CHEM& 151 WINTER 2010 BASIC EQUIPMENT, MEASUREMENT, DENSITY, AND GRAPHING I. INTRODUCTION Any comprehensive chemistry course includes a certain amount of laboratory time. The laboratory portion of this class is meant to do two things for your learning: (1) to bring useful insights about the chemical principles and theories discussed in lecture into your practical experience through real life situations and (2) allow you the opportunity to develop proper scientific laboratory techniques essential to obtaining precise and accurate experimental results. It is therefore important to begin your development in these skills early in your laboratory experience. Among the techniques you will learn in lab, the following are key objectives in all labs you will do in this class: a. Follow a scientific laboratory procedure to achieve the desired result(s). b. Carefully observe and accurately collect experimental results. c. Critically apply chemical principles to interpret your data and arrive at a conclusion rational to your chemical problem. d. Propose a solution(s) to your chemical problem using your data and conclusion. The measurement of the physical properties of pure substances is an important technique as a part of the larger scheme in identifying elements and compounds. In this lab you will learn how to measure the densities of two substances. Through the use of measurement you will also learn how to practically apply significant figures in your calculations and how to analyze the precision of measurements found in a variety of laboratory glassware and equipment. At the end, you will use your data and learn how to correctly generate, manipulate and analyze that data in graphs to obtain a result and reach a conclusion. II. LEARNING OBJECTIVES After completing this experiment, you should feel comfortable with: • The identity, location and use of common laboratory equipment . • Experimentally determining the densities of solid or liquid objects. • Using various types of volume-measuring devices, and understand the difference in precision between the devices. • Performing percent difference calculations and report the values with correct significant figures. • Using a graphing program to graphically render data and analyze the graphs to make conclusions about the data. TO EARN YOUR FINAL STAMP: You may complete the entire assignment in lab, but the following reflects the minimum required to earn your final stamp: Complete Activity 1, the equipment scavenger hunt. Collect the data for Activity 2, and calculate the density of your object. (Complete all of Data Table 1) Collect the data for Activity 3, completing Data Tables 2, 3 and 4. Using a graphing program, use a computer to generate the three graphs needed to analyze the data, and report your three densities in Data Table 5. Prelab attached (see pages 15-16) REMEMBER: You must get a stamp from a laboratory instructor during lab time, before the due date! The lab stamp box can be found on the first page of the lab report sheet. #2 Basic Equipment Rev F09 NF Fall 2009 Page 1 of 16 III. INFORMATION/DISCUSSION A. SIGNIFICANT FIGURES 1. Significant Figures From Measurements: How many digits do you record? General Rule: The number of decimal places that you can legitimately record from an instrument is the precision of that instrument. • On digital instruments (e.g. a mass balance) record every digit given in the measurement. Shown at right, if a balance readout looks like the example, you should record 1.70g, not 1.7g. 1.70g g Helpful Hint: The greater the number of significant figures in a measurement, the greater the certainty in that measurement! • For non-digital measurements (e.g. a ruler or graduated cylinder), you always include an estimated number as your last digit. The estimation is made using the digit after the last marking on the instrument. In the example below (Figure 1), using a centimeter ruler, the pencil could be recorded as having a length of 1.87cm. 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. How did we get 1.87cm? The markings on the ruler are to the tenths place, so the digit we estimate should be in the hundredths place. Thus, in the example, for the number 1.87g, the “7” is the estimated digit and where uncertainty exists within this measurement. Uncertainty meaning that another person might suggest the measurement to be 1.86cm or 1.88cm, depending on how they estimated. Note that reporting 1.86cm is different than reporting any other number with fewer or greater significant figures (or number of decimal places). That is, a reading of 1.9cm would be incorrect as it is below the precision of this ruler. Helpful Hint: Each time you make a measurement, pay attention to the markings (divisions) on the measuring device! General Rule: Use the markings 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. #2 Basic Equipment Rev W10 KB WINTER 2010 Page 2 of 16 2. Significant Figures From Measurements: