Lab 1. What s In A Number? Which measuring device should I use? What do significant figures tell me? Is there really that much sugar in my soda?

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1 Lab 1. What s In A Number? Which measuring device should I use? What do significant figures tell me? Is there really that much sugar in my soda? Prelab Spend 5 minutes doing the following activity. Assign a notetaker. Report to class. Every measurement has error or uncertainty associated with it. When you make a measurement in science and get a number, you want to know which digits in the number you know with certainty and which digit is the uncertain digit. When you look at the lines on a measuring device, you know the quanity and unit represented by each line with certainty. You are allowed to guess in between lines. The guess that you make is the uncertain digit and tells you the error in your measurement. The uncertain digit is the last signficant figure (digit) in your number. 1. In 1880, Lord Rayleigh measured the density of N 2 from air to be g/l. The density of N 2 obtained by burning NH 3 gave g/l. They were not the same. How many significant figures are reported in each number? Rayleigh, along with Ramsay, came to realize air contained an unknown, heavier gas, which proved to be argon. Thus, the noble gases were found. Rayleigh and Ransay won Nobel Prizes in 1904 and Had Rayleigh's work been good to only three significant figures (1.25 g/l), they would have lost their place in history. 2. a. To measure the temperature of water, which device or instrument would you use, your finger (as in stick your finger in the water), a thermometer, a balance, or a spectrometer? b. To measure how heavy your dog is, which device or instrument would you use, your hand (as in hold the dog in your hand), a thermometer, a balance, or a spectrometer? c. To measure the wavelength of the light emitted by a firefly, which device or instrument would you use, your eye (as in look at the firefly), a thermometer, a balance, or a spectrometer? 3. Find a penny or nickel or dime or quarter. a. Each person in your group does this measurement. (i) Look at your index finger. You see two lines between the tip and the base of your finger. Call the line at the base on your index finger 0. The first line from the base is 1, the second line is 2, and the tip of your index finger is 3. (ii) Measure the diameter of the coin with your index finger. What is the error or uncertainty in your measurement? Record the length of the penny using the correct number of significant figures in Table 1. Table 1. Length of coin using finger and ruler. Coin =. Length measuring device Each line represents (include units) Uncertainty s (Name) finger ± s (Name) finger ± s (Name) finger ± ruler ± Length (include units) Uncertain digit b. (i) Use a ruler. What length does each line on your ruler represent? (ii) Measure the diameter of the coin with your ruler. What is the error or uncertainty in your measurement? Record the diameter of the coin using the correct number of significant figures in Table 1. c. See your length measurements. Which digit(s) do you know with certainty? Which digit is the uncertain digit (the digit that has error associated with it)? d. How is the line on each measuring device related to the uncertainty (error)? 15

2 4. Look carefully at the measuring devices in Table 2. Note: there are two different types of pan balances in the balance room. a. For each measuring device, what does each line represent? For the triple beam balance, what does each line on the beam closest to you represent? b. State the uncertainty for each device, e.g., ±1 g. Table 2. Uncertainty of various measuring devices. Measuring device Each line represents (include units) Uncertainty Uncertain digit 10 ml transfer pipet ± 10 ml graduated cylinder ± 50 ml graduated cylinder ± 400 ml beaker ± Triple beam balance ± Pan balance (Type 1) ± Pan balance (Type 2) ± Objectives (i) Make measurements and do a calibration. (ii) Relate significant figures to uncertainty and error. (iii) Use significant figures in calculations. Materials mass measuring devices: triple beam balance and pan balance volume measuring devices: 10 ml and 50 ml graduated cylinders, 50 ml beaker, 10 ml volumetric pipet, 10 ml transfer pipet Vernier LabQuest Mini, USB cable, temperature probe Students: bring a regular and diet soda for Part 2. Part 1. How many numbers should I use when I measure something? Introduction We measure things, i.e., attach a number to an observation, for many reasons: to identify something, to classify something into a group, rank something on a scale, construct something, trade something, to investigate, understand, and control scientific processes, to develop theories, to predict something, etc. What does the number mean? How accurate is it? How much error or uncertainty does the measured number have? Procedure You re making a fancy sauce and the recipe reads, Add 2 teaspoons of vinegar to the sauce and heat gently. You don t have a teaspoon but you know 1 teaspoon is 5 ml so your scientific mind reads the recipe as an experimental procedure which states, Add 10 ml of liquid reactant to the flask. Place the flask in a hot water bath. You don t have a teaspoon but you and your lab partners think, How accurately do I have to measure the liquid? Should I use a 50 ml beaker or 10 ml graduated cylinder or 50 ml graduated cylinder or 125 ml flask? How hot is the water bath? 1. Let s see how accurately a 50 ml beaker, 10 ml graduated cylinder, and 50 ml graduated cylinder reads volume. Calibrate the volume of each container. The groups on each bench will calibrate the same volume measuring device: Bench 1 = 50 ml beaker Bench 2 = 10 ml graduated cylinder Bench 3 = 50 ml graduated cylinder. a. Find a 10 ml transfer pipet in the lab. Your instructor will demonstrate the use of a 10 ml transfer pipet and a 10 ml volumetric pipet. 16

