CHEM 121: Introduction to the Metric System Objectives In this experiment students will: • • • • • Introduction Measure the mass of various objects using two types of balances Calculate the volume of an object by measuring its dimensions Calculate the volume of an object using volume by displacement Compare the measurement of volume using a beaker and a graduated cylinder Estimate the volume of a drop of water using a graduated cylinder In the U.S. the English system of measurement is used almost exclusively. For example, a car’s fuel efficiency is reported in miles per gallon; a person's height is given in feet and inches; one's weight is measured in pounds; ice cream is sold by the cup, pint or gallon; and temperature is reported in degrees Fahrenheit. However, the conversions in the English system are difficult to recall—for example, few people can remember that one mile equals 5280 feet or 1760 yards. A much more effective system uses a decimal system of measurement, where basic units are used in conjunction with prefixes to represent multiple or fractions of the base unit. The metric system is such a system. For example, in the metric system, the base unit for mass is the gram. A multiple of the base unit can be expressed by combining a metric prefix, like kilo representing 1000, with the base unit to give the unit kilogram, which equals 1000 grams. Because of its logic and simplicity, the metric system gained international acceptance with the Treaty of the Meter, establishing the International Bureau of Weights and Measures. Even the United States signed the treaty in 1875, but to date the U.S.'s use of the metric system seems to be the limited to 2-liter bottles for soda and cc's (cubic centimeters) in hospitals. In science, the metric system is used almost exclusively, so most of the equipment and instruments used in a chemistry lab generally measure centimeters, millimeters, milliliters, and grams. In this experiment, students will learn how to use a variety of chemistry laboratory equipment and instruments to become more familiar with the metric system. Students will use graduated cylinders to measure volume, an analytical and a milligram balance to measure mass, and a ruler to measure the length, width, and thickness of a rectangular solid. Students will also learn about a method called volume by displacement, where the volume of an object is determined using the volume of water it displaces. Students will also use mass by difference to determine the mass of a sample. Finally, students will practice determining the number of significant figures for each measurement and expressing the answers for calculated measurements with the correct number of significant figures. Laboratory Rulers: The basic metric unit of length is the meter, but the length of most objects1 in Techniques a chemistry lab is measured in centimeters (cm). A centimeter equals 0.01 m or 100 of a meter, so 1 m≡100 cm—just like 1 dollar≡100 cents (since one cent is equal to 1 of a dollar). 100 Measuring Several instruments are used for metric length measurements, such as€a centimeter Length ruler in the following example. The numbers shown on a centimeter ruler are € centimeters (cm), and the 10 smaller markings between each number represent millimeters (mm). (Note that 10mm≡1cm.) On some rulers, the “0” cm mark is not at the end of the ruler, so the ruler is still accurate even if the ruler becomes rounded at the end. When measuring, always place an object at the “0” mark, as shown with the metal rod and ruler shown: When a measurement is taken, all the digits are known with certainty, except the last digit, which is estimated. For example, the metal rod above appears to end about halfway between 8.5 and 8.6, so its length is recorded as 8.55 cm, 8.56 cm, or 8.57 cm. The last digit is estimated, so different people may report a different final digit depending on their view of the metal rod ending exactly just at the halfway point or just to the left or to the right of halfway point. If the object appears to end on a marking on the instrument, then the estimated digit is 0. For example, in the figure below, the metal rod appears to end right at the marking for 10, so the measurement is recorded at 10.00 cm since a centimeter ruler is always read to 2 decimal places. Measuring Volume Graduated cylinders are used to contain and deliver measured amounts of liquid. They are available in many sizes; for example, 10 mL, 50 mL, and 100 mL graduated cylinders are used in the CHEM121 lab. Students