How many significant figures do I use? • 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: 2.300 x 103g includes 4 s.f. 2.30 x 103g includes 3 s.f. 2.3 x 103g includes 2 s.f. 3. Significant Figures In Calculations: How many significant figures do I report? € • Multiplication and Division: the result is rounded to the same number of significant figures as the least precise number in the calculation: 0.70g 5.67 mL × = 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. €Helpful Hint: It is important to remember that you can gain or lose significant digits when you add and/or subtract numbers together! Helpful Hint: Be aware of significant figures in all your calculations, both in the laboratory and lecture portions of the course. General Rule: To avoid rounding errors over multistep calculations, round only the final answer - DO NOT round at intermediate steps. Instead, record intermediate answers and underline the least significant digit in each. After the final calculation, report the overall answer based on the intermediate alue with the fewest significant figures. #2 Basic Equipment Rev W10 KB WINTER 2010 Page 3 of 16 B. PRECISION VERSUS ACCURACY 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. Thus a measuring device that allowed you to read 5.00g would provide increased precision. Precision is also used to describe data that falls into a narrow ‘window’ measured two ways, depending on how the data was collected: 1. If you make same measurement repetitively (numerous times). If your results are grouped together and the same reading was obtained each time, your results are very precise. Precision is then defined as the reproducibility of each result compared to data set. 2. Similarly, if you make several measurements across a range of values and graph the data to obtain a line or curve, then precision is assessed as the correlation of the data to a best-fit trendline. The linear regression (R2 value) provided by most graphing programs (such as Excel) describes how well the data fits to the best-fit trendline. Any fluctuations due to imprecise measurement is reflected in an R2 value less than one (1.000…). Therefore, R2 values less than one indicate a loss in precision over the range of data. ACCURACY: Accurate measurements are correct measurements. Accuracy is generally measured against an accepted standard or “true value.” This “true value” is obtained from a reputable textbook or handbook, and is a value based on a large collection of experimentally determined data points for a particular experiment. Consider an example using the following set of data collected by a student for the length of a particular object: 42.56cm, 42.55cm, 42.58cm. Based on the data, the students’ average was 42.56cm, however the overall average for all 200 students doing that lab, using the same type of measuring device, was 41.72cm. From the data we can conclude that the student made very precise measurements (their data was clustered within a range of 0.03cm), but their results were not very accurate when compared to the class average. General Rule: When you collect data in the lab, your ultimate goal is for your results to be both precise and accurate. Percent Difference Calculations The percent difference (or percent deviation) is calculated when you want to know how close an experimentally determined value is to an accepted value or “true value.” The calculation involves both a subtraction and a division. Care must be taken to determine the number of significant figures that remain from the subtraction, which is then carried through to the division. The final answer is reported as an absolute value and must reflect the correct number of significant figures based on the data used in the calculation. Percent Difference = accepted value - experimental value x 100% accepted value Helpful Hint: A large part of your lab grade each week will be based on the accuracy and precision in € Percent difference is a popular method to evaluate accuracy. Always double-check your your data. significant figures every time you report a percent difference (to avoid losing points)!! #2 Basic Equipment Rev W10 KB WINTER 2010 Page 4 of 16 C. VOLUME AND MASS MEASUREMENTS Background Information: Refer to the appropriate sections in any Laboratory Handbook for information about using measuring devices. Discussion of Volume Measurements Almost all chemical experimentation requires the accurate measurement of some physical or chemical property. In this experiment you will learn to use the graduated cylinder, the graduated pipet, and the beaker to measure the volume of a liquid. The precision and accuracy of the three methods of measurement will be compared using water as the liquid, whose accepted values of density are known quite accurately under a variety of laboratory conditions. Water is attracted to glass molecules when the two come into contact. Instead of forming a flat surface to read