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Purpose: To learn how to properly use common laboratory measuring devices, to learn the difference between accuracy and precision in measurement, and to compare the reliability of measuring versus estimating. Introduction Have you ever watched a cooking show on television and noticed the chef mixing ingredients without measuring? Well, he is probably able to do that because of years of experience. If you were required to do an experiment that calls for specific amounts of various chemicals, could you, like the chef, estimate well the amount of each chemical and get a good result? Unlikely! When it comes to cooking, a little less or more of an ingredient might not even be noticed but for chemistry, the amount matters. And because the amount matters when doing scientific work, chemists generally do not estimate the amount of the chemicals they use in sensitive experiments but instead they make careful measurements. Measurement is considered to be the foundation of modern chemistry. It is a foundation that was laid by scientists such as Antoine Lavoisier (1743-1794) who was able to make careful measurements that lead to the formulation of the law of conservation of mass. For his work, Lavoisier had acquired a sophisticated balance that was sensitive enough to detect the changes in mass during his experiments. Still, any measuring device, whether sophisticated or simple, has limitations, which affect the accuracy of the measurements that can be made using it. Accuracy and Precision Because all measuring devices have limitations, any measurement made with a laboratory tool has an experimental uncertainty associated with it. Therefore, whenever a scientist records a measurement, it is important to convey how reliable it is, that is, how accurate or precise that measurement is. By accuracy, we mean how close the experimentally measured value is to the correct or true value. The term precision, on the other hand, means how reproducible the experimentally measured values are. That is, if we were to measure the same object several times, precision is how close those experimental values are to each other. To some extent this depends on the expertise of the person doing the measurement, and on the method of measurement, but the type of apparatus being used can also limit the precision of the measurement. To provide information about the accuracy of a measurement, the percent error is generally calculated and reported.

Error = experimental value − true value Percent Error = !""#"

!"#$ !"#$% x 100

A positive error or percent error tells us that the experimental value is too high. A negative value tells us that the experimental value is too low. The size of the error depends on a number of factors but suffice it to say that a small percent error, say between 0 and 5% is acceptable for many chemistry experiments and indicates good accuracy.

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Precision is determined by the deviation of the experimental value from the average value (rather than the true value). In this course you will not be asked to calculate the deviation. However you should be aware of the difference between accuracy and precision. We will concentrate on how the apparatus affects the precision of measurement. To convey precision, the experimental value should be recorded to the correct significant figures. Location of the Uncertain Digit in a Measurement Information concerning the experimental uncertainty associated with measurements made using a particular tool can be obtained by examining the calibrations marked on it. In making a measurement a scientist always reads and records all the digits which can be read directly from the tool plus one additional digit which represents his or her estimate in reading between the calibration lines. This last digit is what is called the uncertain digit. Thus, a correctly determined measurement from a particular tool contains all the digits one is sure of plus a final digit that is the scientist's best estimate between lines. This is true for all measurements made with tools that are marked with calibration lines. If however, the measuring device displays the measured value (as is the case with electronic balances); all the digits displayed must be recorded. For the displayed value, the uncertain digit is the rightmost digit. Thus, all measured values—whether figured-out by an experimenter or displayed by a device—must contain one uncertain digit. All the certain digits along with the one uncertain digit in a measurement are called significant figures or significant digits. In this experiment we will concentrate on how the apparatus affects the precision of a measurement. To convey precision, the experimental value should be recorded to the correct number of significant figures. The general rule is to record all measurements to one-tenth of the smallest division on the measuring device. Table 2.1 shows the size of the smallest divisions on a measuring device and the number of decimal places expected in a measurement made with that device. Table 2.1 Divisions on Measuring Scales and Expected Decimal Places in Measurements Size of Smallest Divisions on a Measuring Device

! !"

of Smallest Division # Decimal Places in Measurement

Place Value of Last Significant Digit

1000 100 none hundreds 100 10 none tens 10 1 none ones 5 0.5 1 tenth 2 0.2 1 tenth 1 0.1 1 tenth

0.5 0.05 2 hundredth 0.2 0.02 2 hundredth 0.1 0.01 2 hundredth 0.01 0.001 3 thousandth

It is important to note that a more precise measuring device can be used to make measurements requiring less precision but a less precise measuring device cannot be used to make a more precise measurement. For example, to measure 25.0 mL of a liquid, we could