should always use the smallest graduated cylinder that will hold the entire volume of sample for the most precise volume measurements. When water is placed in a glass cylinder, a concave surface forms; this curve is called the meniscus. (See figure at the right.) Graduated cylinders are manufactured to give the volume of the liquid by measuring the line at the CHEM 121 Lab Manual W2021 page 2 Parallax error results when a meniscus is viewed from an angle. bottom of the meniscus. In order to read any graduated cylinder accurately, it must be level (sitting on the counter, NOT held in a student’s hand). The student’s eye must be even with the water level. When reading the volume, a student should crouch down so that the eyes are at the same level as the meniscus. Note that the graduations on all cylinders read from the bottom up—that is, they indicate the volume contained in the cylinder. Often in experiments students will be instructed to use a graduated cylinder to obtain a liquid of an approximate amount, and then record the actual volume to the correct number of significant figures (e.g. See Part B step 5 in the procedure for this lab). In cases like these, students should not waste time getting the exact volume indicated when one can simply measure out an approximate volume (usually within a few milliliters unless otherwise specified). However, it is important that students record the actual volume that is measured out in the graduated cylinder when a specific volume is required. 50 mL The 50 mL graduated cylinder in the laboratory has markings every 1 mL, so it is Graduated read to a precision of 0.1 mL (e.g. 31.5 mL and 28.0 mL as shown below). Cylinders Figure 2: Examples of liquids in two 50 mL graduated cylinders. Example A • • • Example B The two examples above show liquids in a 50 mL graduated cylinder. In Example A, the bottom of the meniscus is between the two markings for 31 mL and 32 mL, so the volume of liquid can be read as 31.5 mL. Other students may judge the volume to be 31.4 or 31.6 mL, and all of these readings are correct. In Example B, the bottom of the meniscus lines up with the marking for 28 mL, so the volume of liquid is read as 28.0 mL. 28.1 or 27.9 mL would also be valid measurements, but 28 mL would be wrong, because it does not have enough significant figures. Note that for both of these examples, the volume of liquid is read to one decimal place (to the nearest ±0.1 mL). Thus, when using a 50 mL graduated cylinder with markings for every 1 mL, the volume is always read to the nearest 0.1 mL. CHEM 121 Lab Manual W2021 page 3 Other times students will be asked to measure out a precise volume of liquid. For example, in steps Part C steps 7 and 8 of this experiment, students should count the number of drops of water required to raise the water level from precisely 4.0 mL to precisely 5.0 mL using a 10 mL graduated cylinder. 10 mL Graduated Cylinders The 10 mL graduated cylinder in the laboratory has markings every 0.2 mL, so the situation differs from the examples discussed above. Because the cylinder is quite small and the markings are close together, it would be extremely difficult to read the volume to 0.01 mL. When we use 10 mL graduated cylinders this quarter, you will read the volumes to a precision of ±0.1 mL (e.g. 6.3 mL and 5.0 mL as shown below). Figure 1: Examples of liquids in two 10 mL graduated cylinders. Example A • • • Example B The two examples above show liquids in a 10 mL graduated cylinder. Since the markings are very close, we can only determine if the meniscus lines up with one of the markings or if it falls between two markings. In Example A, the bottom of the meniscus is between the two markings for 6.2 mL and 6.4 mL, so the volume of liquid is read as 6.3 mL. In Example B, the bottom of the meniscus lines up with the marking for 5 mL, so the volume of liquid is read as 5.0 mL. Note that for these two examples, the volume of liquid is read to one decimal place (to the nearest 0.1 mL). The last digit (at a tenth of a mL) is still estimated, and different students may judge this last digit differently. Thus, when using a 10 mL graduated cylinder with markings for every 0.2 mL, the volume is always read to the nearest 0.1 mL. CHEM 121 Lab Manual W2021 page 4 Beakers and Erlenmeyer flasks Beakers and Erlenmeyer flasks are two additional types of glassware that are used to hold liquids and have markings for very approximate volumes. Unlike graduated cylinders, beakers and Erlenmeyer flasks cannot be used to measure