Measuring Mass and Volume Experiment 2 Expt 2 Measurement.wpd INTENT The purpose of this experiment is to introduce some fundamental aspects of the measurement making process as well as to introduce some of the basic laboratory equipment used by chemists for measuring mass and volume. DISCUSSION The Importance of Measurements. Measurements are the means by which scientists gather quantitative information. Thus, in science and technology, it is extremely important to be able to make proper measurements. The quantitative determination of common extrinsic physical properties such as length, mass, and volume, as well as common intrinsic properties like density or heat of reaction per mole, can only be accurately determined by carefully performing experiments which depend on making particular measurements correctly. Therefore the quality of any physical-property determination is only as good as the measurements used in determining that physical property. Proper Measurements. A properly recorded measurement consists of two basic parts, the number and the label (or units) associated with it. Both must be stated clearly when quoting a measurement. The numerical portion of a measurement relates the actual value obtained and the accuracy to which it is known. In your own work, you will always want to convey, exactly, the accuracy to which a value is known. This is so because, even if the exact degree of accuracy is not important to you in your work, it may be important to someone else who, at some later time, may try to use your results for a different purpose. Remember that whenever a measurement is made, there is always some degree of uncertainty in the value of the measurement, i.e., an estimate is involved. One needs to know how to treat this uncertainty in a number and in subsequent calculations. In addition to the numerical portion of a measurement, its units must be clearly stated to avoid any confusion. For example, if you were told the distance between New York and Los Angeles is 125, you would be perplexed since no units are quoted. You are left to guess the units used to make this measurement, and no units with which you are likely familiar seem appropriate. Clearly, units are needed to remove the confusion. Thus, a proper measurement consists of two basic parts, the number and the label (or units) associated with it. 7
Measurements. When making a measurement, you must decide how best to report the value that you obtain. To illustrate the procedure, consider the following measurement: Clearly, a measurement of the length of the line should be reported to two significant figures because the line is obviously longer than 0.3 D but less than 0.4 D. That is, by estimating the second decimal place, a total of two significant figures is obtained. Therefore, to complete our measurement, we need only to make an estimate of the length of the line that extends beyond the 0.3 D marking. To do this, we divide (in our minds) the distance between the 0.3 D marking and the 0.4 D marking into 10 parts. (Tenths of the smallest division.) We can now estimate the length as 4/10 (give or take a tenth) of that distance. Thus 4/10 of 0.1 D (the distance between 0.3 D and 0.4 D) is 0.04 D. Therefore, we quote the measurement as 0.34 D. The reported value, 0.34 D, conveys complete and concise information about our measurement of the length of the line. It would be interpreted, without additional information, by any scientist as indicating that the length was approximated to two figures and that the length is 0.34 D ± 0.01 D, or between 0.33 D and 0.35 D. (This is proper because that is our uncertainty. Remember, we said "give or take a tenth," and a tenth of 0.1 D is 0.01 D.) Therefore, to generalize, if we read a measurement as 1.234 D, then the uncertainty is assumed to be ± 0.001 D; if a measurement is 1.23 D, then the uncertainty is assumed to be ± 0.01 D, and so on. What should be done in those cases where the uncertainty in our estimate is greater than ± one unit in the last decimal place? How should such a measurement be reported? It should be reported so that the measurement explicitly states the actual uncertainty. To illustrate this point, consider the following measurement: Again, the value of the measurement should be quoted to two significant figures because it is certain that the value lies between 0.6 D and 0.8 D. So, to complete the measurement, we divide the distance between 0.6 D and 0.8 D (or 0.2 D) into 10 parts and estimate that the line extends 4/10 (give or take a tenth) beyond the 0.6 D marking. Thus, 4/10 of 0.2 D is 0.08 D and the measurement is 0.68 D. This time however, it would be incorrect to report the value simply as 0.68 D, because this implies that the measurement is accurate to 0.01 D, which it is not. The uncertainty is ± 0.02 D. (Remember our uncertainty was "give or take a tenth" of the distance between 0.6 D and 0.8 D; 1/10 of 0.2 D is 0.02 D.) Therefore, the value should be reported as 0.68 D ± 0.02 D. When expressed this way, it is clear that the uncertainty is 0.02 D, and not 0.01 D. Once again we have conveyed complete and concise knowledge of a particular fact. 8