3 A 10 ml transfer pipet or 10 ml volumetric pipet accurately delivers ml of liquid from the pipet to another container. Each line on the 10 ml transfer pipet represents ml. This means the uncertainty in volume using the 10 ml pipet is ± ml. b. Does your container (volume measuring device) measure volume as accurately as a 10 ml pipet? Pipet 10 ml of water into your assigned volume measuring device. Is the water on the 10 ml mark on the 50 ml beaker? Using the volume lines on your assigned volume measuring device, read the volume. c. Calculate the difference in volume between the ml of water transferred from the pipet and volume reading on your assigned volume measuring device. Record this volume difference in Table 3. Share your ΔV with the other groups on your bench. Then, plot on a graph ΔV from each group vs. volume measuring device. Use Graphical Analysis or Excel. Label this Graph 1. ΔV, ml Graph 1. Calibration of 50 ml beaker, 10 ml graduated cylinder, and 50 ml graduated cylinder. (1 = 50 ml beaker, 2 = 10 ml graduated cylinder, 3 = 50 ml graduated cylinder) d. Based on your Graph 1, what is the uncertainty in volume using your assigned volume measuring device? Record this uncertainty in Table 3. e. How many significant figures or decimal places should you report when you use your assigned volume measuring device to measure volume? Record the volume using the correct number of significant figures in Table 3. Rank the pipet, 50 ml beaker, 10 ml graduated cylinder, and 50 ml graduated cylinder from most accurate to least accurate. Table 3. Uncertainties of volume measuring devices. Volume measuring device Each line represents (include units) Volume, ml Uncertainty, ml Accuracy Ranking To Contain (TC) or To Deliver (TD)? 10 ml transfer pipet 0.1 ml ± 0.02 TD 50 ml beaker ± Volume difference (ΔV) 10 ml transfer pipet 0.1 ml ± ml graduated cylinder ± Volume difference (ΔV) 10 ml transfer pipet 0.1 ml ± ml graduated cylinder ± Volume difference (ΔV) f. Some volume measuring devices are calibrated to contain a volume of liquid. Other volume measuring devices are calibrated to deliver a volume of liquid, such as a pipet. 17

4 Pour the water from your assigned volume measuring device into another beaker. Did all of the water get transferred (delivered) into the other beaker? g. Based on Graph 1, which volume measuring device, the 50 ml beaker, the 10 ml graduated cylinder, or 50 ml graduated cylinder, would you use to Add 10 ml of liquid reactant to the flask? Give reasons. h. Which volume measuring device in your locker would you use for the hot water bath? How much water should you use in the hot water bath? Waste Disposal: water in sink. 2. Calibrate a temperature probe. You want to check the temperature of your hot water bath. You think, How hot is it? Should I put my finger in the water bath to check the temperature? Many instruments have gone digital. Is the last digit shown on the instrument really the uncertain digit? How do you know how accurate the instrument is? a. Hold your finger (choose which digit you want to use) in the air. What is the temperature of the room right now? Record this temperature in Table 4. b. You will measure and collect data using sensors and probes connected to a computer. We have 12 computers in the lab. Turn on a computer. Your instructor will give you the username and password. Find a Vernier LabQuest Mini, USB cable, and temperature probe and connect it to the computer. Open the LoggerPro software (on the desktop). What is the temperature in the room using the temperature probe? How many signficant figures does the temperature reading show? Record your information in Table 3 on the chalk board. Squeeze the tip of the temperature probe between your index finger and thumb for one minute. What is the temperature? Table 4. Temperature (T) Measurements Made in Lab on (date). Group T of room using finger, o C T of room using T probe, o C T of Body, C T of Calibration Substance ( ) T of calibration substance using T probe, o C T Difference (ΔT), o C Uncertainty o C Average Uncertainty/ error c. How do you know how accurately your temperature probe measures temperature? Calibrate a temperature probe. How would you calibrate a temperature probe? Spend 5 minutes designing an experiment to calibrate your temperature probe. Report your calibration experimental design to the class. The class will agree to do the same experiment to calibrate their temperature probe. Calibrate the temperature probe. d. (i) Calculate the difference in temperature between the temperature of the calibration source and the temperature reading of the temperature probe. Record this temperature difference in Table 4. 18