volumes in an accurate or precise manner. For example, the figure at the right shows a 400-mL beaker (left) that has about 150 mL of liquid in it, but the actual volume of liquid could be between 140-160 mL. The 500-mL Erlenmeyer flask (right) contains about 400 mL of liquid with an error of 5%, so it may actually contain between 380-420 mL of liquid. Beakers and Erlenmeyer flasks should be used to obtain approximate amounts of a liquid before a more precise amount is measured out precisely using a graduated cylinder. For example, in part B step 5 of the procedure for this experiment, students are instructed to “Obtain about 50 mL of deionized (DI) water in a 100-mL beaker using the markings on the beaker.” Students will use the rough markings on the beaker to get about 50 mL of water from the deionized water tap—it does not matter if the volume is 40 or 50 or 60 mL because a more precise volume will be measured out in the next step using a graduated cylinder. Balances Balances: In most chemistry labs, balances are used to determine the mass of a sample. The metric unit of mass is the gram. In this course students will use two types of electronic balances: top-loading balances and analytical balances. The top-loading balances can weigh the heaviest objects but are less sensitive and provide masses to the hundredth of a gram (±0.01 grams). The analytical balances are more sensitive, weighing to ±0.001 or ±0.0001 grams, and can be identified as the balances with a pan enclosed in glass doors. These balances are very expensive, very sensitive, and must be used very carefully to avoid damage. The most important rule is NEVER place any chemical directly on the balance pan. Use a beaker, a watch glass, a weighing cup, or weighing paper to avoid contaminating the balance. The general procedure for using an analytical balance follows: • • • • • The balances are to remain “ON” at all times. All doors are to remain closed at all times, unless loading/unloading a sample into/out of the balance. Do not lean on the balance table. (The balance is sensitive enough to measure vibrations on the countertop due to students leaning on it.) Material to be weighed should be placed in a container on the balance pan. The container may be either pre-weighed or “tared” (as explained below). Before weighing, be sure doors are closed and the display reads 0.0000 g (four zeros past decimal) or 0.000 g (three zeros past decimal). If zeroes are not displayed on the scale, gently click the front lever until the balance displays zeros. If 0.00000 g is displayed or if the number displayed continues to drift, consult your instructor or the lab staff. CHEM 121 Lab Manual W2021 page 5 • Tare a • Balance To weigh an object, open the door, and carefully place the item on the center of the pan. Close the door and wait for the digital readout to stabilize (the green light to the left of the readout will go off). Read and record all the numbers in the digital readout. (Never round any numbers reported on any electronic instrument.) Remove the item and close the doors before leaving. When using a container to hold chemicals, you may tare the container as follows. Place the container in the center of the pan. Close the doors. Briefly click on the front lever to zero the balance and watch to make sure the display reads zero before continuing. The container is now “tared out”, and the balance is set to read the weight of any material added to the container. Remove the container from the balance, add material to it, and carefully place the container back on the center of the pan. (Do NOT press the front lever on the the balance again during this process.) Close the door and read the digital scale when stabilized as before. After you have removed the container, shut the doors and gently push the front lever to remove the tare and return the scale to zero. CHEM 121 Lab Manual W2021 page 6 Procedure A. INVESTIGATING MASS 1. Review the instructions in the Laboratory Techniques section for using the electronic balances. 2. In the container at your lab station, you will find various objects. Use the analytical balance to measure the mass of each of the following objects: a small paper clip, a large paper clip, the cap of a ballpoint pen, and one sheet of paper (folded 4 times to fit on the balance pan). Be sure to place each object near the center of the balance pan to weigh it. Record the mass of each object as displayed by the balance. NEVER round the mass reported on an electronic balance! 