our measurement, water forms a concave surface that curves upward at the outer edges inside the glass container. This curvature is called the meniscus. All volume measurements made with water in glass should be read from at the bottom of the meniscus at eye level. Incorrect positioning (called parallax) can result in a volume measurement that is either too large or too small. Figure 2 shows the correct eye position used when reading the volume. Using this technique, the correct reading of the volume in the figure would be 82.0mL. Figure 2: Reading a meniscus 1. Beakers Beakers, by design were made to give only approximate volume measurements. They range in size from those holding only a few mL to those that hold many liters and can be heated and cooled. Beakers have a larger width compared to their height (see Figure 3) which adds difficulty in precisely and accurately reading a volume measurement. The precision and accuracy of volume measurements with beakers depend on their size, but beaker volumes are always whole number readings (i.e., 40Figure or 45 3: mL, never 45.3 mL). A beaker 2. Graduated Cylinders Graduated cylinders are designed to deliver a volume of liquid, not to be heated or have chemical reactions run in them. While they also come in a variety of sizes, you will use primarily the 10.0mL and 50.0mL sizes in lab. Graduate cylinders are considerably smaller in width than in length (see Figure 4) so a meniscus can be more easily read. The height also allows more spacing between marks on the scale, and it therefore has more graduations. The precision for volume measurements 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) #2 Basic Equipment Rev W10 KB WINTER 2010 Figure 4: A graduated cylinder Page 5 of 16 3. Pipets Pipets come in a variety of shapes and sizes. Plastic pipets are disposable and are used only when exact volumes of liquids are not required. For precise and accurate volume measurements, only glass pipets are used. Glass pipets come in two varieties: volumetric and graduated (Figure 5). Pipets are filled by drawing liquids into them via suction, applied from the top using a pipet bulb, and deliver a volume of liquid by gravity. Figure 5: Volumetric and graduated glass pipets Key Differences Between Volumetric and Graduated Pipets: • Volumetric pipets are designed to measure ONLY one volume and are sized accordingly (10.0mL, 50.0mL, etc). These pipets are referred to as ‘to delivery (TD)’, thus a 10.0mL pipet dispenses only 10.0mL. • Graduated pipets are designed to measure a variety of volumes over their calibrated range (a 10.0 mL graduated pipet can dispense 1.0-10.0mL). The pipet graduations are read to determine volume dispensed by difference - that is using the difference between the starting and stopping volumes on the pipet. Key Similarities Between Volumetirc and Graduated Pipets: • All of the liquid in a pipet should be allowed to drain by itself, without using a bulb. • A small amount of liquid should be left in the tip of a pipet. Glass pipets are calibrated to account for a small amount of liquid to remain. This last bit of liquid is never “blown” out of the pipet. • Based on their markings, all pipets must be read to the hundredths place. General Rule: Like all precise measuring tools, glass pipets should never be heated or used with corrosive liquids, as both alter the ability to repetitively dispense a precise volume. To Fill A Pipet: With the pipet immersed in a liquid, squeeze a pipet bulb to expel the air and then gently place it over the top of the pipet. The bulb should rest on top of the pipet, and with gentle, but firm pressure, hold the bulb on top of the pipet to form an airtight seal. By slowly and carefully releasing the pressure on the bulb in your hand, liquid will be drawn into the pipet. When the appropriate volume of liquid is obtained, place a thumb or forefinger on the top of the pipet to hold the liquid level. By releasing pressure with your finger, liquid can slowly be dispensed to reach the desired volume mark on the pipet. Liquid flow is again stopped with a finger, and the exact volume dispensed is read off of the pipet. Helpful Hint: Practice using a pipet with water first! #2 Basic Equipment Rev W10 KB WINTER 2010 Page 6 of 16 4. Discussion of Mass Measurements In the chemistry lab, mass measurements are made using only digital balances, and the mass readings can be read directly from the balance. Like glassware, not all balances measure to the same level of precision. In CHEM&151 and 152, you will be using ‘top-loading’ balances, which have a precision to the hundredths place. This precision can be indicated by stating the balance is “good to ±0.01g”, meaning that the balance gives measurements to two decimal places. If smaller quantities or more precision is required by an experiment, an analytical balance is employed. Like a top-loader , this is also a digital pan balance but is sensitive enough