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use a 50-mL buret with 0.1 mL divisions as well as a 50-mL or 100-mL graduated cylinder with divisions of 1 mL. What we could not use is a 50-mL beaker with divisions of 10 mL. The buret would give 25.00 mL; the graduated cylinder would give 25.0 mL; and the beaker would give 25 mL. Since the 2 and the 5 must be certain, the beaker could not be used because the 5 is an uncertain digit in the measurement made with the beaker. Making Measurements Using various Measuring Devices In this experiment you will use a variety of commonly used laboratory tools to measure length, volume, and mass. As described below, each measuring device must be handled properly and read correctly. (See also Appendix 1 that deals with significant figures.) Length: Length can be measured with a ruler. The size of the calibration marks on the ruler determines the number of decimal places in each length measurement. Consider the ruler in Figure 2.1, for example. The smallest division of this ruler is 0.1 cm. Because you record the length as one-tenth of 0.1 cm, which would be 0.01 cm (to 2 decimal places), you can see the length of the object below could be read as 4.83 cm or 4.84 cm. The last digit we should record is by estimating how far the object extends between 4.8 and 4.9 cm. Obviously there is some uncertainty as to what that last digit might be. One might see it as 4.83 cm; another, as 4.84 cm. Using the ruler pictured in Figure 2.2 below, one could read the length of the same object as being 4.8 cm or 4.9 cm. For this ruler, the smallest division is 1 cm, and one-tenth of 1 cm is 0.1 cm. This means you can record only to one decimal place. Volume: Volumetric wares are designed to contain (TC) or to deliver (TD) a certain volume of a liquid. You can find these letters stamped on the container. It is important to use the appropriate container for best results. Some volumetric wares also provide information about the tolerance. The tolerance is the allowed deviation of the measuring device. The tolerance is generally printed on the measuring device as a ± value. For example, on a 10- mL volumetric flask you might see ±0.08 mL meaning that when the flask is filled, the volume could be any value between 9.92 mL and 10.08 mL. The volume should therefore be written as 10.00 ± 0.08 mL. The graduated cylinder is generally used for measuring the volume of a liquid. In a narrow tube such as a graduated cylinder or a buret, many liquids such as water and aqueous solutions have a curved surface called a meniscus. The proper way to measure the volume

cm

Figure 2.1

cm

Figure 2.2

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of such a liquid is to read the bottom of the meniscus at eye-level as shown in Figure 2.3. This is easier said than done with water being colorless. For this reason you will prepare a Volume-Reading Card to make the bottom of the meniscus more visible.

Figure 2.3 It is important to note that for most volume measurements only one reading of volume is required. However, when using the buret to measure volume, two readings are required—an initial reading and a final reading. The volume dispensed is determined by taking the difference between them. Volume dispensed from buret = final buret reading – initial buret reading Mass: Mass is measured with a balance. Some balances have to be read manually but the balances used in this experiment are electronic balances and they are designed to display the masses for you. The last digit in a displayed mass is the uncertain digit in that mass measurement. And, because all measurements should have one uncertain digit, it means that all of the digits displayed on the balances are significant and should be recorded. The use of the electronic balance is simple. Generally, a substance to be weighed is placed in the container in which it will be used and weighed with the container. This method of weighing is called weighing by difference and it is generally a more accurate way of weighing than weighing directly. To get the mass of the substance, the empty container is weighed first. Next the substance is placed in it and the two are weighed together. Finally, the mass of the empty container is subtracted from the mass of the container and substance. Figure 2.4 shows diagrams of two kinds of balances you are likely to use.

Always remember to read the meniscus at eye-level.

Volume-Reading Card

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Figure 2.4 In addition to paying attention to the significant figures, you must learn to always convey what units you are using. For example, if you are measuring dimensions with a ruler, you need to specify whether you are measuring in inches, centimeters, millimeters, or some other unit. It is gross carelessness to leave off the units of a measurement. And in real life situations, such carelessness could lead to loss of lives and property. Equipment/Materials Metric ruler, index card, black marker, 50-mL and 100-mL beakers, 50-mL buret, ring stand, buret clamp, 100-mL volumetric flask, 25-mL pipet, pipet pump, 10-mL graduated cylinder, 50-mL graduated cylinder, 100-mL graduated cylinder, 100-mL plastic beaker, metal shots, 100-gram standard, electronic balance Procedure (Using a pen or pencil, record by hand all of your data and results and perform all calculations on the Data Collection and Results Pages.)

I. Length Measurement 1. Obtain a metric ruler. 2. Note and record the size of the smallest divisions on the ruler. 3. Use the ruler to measure the length of Rod A below in cm.

Rod A

II. Volume Measurement 1. Preparation of the Volume-Reading Card: Obtain an index card. With a black marker,

draw a thick black line (about 1 cm thick) across the length of the card.

2.

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3. Obtain the following volumetric wares: 50-mL beakers (2), 50-mL buret, 100-mL volumetric flask, 25-mL pipet, 50-mL and 100-mL graduated cylinders. Make sure all these items are clean and dry.

4. Examine each piece of glassware to determine whether it is designed as TC, TD, or both TC and TD, or neither.

5. Note and record the size of the smallest division on each piece of glassware or the tolerance.

Measuring with a beaker:

6. Pour tap water into one of the 50-mL beakers until the water level is somewhere between the 30-mL and 40-mL marks. Read and record the actual amount of water in the beaker.

