Introduction to Density

Transcription

1 Introduction to Density INTRODUCTION Which is heavier, a pound of aluminum or a pound of lead? The answer, of course, is neither, but many people confuse the words "heavy" and "dense". "Heavy" refers to mass only. Density is the mass of a substance contained in a unit of volume. Lead is a very dense metal and contains a large quantity of matter in a small volume, while aluminum, being much less dense, contains a smaller quantity of matter in the same volume. This eperiment is designed as an eercise to refine your skills in weighing, measuring a volume of liquid using a graduated cylinder and beaker, precision in measuring, the use of significant figures in measurement and calculations, and the determination of density. Accuracy and precision are fundamental to all scientific measuring and this eperiment will provide practice in both. Accuracy is defined as a measure of how closely individual measurements agree with the accepted or correct value and is, in part, dependent on the measuring device (see information section on Significant Figures). Precision is defined as the closeness of agreement among several measurements is. Ideally, any series of measurements should be both accurate and precise. Density, like color, odor, melting point, and boiling point, is a basic physical property of matter. Therefore, density may be used in identifying matter. Density is an intensive property (This means that the value of density is independent of the quantity of matter present. For eample, the density of a gold coin and a gold statue are the same, even though the gold statue consists of the greater quantity of gold. This is in contrast to etensive properties, like volume (the amount of space occupied by matter), which depend of the quantity of matter present. The more matter present, the larger the volume. In this lab you will determine and understand the meaning and significance of the density of a substance. The determination of density is a nondestructive physical process for distinguishing one substance from another. Density is the ratio of a substance's mass to its own volume. It is epressed mathematically by: Density (D) = mass = m Volume v The volume of 20.0 grams of lead is 1.77 ml. The mass of lead contained in each ml is its density. Density of lead = mass = 20g = 11.3 g/ml volume 1.77 ml The volume of 20.0 g of aluminum is 7.41 ml. Density of aluminum = 20 g = 2.70 g/ml 7.41 ml

2 In the metric system the unit of density for a liquid or solid is measured in g/ml or g/cm 3. The cm 3 volume unit used with solids is numerically equal to ml volume unit used with liquids. That is, 1 ml = 1 cm 3. Determination of density of certain physiological liquids is often an important screening tool in medical diagnosis. For eample, if the density of urine differs from normal values, this may indicate a problem with the kidneys secreting substances that should not be lost from the body. The determination of density is almost always performed as part of an urinalysis. Another eample utilizing density is the determination of total body fat. Muscle is more dense than fat; therefore, by determining total body mass and volume, the muscle-to-fat ratio can be calculated. In this eperiment you will determine the density of several liquids and compare the physical properties of those liquids. From the definition of the gram and the milliliter, we can see that 1 ml of water at 4 o C would have a mass of eactly 1 gram. The density of water, then, is 1 g/ml at 4 o C. Since the volume occupied by one gram of water varies slightly with temperature, the density also varies slightly with changes in temperature. It follows then, if something has a density greater than 1g/ml it will sink in water and less than 1 g/ml density will float! We can use conventional methods to determine mass and volume of regular solids and liquids. It is more difficult to determine the volume of an irregular solid. The method commonly used is to measure the change in the volume of water when the object is immersed in the water. The object displaces a volume of water equal to its own volume. If the solid material is soluble in water, another liquid, in which the solid is insoluble, is used (e.g. carbon tetrachloride for salt). In this eperiment you will determine densities of various substances by measuring their mass with a balance and their volume with graduated cylinders. You will further determine the percent concentration of salt dissolved in water in an unknown solution graphically based on eperimentally determined densities of known salt solutions. Measuring the Volume of a Liquid The graduated cylinder markings are every 1-milliliter. When read from the lowest point of the meniscus, the correct reading is 30.0 ml. The first 2 digits 30.0 are known eactly. The last digit 30.0 is uncertain. Even though it is a zero, it is significant and must be recorded. PROCEDURE Part 1: A. Determining the Density OF WATER Record the mass of a clean and dry ml graduated cylinder to 0.001g. Fill this 10 ml graduated cylinder approimately halfway with distilled water. Record the mass of your graduated cylinder with this volume of water in it. Calculate the mass of the water. Remember to read the volume of water using the bottom of the meniscus! Record your volume to the hundredth decimal place value (i.e ml). [Remember that sig figs are the number of units known plus one estimated value

