the graduated cylinder you will either break the graduated cylinder or splash water out, which makes your volume measurement inaccurate. Make certain that the measured volume of water will completely cover the immersed object and that the graduated cylinder used is large enough to produce measurable results. 3. Using the mass of the solid from Method 1, calculate the density of your solid. Solid Density, Method 2. Volume via displacement initial volume of water _ ml volume with object and water _ ml Calculations Volume of object: ml Density of object: g/ml #2 Basic Equipment Rev W09 AEM Winter 2009 Page 10 of 18

Questions: 1. Look carefully at your object and see if you can identify it; note any symbols on it (Zn, Cu, Al, etc). If you find no clues, ask your lab instructor to help identify your solid. Then look up its accepted value for the density in the Handbook of Physics and Chemistry, and determine the percent difference for both Method 1 and Method 2 using the formula explained previously. True value of density for my unknown object % difference calculations: show your work! pay careful attention to sig figs especially while performing the subtraction! Method 1. Method 2. 2. Describe in words how your results for both methods compare with the accepted value. 3. Calculate the average density using the values from Method 1 and Method 2. List a possible source of error between your average experimental value and the true value. Explain how it affected your value. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 11 of 18

SECTION E: DENSITY AND GRAPHING This section will give an example of how to record the data in tabular form. Tables are easier for you to write, easier for your reader to read, and easier to understand, than data in narrative form. For this experiment, a suitable Data section is included. Labeling of all data and units for data must be included. Density of a Liquid (Water) Procedure 1. Obtain a clean dry 100- ml beaker. Weigh it and record the mass in the table below (page 13). 2. Fill the buret with distilled water, taking care that there are no trapped air bubbles. Open the stop-cock to fill the tip. Close the stop-cock, add more water to the buret if needed. Record the volume to the nearest 0.01 ml (or set it at 0.00 ml). Be sure the tip is filled with water! 3. Draw off between ~3.00 - ~7.00 ml of water into the pre-weighed l00 ml beaker; record the total volume drawn from the buret to the nearest 0.01 ml. Do not spend time adjusting the volume to a specific number, simply write down the volume you dispensed. 4. Determine the total mass of the beaker and water by weighing on the same electronic balance as your original beaker was weighed; record the mass to the nearest 0.01 g. 5. Without emptying the water from the beaker, repeat steps 2 and 3 at least 4 more times (a total of 5). 6. Record the data to be used on the graph in a table as shown. Graph your results using the techniques of Part F. Always use graph paper. 7. After you have graphed the data, determine the slope of your line using arbitrary x and y (x n, y n ), (x m, y m ) coordinates as the points of reference; do not use data points. Be sure to use the proper units in your answer, and show formulas and substitutions in your solution process. Show work and calculations on your graph. m = y x ( ) ( ) = slope = y m - y n x m - x n #2 Basic Equipment Rev W09 AEM Winter 2009 Page 12 of 18

Data Table for Liquid Density. (use the space provided in the volume column to perform difference calculations to determine the total volume of water added from the buret into the beaker) Buret drawing Cumulative volume dispensed (ml) (total volume of water in the beaker), x-axis Cumulative Mass of Water + beaker (g), y-axis 0 Initially there is 0.00 ml in the beaker of water grams 1 TOTAL volume: ml grams 2 TOTAL volume: ml grams 3 TOTAL volume: ml grams 4 TOTAL volume: ml grams 5 TOTAL volume: ml grams Remember: the total volume will be the overall cumulative volume of water that is in the beaker after each addition of more water NOT individual volumes total volume! You will plot the above data by hand on the graph paper provided (pg 15). Please review prelab question 3 and re-read the good graphing techniques (part F, pg 14)! #2 Basic Equipment Rev W09 AEM Winter 2009 Page 13 of 18