to need side and top shields to isolate the pan from air currents that can affect the measured mass. An analytical balance measures masses to ±0.1 mg or ±0.001mg, four decimal places. Helpful Hint: Most digital balances also measure mass in different units (grams, ounces, etc…). Always be sure that the balance is set to gram units (g) before measuring a sample. Balances have a tare or “zero” function that allows them to be reset, with or without objects on the pan. By pressing the “Zero/Tare” button on the balance, any mass measurement can be reset to zero. In the laboratory we often measure chemical reagents by difference. That is, measurement is taken for an empty container, and for the container once a sample has been placed inside; the difference between the two is the mass of the material itself. By measuring by difference, even if a balance is not properly calibrated, the mass difference will still be accurate. General Rule: Always use the same balance for all your mass measurements throughout an experiment. This will reduce the chance of introducing systematic errors from other balances into your measurements. Helpful Hint: Always record the mass of any empty container in your lab report or lab notebook before leaving the balance area. Balances are use by everyone in the lab, and could easily be reset before you returned to it. D. DENSITY DETERMINATION Density is defined as mass per unit volume. There are a variety of different methods to determine the density of a substance; the method chosen depends largely on the phase and the shape of the substance being tested. In this experiment you will investigate density using two methods: direct measurement and volume displacement. Measuring the Density of a Liquid Measuring the density of most liquid samples is fairly straightforward: A measured volume of the liquid is weighed directly on a balance. Density can be directly calculated from your mass and volume measurements. Measuring the Density of a Solid The density of any solid can be measured regardless of shape by measuring the volume displaced in water. First, the mass of the dry object is measured with a balance. The object is then submerged in a container where the volume of water can be precisely measured. As the water level rises, the difference in volume represents the volume of the solid object. The density is then calculated from the mass and this displaced volume. #2 Basic Equipment Rev W10 KB WINTER 2010 Page 7 of 16 Turn in THIS page and all that follow for your lab report! Name _____________________ Partner ___________________ Stamp Here Lecture Instructor Date ______________________ ____________________ Fill-in - Refer to the Laboratory Syllabus for how to complete your lab reports. This experiment consists of three activities: Activity 1: Equipment Scavenger Hunt Activity 2: Determination of the Density of a Solid Activity 3: Investing the Precision of Volumetric Measuring Devices ACTIVITY 1: FINDING EQUIPMENT IN THE LAB: A SCAVENGER HUNT This activity must be completed in the lab to obtain a final stamp. 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”. PROCEDURE: Find each of 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, return the items back to the appropriate locations in the lab. Helpful Hint: Some items you will need for the next activity. Read ahead and keep those items at your bench-top until you have finished the experiment. #2 Basic Equipment By instructor _______ _______ _______ _______ _______ _______ _______ _______ _______ _______ _______ Item Utility clamp Buret Clamp 100-mL beaker 125-mL Erlenmeyer flask Thermometer Tongs Ring stand Test tube Spatula/scoopula 10-mL Graduated pipet 25-mL Graduated cylinder Instructor Initials: __________________ Rev W10 KB WINTER 2010 Page 8 of 16 ACTIVITY 2: DENSITY DETERMINATION OF AN UNKNOWN SOLID OBJECT PROCEDURE: Technique Alert: Remember to use the same balance for all mass measurements. 1. Obtain one solid sample from the reagent bench. Record the object identification in the data table below. 2. Use an electronic ‘top-loading’ balance to determine the mass of the solid. Record this mass in the data table to the appropriate precision. 3. Obtain a 50-mL graduated cylinder and add roughly 30 mL of water to it. Carefully read and record this volume to the proper precision in the data table. 