PROCEDURES General Procedure for Reading a Graduated Cylinder The volume of liquid contained in a graduated cylinder is measured by reading the liquid meniscus level (the curved boundary between the liquid and the air). When making a meniscus reading you should always read the center of the curve, making sure your eye is LEVEL with the meniscus. In the case of water this will be the bottom or lowest point visible. A piece of paper or your hand placed behind the cylinder will help you to estimate your last significant figure. Remember, when reading graduated cylinders or any other calibrated equipment, "read between the lines." That is make the estimate to 1/10 of the smallest calibrated marking. General Procedure for Using a Buret Burets are used for dispensing a desired volume of liquid. If the buret is not known to be both clean and dry the following rinsing procedure should be performed prior to its use. First, the stopcock is completely closed and a small sample of the liquid which is to be dispensed is poured into the buret. The buret is tilted and rotated to rinse all of the inside surfaces of the buret barrel with the liquid. The buret is then returned to the upright position and the stopcock is opened fully so that the liquid may drain through the tip. Finally, the buret is shaken to remove the last traces of liquid from the buret. The buret is now ready for use. To use a buret, close the stopcock tightly then clamp the buret in an upright position on a buret stand using a buret clamp. Fill the buret with the desired liquid using a funnel and then open the stopcock slowly. Allow enough liquid to run out to fill the tip of the buret completely with liquid. If a bubble is lodged in the tip, open and close the stopcock repeatedly in a clockwise manner until the bubble is dislodged. This last step is very important. Air bubbles trapped in the tip of the buret will cause a significant error in the measurement of the volume of liquid dispensed. If a drop is hanging from the buret tip it should be removed by blotting it with a paper towel prior to taking any measurements. Now, an initial buret reading is made and recorded. The stopcock is then opened and the approximate volume of liquid is dispensed. After closing the stopcock any hanging drops should be added to the collection flask by gently rubbing the tip of the buret with the inside lip of the collection flask. A final buret reading is now made. The accurate volume of liquid dispensed is found by subtracting the initial reading from the final reading. Most burets are calibrated in tenths of milliliters and therefore accurately dispense volumes to hundredths of milliliters (or two decimal places). 9
General Procedure for Using a Pipet Volumetric pipets are used for dispensing specific volumes. Each pipet delivers only one volume accurately; that volume which is stamped on the pipet itself. NOTE--Volumetric pipets are usually accurate to two decimal places or to a hundredth of a milliliter even though the number stamped on the pipet is an integer. Unless the pipet is known to be both clean and dry it must be rinsed prior to use. This is accomplished by pouring a small sample of the liquid to be pipeted into a clean beaker. Then, carefully place a pipet bulb on top of the pipet to be rinsed. With the pipet held firmly in one hand the bulb is squeezed with the other hand to displace the air from the bulb. The tip of the pipet is then placed in the sample of the desired liquid with the bulb still tightly squeezed. As the pressure on the bulb is slowly lowered the liquid is drawn up into the pipet. When the pipet is approximately 1/4 full the bulb is rapidly removed with one hand while the thumb of the other hand is pressed over the top of the pipet. The pipet is removed from the sample beaker and turned in a horizontal position. The pipet is now rotated to rinse all of its inside surfaces. The sample in the pipet is now discarded. After rinsing a second time the contents of both the beaker and pipet are discarded. The pipet is now ready for use. To use a pipet, carefully place a pipet bulb on top of the pipet and draw up a sample into the pipet. When the liquid reaches a level approximately 3 cm ( 1 inch) above the full mark on the neck, pressure is applied again on the bulb so as to keep the liquid at this level and not allow it to enter the bulb itself. Now, with one smooth yet rapid motion the bulb is removed with one hand while the thumb of the other hand is pressed over the top of the pipet. The liquid level in the pipet should still be above the full mark. This liquid level must now be lowered to the full mark by simply relaxing or rolling the thumb on the top of the pipet. DO NOT TRY TO LIFT AND REPLACE THE THUMB TO LOWER THE LEVEL - YOUR REFLEXES ARE NOT FAST ENOUGH. When the level reaches the