3. Repeat step #2 with the same four objects using a top-loading balance. B. INVESTIGATING LENGTH AND VOLUME Volume by 1. Review the instructions in the Laboratory Techniques section for using centimeter rulers. Be sure to measure in centimeters (not inches). Calculation 2. Obtain a metal block from the instructor. Measure the length, width, and thickness of the rectangular metal solid. Record each dimension to the appropriate number of significant figures. 3. Calculate the volume of the rectangular object using the following formula: volume = length × width × thickness Be sure to report the answer with the correct units and significant figures. 4. Review the instructions in the Laboratory Techniques section for using 50-mL graduated cylinders. Volume by 5. Obtain about 50 mL of deionized (DI) water in a 100-mL beaker using the Displacement markings on the beaker. Then, use the water in the beaker to fill a 50-mL graduated cylinder to approximately 30 mL. Record the actual volume of water with the proper number of significant figures. 6. Some of the metal samples are very dense and can shatter the glass bottom of a graduated cylinder. To avoid breaking the graduated cylinder and incurring the additional cost, slowly lower the metal sample into the graduated cylinder. Tilt the graduated cylinder until it is at about a 45° angle, and carefully lower the rectangular solid so as not to splash any water out of the graduated cylinder. Allow the metal sample to sink to the bottom of the graduated cylinder before raising the graduated cylinder to an upright position. This prevents the metal piece from striking and breaking the glass bottom of the graduated cylinder. Read and record the new volume of water. 7. Subtract the original volume of water from the final volume of water, and record the difference with the appropriate units and number of significant figures. CHEM 121 Lab Manual W2021 page 7 Mass by C. INVESTIGATING WATER Difference 1. Review the instructions in the Laboratory Techniques section for using Balances, particularly the section on how to Tare a Balance. 2. Obtain about 20 mL of deionized (DI) water in a 50-mL beaker using the markings on the beaker. 3. Carefully place a dry plastic weighing boat in the center of the pan in an analytical balance. Close all the doors, and tare (or zero) the balance. The display should now read 0.0000 g. 4. Open the door, and carefully remove the plastic weighing boat. Use a disposable pipet to add one drop of water into the plastic weighing boat. Return the cup to the balance, close the door, and record the mass of the drop of water. 5. Review the instructions in the Laboratory Techniques section for using 10-mL graduated cylinders. 6. Use a disposable pipet to add DI water to a 10-mL graduated cylinder as close to the 4-mL mark as you can get. 7. Make sure the outside of the graduated cylinder is completely dry, then measure and record the mass of the graduated cylinder with 4.0 mL of DI water. 8. Next, you will determine the number of drops of water in one milliliter by carefully counting the number of drops required to raise the water level in the graduated cylinder to the 5-mL mark. (Be careful not to go beyond 5.0 mL, or you will have to start again at Step 6.) Record the number of drops of water used to get to the 5.0 mL mark—i.e., the number of drops equal to 1.0 mL. 9. Measure and record the mass of the graduated cylinder with 5.0 mL of DI water. 10. Subtract the initial mass (of graduated cylinder + 4.0 mL DI water) from the new mass (of graduated cylinder + 5.0 mL DI water) to get the mass of 1.0 mL of DI water. Record the difference with the appropriate units and the correct number of significant figures. 11. Calculate the number of drops of water in 1.0 mL by dividing the mass of 1.0 mL of DI water by the mass of one drop of water. Compare your answer with your experimentally determined number of drops from step 8 above. D. INVESTIGATING THE ACCURACY OF BEAKERS 1. Use a 100-mL beaker for the final part of this lab. Obtain approximately 40 mL of water in the beaker using the markings on the beaker to “eyeball” this volume the best you can. Then, measure the volume of this water in a 50-mL graduated cylinder. 