4. Carefully add your solid object to the graduated cylinder by tilting the graduated cylinder at an angle to allow the solid to slide down into the cylinder. Simply dropping the object into the graduated cylinder will either break the graduated cylinder or splash water out, making your volume measurement inaccurate. Helpful Hint: The graduated cylinder must be large enough to produce measurable results. Be sure the measured volume of water completely covers the immersed object. Data Table 1: Density of a Solid Object This table must be completed in lab to earn a final stamp. Object Identification Letter Mass of Solid Object Volume of Object + Water Initial Volume of Water Volume of Solid Object Calculated Density of the Object (show calculation below) Density Calculations #2 Basic Equipment Rev W10 KB WINTER 2010 Page 9 of 16 Questions: (may be completed at home or in lab) 1. Consider the calculated density of your object. Compare your value to the densities in the table you completed in the prelab. a. Based on the information provided, what is the chemical identity of your object? b. Calculate the percent difference for your experimentally determined density from the accepted value. Show this calculation below and pay careful attention to significant figures! ACTIVITY 3: Investigating the Precision in Volumetric Glassware Technique Alert: Review the section of this handout regarding volume measurements and significant figures for laboratory glassware. Obtain the following pieces of glassware and equipment: • Four beakers: 100mL or 150mL in size; they do not all need to be the same size, but at least one should have volume markings. o make sure they are all clean and dry, and that they are clearly labeled 1 – 4 with lab tape. • One large beaker (400 or 600mL) with approximately 300mL of distilled water. • One 25mL graduated cylinder. • One 25mL graduated pipet. (These will be on the reagent bench). PROCEDURE A. Beaker Measurements 1. Weigh one empty beaker (clean and dry) with markings and record its mass in the Data Table 2. 2. Add approximately 20mL of water to this beaker. Record the exact volume of water under ‘Trial A’ to the appropriate precision. 3. Weigh the beaker with water and record the mass. Calculate the mass, by difference, for the water in the beaker. 4. Add an additional 20mL of water (for a total of 40mL) to the beaker. Record the total volume and mass for this addition in the table under ‘Trial B’ 5. Repeat the process two additional times, so that you record the volumes and masses for 60mL and 80mL of water (Trials C and D). 6. Calculate the mass, by difference, for the water in the beaker for all remaining trials. #2 Basic Equipment Rev W10 KB WINTER 2010 Page 10 of 16 Data Table 2: Density of Water Measured by a Beaker (must be completed in lab) Mass of Empty Beaker Trial Volume of H2O Mass of Beaker + H2O Mass of H2O A B C D Obtain instructor initials when Data Table 2 above is complete. _______ B. Graduated Cylinder Measurements 1. Use all four labeled beakers for this portion of the experiment; make sure they are clean and dry. 2. Weigh each beaker on a balance and record each mass in Data Table 3 below. 3. Using a 25mL graduated cylinder, measure 10mL of water. Record the exact volume of water from the graduated cylinder in Data Table 3. 4. Transfer the water to the beaker labeled 1, then weigh the beaker with water and record the mass. 5. Repeat the process three additional times (in beakers 2, 3 and 4), so that you record the volumes and masses of 15mL, 20mL and 25mL of water. 6. Calculate and record the mass, by difference, for the water in all four beakers Data Table 3. Data Table 3: Density of Water Measured by Graduated Cylinder (must be completed in lab) Trial Volume of H2O Mass of Empty Beaker Mass of Beaker + H2O Mass of H2O 1 2 3 4 Obtain instructor initials when Data Table 3 above is complete. _______ #2 Basic Equipment Rev W10 KB WINTER 2010 Page 11 of 16 C. Pipet Measurements 1. Use all four labeled beakers for this portion of the experiment; make sure they are clean and dry. 2. Weigh each beaker on a balance and record the masses in Data Table 4 below. Technique Alert: Be sure to weigh each beaker again! Do not use masses from the previous measurements! Helpful Hint: Practice drawing water into the 25mL graduated pipet and controlling the flow of water from the pipet before moving on. Ask a lab instructor for help if you need it!. 3. Using a 25mL graduated pipet, draw in enough water to fill the pipet to the zero mark. Into the beaker labeled ‘1’, dispense about 10mL of water, and record the precise volume of water in Data Table 4. Weigh the beaker with water and record the mass. 4. Repeat the process three additional times (trials 2, 3 and 4), so that you dispense and record the volumes and masses of 15mL, 20mL and 25mL of water in the remaining beakers. 