3 Calculate the density of the water. (density = mass/volume) Part 1: B. Determining the Density of a Liquid. Obtain some alcohol. Weigh a dry 25 ml graduated cylinder. Add 10 ml of alcohol, reading the volume to the nearest 0.1 ml. Re-weigh the graduated cylinder and record its weight. Calculate the density of alcohol. Repeat this procedure two more times. Once with oil and again with vinegar. Rinse out your cylinder in the sink and wash with soap and water. Scrub the oil test tubes well. Determine your percent error based on the densities listed below from the CRC Handbook. Scientists use reference books which already have calculated the densities of many pure substances. One that is commonly used in chemistry is called the Merk Inde. Another common reference book is the CRC Handbook of physics and chemistry. We cannot look up the density of vinegar in a reference book because it probably is not reported since vinegar is a miture and not a pure substance. Below are the densities of alcohol and vegetable oil. Water: g/ml at 20 C Methanol: g/ml at 25 C Isopropanol: g/ml at 25 C Vegetable oil: 0.91 g/ml at 25 C Aluminum: 2.7 g/cm 3 Copper: 8.92 g/cm 3 Polyvinylchloride (PVC): 1.35 g/cm 3 Teflon: 2.20 g/cm 3 Iron: g/cm 3 Lead: g/cm 3 Tin (Sn): 7.31 g/cm 3 Zinc: 7.14 g/cm 3 Yellow Brass: 8.47 g/cm 3 Stainless Steel: g/cm 3 Some other helpful formulas to remember: Volume of a cylinder = πr 2 h h = cylinder height or length r = cylinder radius = ½ the diameter Volume of a rectangle = length width height As with any eperiment, you should always check how accurate your eperimentally obtained value is compared to the "true" or accurate value. This eperimental error is also known as percent error and it describes the percentage the eperimental value is off from the actual value. percent error: (Actual/theoretical Eperimental) / Actual 100% If you used the graduated cylinder and balance correctly, you should have an eperimental error of less than 1%. A 1% error or less is generally accepted. If your error is greater than 2% you would want to repeat your eperiment until you have a smaller percent error. Part 1: C. Determining the Density of a Solution NOTE: The concentration of a solution is sometimes described in terms of the solution's percentage composition on a weight basis. For eample, a 5% salt (NaCl) solution contains 5 g of NaCl per 100 g of solution, which corresponds to 5 g of salt per 95 g of water.

4 Get a dry 10 ml graduated cylinder. Get its mass empty, then fill the graduated cylinder halfway with the 5% NaCl solution. Record the mass of the graduated cylinder and salt solution. Calculate the mass of the salt solution. (Dispose of the solution in the sink; do not return to reagent bottle!) Record the volume of the solution and Calculate the density of the 5% NaCl solution. Repeat this procedure for the 10%, 15%, and 20% NaCl solutions. Obtain an unknown solution. Record its letter. Repeat the procedure for the unknown solution. You will now use your know solutions to determine the concentration of your unknown solution. Graphing: Construct a graph using pencil. Title the graph and label the y-ais as density (g/ml). Label the - ais as weight percent composition (%). Spread the aes out so that the data covers as much of the graph as possible. You will need to decide on the size of divisions to mark your graph. Make sure that all divisions are equal. Recall that you will have five known data points from part A and part C (0% (water only), 5%, 10%, 15%, 20%). To determine your divisions of your density (y-ais) you do not need to begin at zero. Plot your five known solutions. Do not plot your unknown on the graph yet! Using a ruler, draw a best fit line on your graph. Do not connect the dots! A best fit line does not intersect all data points. It does not always go through the origin. If your data are scattered, estimate where to draw your best straight line. Roughly an equal number of points should be above the line as below the line. (This approimates a mathematical technique called linear regression which judges where to draw the line to minimize the distance from each point to the line.) To determine your unknown % concentration, use a ruler and draw a dotted line from the calculated density of your unknown on the y-ais until its intersection with the best fit line. Mark this intersection. Net draw a dotted line from this intersection to the -ais to determine the % weight concentration at this point on your graph. Record the concentration of your unknown solution. Part 2: A. Determining the Density of a Solid. Obtain an unknown solid and record its ID #. If it is a regular solid (cube or cylinder), determine its volume using the correct mathematical formula. Be as precise as possible in your measurements! If it is an irregular solid, determine its volume by water displacement. Calculate the density of the solid. Repeat for 3 more unknown solids. Determine the identity of your solids by comparing your calculated densities to the densities of known solids in the CRC Handbook (see list above). Take one of your regular solids and determine its volume using water displacement method. Calculate its density and compare it to the density you determined from mathematical formula. Which was more accurate? How do you know? Part 2: B. Determine the thickness of aluminum foil. Could you measure the thickness of a piece of aluminum foil? Probably not. But we can use what we know of aluminum s density to determine its thickness!