5 (ii) What is the uncertainty (± error) in the temperature probe? (iii) Based on this uncertainty, how many significant figures should you report for temperature using the temperature probe? (iv) Should you adjust or correct the temperature of the room or body temperature based on the temperature probe calibration? e. Let s see how the data looks for the entire lab class. (i) Calculate the average body temperature and the average temperatures of the room using the finger and temperature probe. (ii) Calculate the % difference for each set of temperatures. (See Eq. (3) in the Scientific Measurement and Significant Figures section of this book.) (iii) Which set of temperatures is the most precise? (iv) Should every group s temperature reading for the room using their finger been the same? Why? (v) Should every group s temperature reading for the room using the temperature probe been the same? Why? (vi) Should every group s body temperature reading been the same? Why? Waste Disposal: water in sink. Note: You ll use other sensors and probes later this semester. How accurate is each sensor? What is the uncertainty? How many significant figures should I report? Questions 1. a. Show your Tables 3 and 4. Check significant figures in each number. b. Show your Graph 1. Calculate an average ΔV for each measuring device. Which measuring device is the most accurate? Give reasons. Which measuring device is the most precise? Give reasons. 2. You see the following volumes in a report. Identify the volume measuring device (beaker, 10 ml or 50 ml graduated cylinder, pipet) used in each volume: a ml b ml c. 25 ml 3. Determine the uncertainty, e.g., ±10 ml, of each measuring device. Include units. a. pan balance b. 10 ml graduated cylinder c. 50 ml graduated cylinder d. 50 ml beaker e. 400 ml beaker f. 125 ml Erlenmeyer flask 4. Which volume measuring device (400 ml beaker, 50 ml graduated cylinder, 10 ml pipet) should you use: a. For water in a water bath b. To make a cup of coffee c. To add a specific volume of liquid in a reaction d. To dilute 25 ml of a 1 M solution to 50 ml of a 0.5 M solution. BRING A REGULAR SODA AND DIET SODA TO LAB FOR PART 2. 19

6 Part 2. Does Regular Soda and Diet Soda have the same density? You are on a diet and will only drink diet soda because there is tooo much sugar in regular soda. Someone gives you an unlabeled soda. How will you determine whether this soda is regular or diet? Prelab Spend 5 minutes doing the following activity. Assign a notetaker. Report to class. 1. Some days, I feel like an air head; other days, I m pretty dense. Today, I measured the mass of my head to be 11.5 kg. I dunked my head in water and it displaced 6.2 liters. I plugged these numbers into my calculator and I got kg/l for the density. It looks like I m a little dense today. a. What is the uncertainty in the mass measurement? b. What is the uncertainty in the volume measurement? c. Based on your answer to (a) and (b), you can calculate a high density and low density: high density = (mass + uncertainty in mass)/(volume uncertainty in volume) low density = (mass - uncertainty in mass)/(volume + uncertainty in volume) Compare the high density and low density. What is the uncertainty in the density calculation? d. How many significant figures should be reported in the density calculation? (See Prelab Question 1 from Part 1 about the discovery of Argon.) e. See Section 5 in the Scientific Measurement and Significant Figures section in this book. Apply the significant figures in calculation rules for this example. Does your answer match the number of significant figures you determined in part (d)? 2. Do the following conversions with a calculation. Use the correct number of significant figures in your answer. a. How many moles are in 18 g of water? (Molar mass of water = g/mole) b. How many grams are in 1 cup of ethanol? (1 cup = 240 ml, density of ethanol = 0.79 g/ml) c. How many moles of acetic acid are in l of 0.89 M vinegar? (0.9 M = 0.9 moles/liter) d. You are heating up 240 ml of water from 25 o C to 66 o C. Calculate heat = q = m s ΔT. (s = specific heat = 4.18 J/g o C) e. The red laser light in a supermarket scanner has a wavelength of 633 nm. Calculate the frequency. (frequency units = 1/sec, frequency = speed of light/wavelength in m, speed of light = 3.00 x 10 8 m/sec) f. What is the volume in liters of 1.00 moles of gas at P = 1.0 atm and T = 273 K. Use P V = n R T where R = l atm/mole K. 3. Estimate the density of each soda by placing an unopened can or bottle of soda in water. Based on your observation, what can you conclude about the density of the soda? 4. Open a soda can or bottle. Pour a small amount of soda into a container. a. What are the bubbles in the liquid? b. To determine the density of a soda, do you want to measure the mass and volume of the liquid only or the liquid with bubbles? Introduction You see a few sodas a ice chest. The ice has melted. Some sodas float; others sink. Why? Your car is having a hard time starting. You could check to see if your car battery is ok by using a hydrometer to measure the density of the battery acid. In the old days, soap makers checked the concentration of their lye (NaOH) solution by seeing by placing an egg in the solution and seeing whether it floated or sank. The concentration of the solution is proportional to the density of the solution. You don t float as well in the pool. What does this tell you about body composition? In this lab activity, you will make mass and volume measurements to calculate density. Density is related to mass and volume by: 20