5. Calculate and record the mass, by difference, for the water in all four beakers Data Table 4. Data Table 4: Density of Water Measured by Graduated Pipet (must be completed in lab) Trial Volume of H2O Mass of Empty Beaker Mass of Beaker + H2O Mass of H2O 1 2 3 4 Obtain instructor initials when Data Table 4 above is complete. _______ 4. Processing the Data (This must be completed in lab and, is required for a final stamp.) Helpful Hint: Refer to the “Graphing handout” in your lab packet or topics related to “Representing Data and Results Using Graphs” in any laboratory handbook. You will need to determine the average density of water for each measuring device (the beaker, graduated cylinder and graduated pipet). This will be done graphically plotting the mass of water versus the volume for each device. Be sure to label your axes and title each graph appropriately. To measure your accuracy, add a linear trendline to each graph and display the equation for the best-fit line with the R2 value (the correlation factor) on the graph. Each graph needs to be printed separately. Use your graphs to complete Data Table 5 and answer the following questions. Technique Alert: Use your experimental data, not the computer graphing program, to determine the correct number of significant figures to report in your density values! #2 Basic Equipment Rev W10 KB WINTER 2010 Page 12 of 16 Data Table 5: Average Densities of Water Based on Measuring Device (must be completed in lab) Measuring Device Density of Water Correlation Factor (R2) Beaker Graduated Cylinder Graduated Pipet QUESTIONS: (Completing this section is not required for a final stamp.) 1. An acceptable value for the density of water at 25.0ºC (room temperature) is 0.998 g/mL. For each of piece of glassware tested, calculate the percent difference between your average density values for each piece of glassware and the accepted density given. Show your work for each calculation and and pay careful attention to the significant figures you report in your final answer! Percent Difference = € accepted value - experimental value x 100% accepted value Beaker: Graduated cylinder: Pipet: 2. Using your experience from this lab, briefly describe which volume-measuring device was easiest to use and why? #2 Basic Equipment Rev W10 KB WINTER 2010 Page 13 of 16 3. Which device was the most accurate in this experiment? Which was the most precise? Explain how you arrived at these conclusions. 4. Based on your answers in the prelab, the pipet was chosen as the measuring device that can be read with the greatest precision (the greatest number of decimal places). Based on your results, was the pipet more precise than the other glassware tested? What factors might affect the precision of a measuring device? 5. Why was the slope of the best-fit line used instead of individual data points to determine the density of water? Explain your answer by choosing one of your data points, calculate the density and make a comparison. 6. A student in another chemistry class needs an accurate way of determining the density of a liquid, and comes to you seeking guidance. Which technique would you recommend to the student to use? Provide advice you would give this student to help them with this technique. 7. On a separate sheet, attach a written conclusion for this experiment. Use your answers to the questions to guide your response. Have you attached the graphs and the conclusion? #2 Basic Equipment Rev W10 KB WINTER 2010 Page 14 of 16 Basic Equipment PRELAB Stamp: Name ________________________ Prelab Questions: Answer these questions before you come to the laboratory. Always read the experiment before starting the prelab. Your textbook, THIS lab handout and a 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 b) graduated cylinder 0 1 2 c) pipet 0 1 2 3 3 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 of the sample 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 3) Percent difference = 3. Look up the densities for the following pure elements. You can look them up in your text, in a handbook (available in the library), or online, but you must cite your source. A space is provided for the citation below the table. Element Density (g/mL or g/cm3) Element Iron (Fe) Zinc (Zn) Nickel (Ni) Copper (Cu) Aluminum (Al) Titanium (Ti) Density (g/mL or g/cm3) Citation: #2 Basic Equipment Rev W10 KB WINTER 2010 Page 15 of 16 4. The following data was collected by using two different types of glassware to measure the volume. The data was graphed with the masses on y-axis and volumes on the x-axis. Glassware A Glassware B Mass of Water (g) Volume of Water (mL) Mass of Water (g) Volume of Water (mL) 10.01 14.92 19.89 24.89 10.00 15.00 20.00 25.00 10.50 14.86 20.23 25.12 10.0 15.0 20.5 25.0 Use the graphs below to answer the following questions. Glassware A: Glassware B: 30.00 30.0 25.00 25.0 20.00 20.0 15.00 15.0 10.00 y = 0.9922x + 0.0640 R² = 0.99998 5.00 0.00 0.00 10.0 5.0 y = 1.0246x ‐ 0.4881 R² = 0.99787 0.0 5.00 10.00 15.00 20.00 25.00 30.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 Label the axes and put appropriate titles on the graphs. See the ‘Graphing Techniques’ document in your lab packet for assistance. a. What are the units on the slope for the best-fit lines? b. What physical property is represented by the best-fit lines? c. Report the slopes of the best-fit lines, with correct significant figures and units. d. Which piece of glassware is the most precise? How did you make this decision? #2 Basic Equipment Rev W10 KB WINTER 2010 Page 16 of 16
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