F: GRAPHING TECHNIQUES (Also refer to the section on Representing Data and Results Using Graphs in your Laboratory Handbook where there is an example.) You need to employ the techniques of graphing to determine the density of water from the data you collected in Part E. You will plot your data on graph paper, putting total volume on the x-axis (abscissa) and mass on the y- axis (ordinate), remembering the following graphing techniques: 1. Label each axis with the type of measurement it represents and the type of units used, e.g., volume in milliliters, and mass in grams. Always label so that numbers increase toward the right on the x-axis and upward on the y-axis. 2. Choose a size of graduation so that your data will spread over as much of the entire graph as possible. The graduations on the two axes need not be of the same magnitude, but the magnitude of a given graduation along one axis must not change. 3. Number the graduations on each axis. It is not always necessary to start with the origin being zero (for the volume measurement in this experiment use 0; begin the mass graduations at about 10 grams less that your first mass reading). 4. When locating a point on the graph, it is a good practice to circle the small point with a small o, rather than use large dots or x's. 5. When drawing the line on a graph, always draw a smooth line using a ruler through the average location of the points, rather than connecting the points in a draw by numbers method. 6. When extrapolating a curve (extending the curve beyond the range of the actual data points), continue the curve using a dotted line rather than a solid one, to distinguish it from the part of the curve based on actual data. 7. Show all data and calculations for the slope on the graph itself. Indicate the arbitrary (not data) points used for the slope and indicate the y-intercept where appropriate. Do not use actual data points in your calculations!!! Use two points that are on that are on the best-fit line and that are within the range of your data. 8. Make sure that all axes are labeled with the quantity and the units, and that the graph has an appropriate title. Y vs. X is NOT an appropriate title. Your title should be a descriptive sentence that tells the reader what the point of the graph is. Why did you plot y vs. x? What information does it give to the reader? Remember, you spent valuable time collecting this data. Make the graph large enough (the data should take up the WHOLE page) so that it can be read accurately and so that you can draw your line, calculate slopes, and find the intercepts with some precision. Please use the graph paper on the next page. #2 Basic Equipment Rev W09 AEM Winter 2009 Page 14 of 18

Final Graph: Part E #2 Basic Equipment Rev W09 AEM Winter 2009 Page 15 of 18

Questions: (Show all calculations on your graph or as appropriate in the question review pre-lab question 3 if you need help) 1. What do scientists call the physical property represented by the slope of your line? Hint: what would the units of the slope be? 2. What numericalvalue did you find for this property, give units as well? 3. Extrapolate your graph past the y-axis. What is the mass at zero volume? Estimate this value from your graph to as many significant figures as your graph allows! 4. This mass represents the mass of what object? (Do you realize that you have just determined the mass of an object without weighing it directly?) 5. The known density of water at 20 C (approximate laboratory temperature) is 0.998 g/ml. Calculate the percent difference for the density of water that you obtained from the slope of your graph, versus the known density. Show your calculation pay attention to sig figs!! 6. Calculate the percent difference for the mass obtained from y-intercept in comparison with the mass of the beaker as weighed in step 1 of the procedure. Show your calculation 7. Write a concluding paragraph on a separate sheet of paper restating your results and possible errors, regarding this section (E). Follow the format for the concluding paragraph in the example formal report. Use complete sentences. Do not use personal pronouns in your concluding paragraph!! Attach the paragraph and your graph to the end of this report. Have you attached the conclusion? #2 Basic Equipment Rev W09 AEM Winter 2009 Page 16 of 18

Stamp: Basic Equipment Prelab Questions: These questions are to be answered before you come to the laboratory. Always read the experiment before starting the prelab. Your textbook, Lab handout (this packet) and the Laboratory Handbook are excellent resources. It is your responsibility to get this stamped by the Lab Instructor before you begin working on the experiment! 1. How many digits after the decimal place can you read a (circle one): a) beaker 0 1 2 3 b) graduated cylinder 0 1 2 3 c) buret 0 1 2 3 d) pipet 0 1 2 3 2. You have a sample of titanium metal. You mass it on an electronic balance and it has a mass of 7.52 grams. You decide to measure the volume by volume displacement. You fill a graduated cylinder with 35.2 ml of water. After dropping the titanium into the graduated cylinder, the volume now reads 36.9 ml. Determine the density of titanium: Density = If the density of titanium is 4.51 g/ml, what is the percent difference between your value for density calculated above and the accepted value for the density? Show your calculations. (see formula on pg 8) percent difference = 3. Using the following data to graphically find the density of a substance. Graph the data by hand, on the graph paper on the back of this page. Draw a best-fit line through the data and determine the slope of this line. Make sure that you label the axes and title the graph appropriately. Show this graph to the Lab Instructor. FOLLOW THE GOOD GRAPHING TECHNIQUES (pg 14) Total Volume dispensed (ml) [x-axis] Cumulative Mass of substance + beaker (g) [y-axis] 13.25 48.67 22.98 55.35 33.15 66.37 42.67 72.15 density = #2 Basic Equipment Rev W09 AEM Winter 2009 Page 17 of 18

Pre-lab Graph #2 Basic Equipment Rev W09 AEM Winter 2009 Page 18 of 18