5 Work out how you would use the information you have to determine the thickness of the piece of foil supplied by your instructor. Remember there is a relationship between density, volume and mass. Part 2: C. Challenge use your new skills Within the last 35 years, the composition of the US penny was changed from pure copper to a coppercoated zinc coin. Your instructor will demonstrate this for a new penny by dissolving the zinc inside the penny with hydrochloric acid, leaving the copper shell. Your challenge is to collect (and share) data with your classmates to answer these questions: What year did the composition of the penny change? What is the percent copper in a modern penny? Use this procedure to help you obtain data. Obtain a set of pennies (10 pennies) from your instructor and weigh them to the nearest 0.01 g. Record the identity of this sample by the date of the pennies. Net add about ml of water to a graduated cylinder and record the volume to the nearest 0.1-mL. Place the sample carefully in the filled graduated cylinder, being careful not to lose any water. Tip the cylinder and slide the pennies down the side so they do not break the glass by being dropped in. Record the level of the water after addition of pennies, to the nearest 0.1 ml. Calculate the density of the sample pennies. Obtain a second set of pennies and repeat your determination of density for this sample. Now obtain additional penny data from your lab partners. Show an eample of your calculation for % of copper:

6 Introduction to Density Lab Name: POSTLAB QUESTIONS: Answer the following on a separate sheet of paper. Attach this to the paper and turn in. 1. Compare a 50 ml beaker and a 50 ml graduated cylinder. Which is more precise? Why? 2. What is the reason we calculate % error? How is error introduced during a lab procedure? How is this related to accuracy? 3. Why is it important to represent your measured/computed values using significant digits? 4. Show the data you obtained in Part 2 A for the density of the solid you determined through both direct measurement and then water displacement. Which was more accurate? How do you know? Justify your answer by showing your calculations. 5. In the original Indiana Jones movie, our hero is attempting to claim a precious ancient gold relic from a poor third world country. He estimates the size of his prize and carefully adjusts the volume of sand in his bag to equal that of the gold relic. With the great deterity that only Indiana Jones possesses, he swiftly but delicately swaps the sand for the gold. After a moment of delight, he realizes he has misjudged and the ancient tomb is not fooled. Why? 6. While panning for gold, you find a nugget that looks like gold. You find its mass to be 1.25g. You know that the density of pure gold is about 20.0 g/cm 3 and that the density of iron pyrite (fool's gold) is 5.0 g/cm 3. Determine if a cubic nugget about 0.40 cm on each side is fool's gold or pure gold. (Show all work)

7 Creating a Line of Best Fit Pairs of values will be plotted on graph paper as a scatter plot. Remember DRY MIX (dependent/responding variable on the y- ais and the independent/manipulated variable on the -ais) In this eperiment you will have mass plotted on the y-ais and volume plotted on the -ais. When the plotted data generate (or at least approimate) a straight line, a best-fit line can be added to the graph. A best-fit line is a single line that comes as close as possible to all the plotted points. The equation of this best-fit line will have the familiar form y = m + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in the figure below. mass b Δ Δy Best-fit line equation: y = m + b b = y-intercept m = slope (Δy/Δ) The y-intercept (b) is the point on the y- ais where the line crosses volume The y-intercept (b) is the point on the y-ais where the line crosses the ais. In this eperiment, the value of b should be equal to zero. This is because if there is no mass, the volume must also be zero. However, note that your best-fit line might not pass eactly through the origin (0,0) due to eperimental error but it should be quite close. The slope of the line (m) is the change in the y-ais values divided by the change in -ais values (or, rise over run): slope (m) = Δ y = y 2 y 1 = Δ mass = density Δ 2 1 Δ volume Since Δy is really the change in mass (Δmass), and Δ is really the change in volume (Δvolume), this means that the slope of the best-fit line yields the density of the unknown material.

8 According to the US Mint: From 1837 to 1857, the cent was made of bronze (95% and 5% tin and zinc). From 1857, the cent was 88% copper and 12% nickel, giving the coin a whitish appearance. The cent was again bronze (95% copper and 5% tin and zinc) from 1864 to 1962, ecept: In 1943, the coin's composition was changed to zinc-coated steel. This change was only for the year 1943 and was due to the critical use of copper for the war effort. However, a limited number of copper pennies were minted that year. In 1962, the cent's tin content, which was quite small, was removed. That made the metal composition of the cent 95% copper and 5% zinc. The alloy remained 95% copper and 5% zinc until 1982, when the composition was changed to 97.5% zinc and 2.5% copper (copper-plated zinc). Cents of both compositions appeared in that year. The penny's original design was suggested by Ben Franklin. The word "penny" comes from the British "pence." More than 300 billion pennies have been minted, according to pennies.org. Here's a neat fact. The faces on all coins currently in circulation face left, ecept for Abe Lincoln on the penny. Lincoln's likeness is an adaptation of a plaque done by sculptor Victor David Brenner. The direction that Lincoln faces on the cent was not mandated but was simply the choice of the designer. Date of pennies % copper Date of pennies % copper (zinc coated steel) (5% tin/zinc) (5% zinc) (12% nickel) after % (97.5% zinc) Bronze* Bronze is an allow made of 95% copper and 5% tin/zinc