7 The mass and volume of a substance can change, but the ratio of mass to volume, i.e., density, will be the same for that substance. Density is a unique property of a substance and is used to identify a substance and distinguish one substance from another. Procedure 1. Assign each person in your group to measure the density of a specified volume (5 ml, 10 ml, 25 ml, 50 ml) of regular soda and diet soda. a. Design an experiment to measure the density of a regular soda and a diet soda. Make your soda go Flat ( De-Gas the soda). Pour the soda into a beaker and heat it up on a hot plate until you don t see any more bubbles. Use the appropriate measuring devices, significant figures, and units when you report your density. Summarize your data and results in Tables 5 and 6 on a spreadsheet. USE THE SPREADSHEET AS A CALCULATOR (instead of doing the calculations on your calculator and transcribing the numbers onto a spreadsheet). What other quantities should you put in this table? Table 5. Density measurements of regular soda. What else goes in this table? Quantity Measuring device Units Uncertainty + Volume of Experimental Density Average Density % difference Regular Soda Run 1 Regular Soda Run 2 Regular Soda Run 3 Regular Soda Run 4 Table 6. Density measurements of diet soda. Quantity Measuring device Units Uncertainty + Volume of Experimental Density Average Density % difference Diet Soda Run 1 Diet Soda Run 2 Diet Soda Run 3 Diet Soda Run 4 21

8 b. Using Graphical Analysis or Excel, plot mass of regular soda (y axis) vs. volume of soda (x axis). On the same graph, plot mass of diet soda vs. volume of soda. Call this Graph 2. Calculate the slope of each set of data by doing a linear fit. What quantity does the slope represent? Does the sample size change the density? Is a property of a substance an intensive or extensive property? c. From Table 5 and Table 6, calculate the average density of each soda. Compare each average density to the slope in Graph 2. How are these two quantities related? d. Compare the average densities of the regular soda to the diet soda. Calculate the difference in density. Does Regular Soda and Diet Soda have the same density? 2. a. On a food label, the ingredients are listed in order of amount present (highest to lowest). Nutrition information gives the masses of various ingredients in the food product. Based on your data and results, determine the ingredient that causes the discrepancy in the density between regular soda and diet soda. Describe how you determined the ingredient that causes this discrepancy. b. See the density of regular soda and diet soda. Determine the mass of the ingredient that you would need to add to a can or bottle of diet soda so that its density is the same as regular soda. Show your calculations. c. Compare the mass of this ingredient from part b to the mass of this ingredient on the soda label. Calculate % error. Waste Disposal: soda in sink. Questions 1. a. Show your Tables 5 and 6. Check significant figures in each number. b. Show your Graph 2. Compare the density from the graph to the average density from your Tables 5 and 6 of each soda. 2. a. Identify the ingredient that is responsible for the difference in density of regular and diet soda. b. Show your Procedure 2b calculation using a dimensional analysis (factor-label method). c. Report your Procedure 2c results. How could you make your experiment more accurate? 3. See a soda label. State the soda brand and mass of sugar in one can or bottle of this soda. a. If a person drinks one regular soda each day for a year, how many pounds of sugar will this person eat in a year? b. See the soda label. How many calories are in 1 gram of sugar? What quantity does calories represent? c. Calculate the calories this person consumes on one year from the mass of sugar you calculated in 3a. d. About 3500 calories equals one pound of body weight ( If the one soda per day a person drinks is extra calories beyond what the person needs, calculate the weight this person gains in one year. Reference 1. H.R. Hunt, T.F. Black, Laboratory Experiments for General Chemistry, 3rd ed., 1990, p