full mark, thumb pressure is increased to stop the flow of liquid out of the pipet. If a drop is hanging from the tip it should be blotted with a paper towel prior to delivery of the liquid from the pipet. The accurate volume may now be delivered by simply removing the thumb from the top of the pipet. Any hanging drops should be added to the collection flask by gently touching the tip of the pipet with the inside lip of the collection flask. For additional details on pipet use see Appendix A at the back of your laboratory manual. General Procedure for Using an Electronic Balance Modern electronic balances have removed much of the labor involved in making mass measurements. The laboratory balances you will generally use are accurate to three decimal places or a one-thousandth of a gram. These balances are very sensitive yet easy to use. First place the balance in an area shielded from air drafts. Next, turn on the balance by pressing down on the instrument bar. When ready the balance will read "zero" and should indicate this mass for several seconds. If the balance does not read "zero" then press down on the bar again. Should the balance reading fluctuate, move the balance to a more shielded area. Once "zeroed" the balance is ready and the sample should be carefully placed on the pan. The mass of the sample is read directly off of the scale in grams. 10
Data / Report Name: Experiment 2 Partner: CHM 1025 Section: Date: EXPERIMENTAL Trial Graduated Cylinder and Buret Readings Measuring Mass and Volume After re-reading the discussion section above, verify that you are able to make accurate measurements by making the following measurements and comparing your values with those listed beneath each picture. a. 2.2 ± 0.1* ml b. 5.2 ± 0.2 ml c. 7.0 ± 0.5 ml *usually omitted d. 1.18 ml e. 6.64 ml f. 12.07 ml 11
"Unknown" Graduated Cylinder and Buret Readings Now that you are convinced that you know how to read graduated cylinders and burets, it's time to convince your instructor. Make the following readings and record them in the spaces provided beneath each picture. a. b. c. d. e. f. HAVE YOU INCLUDED THE CORRECT NUMBER OF SIGNIFICANT FIGURES, THE UNCERTAINTY (IF NEEDED), AND THE PROPER UNITS FOR EACH MEASUREMENT? OK: 12
Volume and Mass Measurements When graduated cylinders are manufactured the inside diameter of the cylinder and the distance between calibration marks can be maintained with high accuracy. However, there is often enough variation in the process of joining a base to a tube that noticeable inaccuracies can result when measurements are made from the bottom of the cylinder. Graduated cylinders provide accurate measurements only BETWEEN CALIBRATED markings NOT from the bottom up to an individual marking. However, one normally DOES use this first ml of a graduated cylinder. Therefore, when using a graduated cylinder to measure a volume one should be aware of this potential (minor?) inaccuracy. We will preform an experiment with a graduated cylinder AND deliberately avoid using this first ml of the graduated cylinder for just this reason. Estimation of the Volume of a Drop Using your medicine dropper, fill the 10 ml graduated cylinder to approximately the 5 ml mark and wipe off any stray droplet from the inside of the cylinder with a rolled paper towel. Then, record the graduated cylinder reading as accurately as possible in the table below as the "initial reading." Now, count out 20 drops, making sure they do not adhere to the sides of the cylinder, and record the new cylinder reading in the table as the "first cylinder reading." Continue adding and counting drops until 40 drops have been added. Record this volume in the table as the "second cylinder reading." Finally, continue this process until 60 drops have been added. Record this total in the table as the "final cylinder reading." Suggested data collection Table Initial Cylinder Reading First Cylinder Reading Second Cylinder Reading Final Cylinder Reading By subtraction calculate the volume occupied by the 20, 40, and 60 drop samples respectively and record them in the table below. Show the setup of each volume calculation. Volume occupied by 20 Drops Volume Occupied by 40 Drops Volume Occupied by 60 Drops 13
Now, in a table like the one below calculate the number of drops per milliliter for each experiment and show the correct setup for your work. Setup # of drops / ml Expt. #1 Expt. #2 Expt. #3 Calculate the average number of drops / ml from your three results above and show your setup for the calculation below. Now, using the above answer calculate the average volume of one drop in ml/drop and show the setup below. Round the answer to two significant figures. 14