2. Talk with three other students to collect values measured from other beakers, and copy their measurements into the table provided. CHEM 121 Lab Manual W2021 page 8 CHEM 121: Introduction to the Metric System Pre-Lab Assignment Name: _____________________________________ 1. Measure the length for each object using the centimeter rulers below and the proper number of significant figures. In each measurement, circle your estimated digit and include units. Be careful with the second one! a. ____________________ b. ___________________ 2. Read the volume of liquid in the following graduated cylinder, with the correct number of significant figures. Circle your estimated digit. Volume = _________ mL 3. Indicate the appropriate piece of laboratory equipment needed to make each of the following measurements: a. Measure the volume of about 5 mL of liquid to a precision of 0.1 mL: _________________ b. Measure the mass of an object to a precision of 0.0001 grams: _________________ c. Measure the volume of about 35 mL of liquid to a precision of 0.1 mL: _________________ d. Obtain approximately 30 mL of water, later to be poured into a graduated cylinder: ______________________ CHEM 121 Lab Manual W2021 page 9 CHEM 121 Lab Manual W2021 page 10 CHEM 121: Introduction to the Metric System Name: ______________________________ DATA LAB REPORT A. INVESTIGATING MASS Using the analytical balance: OBJECT MASS # of Significant Figures MASS # of Significant Figures small paper clip large paper clip cap of a ballpoint pen one sheet of blank paper Using the top-loading balance: OBJECT small paper clip large paper clip cap of a ballpoint pen one sheet of blank paper B. INVESTIGATING LENGTH AND VOLUME: Unknown metal Number: ________ Volume by Calculation Dimension Measurement Volume by Displacement # of Sig Figs Volume Measured length Water Level # of Decimal Places initial (w/o metal) width final (with metal) thickness Volume of metal by Calculation: __________________ Volume of metal by Displacement: __________________ with correct # of decimal places and units with correct # of sig figs and units Show your calculation of volume using data from the two tables above below or on a separate page: CHEM 121 Lab Manual W2021 page 11 DATA: PART D: INVESTIGATING THE ACCURACY OF BEAKERS Student Name Water volume using beaker Water volume using graduated cylinder (Your data) 40 mL 40 mL 40 mL 40 mL Based on your results above, what can you conclude about the accuracy of a beaker when used to measure volumes? Post-Laboratory Questions 1. Fill in the blanks below—e.g., you can write 1 L ≡ 1000 mL or 0.001 L ≡ 1 mL for the first one, where the “≡” symbol means “exactly equal” and applies to metric-metric unit equations. 2 a. _______ L ≡ _______ mL d. _______ kg ≡ _______ g g. _______ g ≡ _______ mg b. _______ g ≡ _______ cg e. _______ m ≡ _______ mm h. _______ L ≡ _______ mL c. _______ km ≡ _______ m f. _______ L ≡ _______ cL i. _______ g ≡ _______ µg If the density of water is 1.00 g/mL, calculate the mass (in kg) for 1.00 L of water. Show all work and express the answer with the correct units and the correct number of significant figures to receive full credit. CHEM 121 Lab Manual W2021 page 12 Post-Laboratory Questions (Continued) 3. Compare the masses you measured for the four objects in Part A, as measured by the analytical balance versus the top-loading balance. Describe any similarities and/or differences for the masses measured from the two balances. 4. Compare the volume of your unknown metal calculated using two different methods in Part B. (The units may seem to be different, but remember that 1 cm3 ≡ 1 mL, so they are actually the same.) Are the two volumes similar? Give an example of an object for which it would be better to determine its volume by water displacement rather than by calculation. 5. Based on your calculations in Part B, which method for determining volume should you use if you want to calculate a volume that has the most significant figures? 6. Suppose a student was performing Part B step 6 of this experiment. He correctly read and recorded the initial volume of the water in the graduated cylinder, but when he dropped the metal sample into the water, several drops of water splashed out of the cylinder. He chose to ignore this splashing and recorded the final volume. How would his volume of the metal object be affected? As a result of his error would the calculated volume be too high or too low? Explain why. 7. Part B step 5 required you to record the actual volume of liquid measured in a 50-mL graduated cylinder. Circle all of the following sample measurements that are NOT appropriate or NOT recorded to the correct number of decimal places using a 50-mL graduated cylinder: 9.00 mL CHEM 121 Lab Manual W2021 25.6 mL 30 mL 31.11 mL page 13 44 mL 52.5 mL
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