Measured Volumes Using a Buret After cleaning and drying a 125 ml Erlenmeyer flask, label the flask as #1 and put a cork or rubber stopper in the top. Weigh the flask and stopper using an electronic balance and record the mass in the table below. Next, fill a buret with deionized water up to approximately the 5 ml mark. Read and record this initial volume in the buret to two decimal places. Now, dispense a volume between 10 and 40 ml into flask #1. Read and record this final volume to two decimal places. Finally, re-stopper the flask and re-weigh the apparatus. Record the mass of the flask, stopper, and water in the table. Suggested Table for Data Collection and Calculations Flask #1 with stopper and water......................... Flask #1 with stopper... Mass of water in flask #1... Mass in g Final buret reading... Initial buret reading... Volume of water in flask #1... Volume in ml Measured Volumes Using a Volumetric Pipet After cleaning and drying a 125 ml Erlenmeyer flask, label the flask as #2 and put a stopper in the top. Weigh the flask and stopper using an electronic balance and record the mass in the table below. Next, fill a 50 ml beaker with deionized water. Now, using a pipet of at least 10.00 ml capacity and a pipet bulb, dispense a sample of deionized water from the beaker into the Erlenmeyer flask. Record the volume of water dispensed in the table below. Finally, re-stopper the flask and re-weigh the apparatus. Record the mass of the flask, stopper, and water in the table. Suggested Table of Data Collection and Calculations Flask #2 with stopper and water......................... Flask #2 with stopper... Mass of water in flask #2... Mass in g Volume of water dispensed into flask #2................... 15
Calculated Volumes Using Mass Measurements and Density If the density of a substance is known, the volume of a given mass of substance can be calculated. Remember... T h e density of any substance changes with temperature. Therefore before you can calculate the volumes occupied by your two samples of water, you must measure the temperature of the samples so that the density of water at that temperature can be looked up in a density table. Measure the temperature of one of your samples to the nearest 1 C and record this temperature in the space provided below. Suggested Data Collection Format. Temperature of water in C... Using the information on the density of water in the table below and the individual masses of water in flasks #1 and #2 calculate the volumes of water in the two respective flasks. Temperature Density Temperature Density Temperature Density (in C) (in g/ml) (in C) (in g/ml) (in C) (in g/ml) 16 0.9989 21 0.9979 26 0.9967 17 0.9988 22 0.9977 27 0.9965 18 0.9986 23 0.9975 28 0.9962 19 0.9984 24 0.9972 29 0.9959 20 0.9982 25 0.9970 30 0.9956 Show your setups for the volume of water calculations for the two flasks below. Make sure your answers have the correct number of significant figures and the corrects units. Add an OK box at this point in your Laboratory Notebook. OK: 16
Comparison of the Calculated and Measured Volumes Copy your measured volumes and your calculated volumes into a table like the one below. Measured Volume in Flask #1 Measured Volume in Flask #2 Calculated Volume in Flask #1 Calculated Volume in Flask #2 If the measured and calculated volumes for the two flasks are in complete agreement, your techniques for measuring mass and volume are good. If these volumes do not agree exactly, calculate the percent (%) error in your respective results. The percent error is defined as Show the setups for the calculation of the percent error in your results in your laboratory notebook. Make sure your setups and answers contain the proper units and significant figures. Add an OK box at this point in your Laboratory Notebook. OK: 17
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Homework Problems 1. Select the correct answer for each of the following problems. Show the set-up for each calculation. i) The sum of 9.9 ml plus 0.09 ml SET-UPS a. 10 ml b. 9.9 ml c. 10.0 ml d. 9.99 ml e. 10.00 ml ii) The difference of 10.1 ml minus 9.91 ml a. 0.2 ml b. 0.19 ml c. 0.20 ml d. 1.19 ml e. 0.190 ml S3 2 iii) The product of 2.0 10 cm times 0.2 cm a. 4 cm 3 b. 0.0004 cm S4 c. 4 10 cm d. 0.00040 cm 3 e. 0.0004 cm 3 3 2 iv) The quotient of 2.00 10 cm divided by 0.020 cm 5 S1 a. 1 10 cm S5 1 b. 1.0 10 cm 1 3 c. 1.0 10 cm 5 S1 d. 1.0 10 cm 1 3 e. 1.00 10 cm (OVER) 19
2. A student counts 20 drops in 1.0 ml in a graduated cylinder. The student then counts 39 drops in 2.0 ml. Finally, the student counts 65 drops in 3.0 ml To the nearest whole number, should this student report the average volume of 1.0 ml as 20 or 21 drops/ml? Show the arithmetic which defends your answer. 3. A student determines the volume of a 10 ml graduated cylinder to be 9.80 ml (i.e., this is the experimentally determined volume to the 10 ml calibration mark on this cylinder). Another student obtains 9.81 ml for the same cylinder. Two other student each get 9.85 ml for this cylinder. Based on these data, what is the accurate volume of this cylinder when filled up to the 10 ml mark? Show the arithmetic which defends your answer. 4. Discuss the advantages of the pipet and of the buret. Why would you use one as opposed to the other? 20