7. Transfer the water from the 50-mL beaker into the 50-mL graduated cylinder. Do your best to transfer all of the water from the beaker to the graduated cylinder. Read and record the amount of water in the graduated cylinder. Use your Volume-Reading Card to help you see the meniscus more clearly.

Measuring with a buret:

8. Take the clean and dry 50-mL buret and pour tap water into it until it is filled. You may need to use a filling funnel to help channel the water into the buret.

9. Set up the buret on a ring stand. Place a small beaker under the tip of the buret. Open the valve at the bottom of the buret and allow the water to drain down until the bottom of the meniscus is on the 1-mL mark. Make sure there are no air bubbles in the liquid. If there are bubbles, drain some more of the water out of buret and fill the buret back up to the 1-mL mark. Remove the filling funnel (if you had used one) and then read and record the volume as initial buret reading.

10. Place a dry 50-mL graduated cylinder under the tip of the buret and drain the water down until the level of the water in the buret is at the 26-mL mark. Read and record the volume in the buret as final buret reading. Then, calculate the volume of water dispensed from the buret. Next, read and record the volume of water collected in the graduated cylinder.

Measuring with a pipet:

11. Pour tap water into the other 50-mL beaker up to about the 40-mL mark. Use the 25-mL pipet to transfer 25 mL of the water from the beaker to a 50-mL graduated cylinder. After the liquid is run out of the pipet, touch the tip of the pipet to the side of the graduated cylinder to dislodge any adhering droplet and examine the pipet tip. You will note that there is a tiny amount of the liquid remaining in the narrow tip. This is supposed to remain in the tip. Do not blow this into your pipetted sample.

12. Read and record the volume of water in the graduated cylinder.

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Pipetting with a pipet pump: To pipet a liquid, do the following:

i) make sure the plunger is all the way down into the barrel; ii) insert the mouth of the pipet into the chuck with a slight rotating motion;

Warning: Be careful when placing a glass pipet into the pump. Glass may break or shatter when forced.

iii) using your dominant hand, immerse the pipet tip beneath the surface of the liquid in the beaker and roll the wheel to bring the plunger up and draw the liquid into the pipet until the bottom of the meniscus is at the scratch mark on the neck;

iv) remove the tip of the pipet from the liquid and place the tip over the container that you are transferring the liquid to;

v) then roll the wheel in the opposite direction to bring the plunger down and dispense the liquid or press the quick release lever to quickly dispense the liquid.

Pipet Pump

Measuring with a volumetric flask: 13. Take the clean and dry 100-mL volumetric flask. Find and record the tolerance of the

flask. The tolerance is usually stamped on the bulb region of the flask.

14. Take a clean and dry 100-mL graduated cylinder and fill it with tap water to the 100-mL mark.

15. Carefully transfer the water from the graduated cylinder to the 100-mL volumetric flask

using a small funnel. There should be no droplets of water remaining in the cylinder or adhering to the neck of the funnel and volumetric flask. Note where the bottom of the meniscus of the water is in relation to the scratch mark on the volumetric flask (that is, at, above, or below the scratch mark).

III. Precision of Measuring Volumes Effect of Eye-Level on Accuracy of Reading Volumes

1. Place exactly 7.00 mL of deionized water into a 10-mL grad cylinder. Use a disposable pipet to help you add or remove excess water so that the bottom of the meniscus is at exactly the 7-mL mark when held at eye-level.

plunger thumb wheel quick release lever barrel chuck with threaded collar

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2. Hold the cylinder so that the meniscus is well above your eye-level. Record the volume. (Remember to record to the correct sig. fig.)

3. Repeat with the cylinder at eye-level and below eye-level. 4. Calculate the error for each reading. Precision of Volume Using Various Apparatus 1. Pour the 7.00 mL of deionized water from the 10-mL grad cylinder into your 50-mL

grad cylinder and record the volume as precisely as you can. 2. Pour the water from the 50-mL grad cylinder into your 50-mL beaker and record the

volume as precisely as you can. Take the time to figure out how many decimal places you need to record.

IV. Mass Measurement

1. Obtain a plastic beaker or small plastic cup, 100-gram standard weight, and metal shots.

2. Hold the empty plastic beaker or cup in one hand and the 100-gram weight in the other hand.

3. Have someone add metal shots into the plastic beaker or cup while you try to use the weight in the other hand to help you judge when the beaker and shots together are about the same weight as the 100-gram standard.

4. Once you feel that the beaker with the shots is about 100 g, weigh it. 5. Switch with the other person and repeat. 6. For these data calculate the error and % error for each result.

Clean-up

1. Empty water from containers into the sink. 2. Pour the metal shot back into the containers. 3. Return all equipment and materials back to their original location. 4. Clean up your work area. 5. Wipe off and return the safety goggles to the cabinet (or place it in your drawer if

it belongs to you). Note that once you put away your safety goggles, you must leave the lab. Remember to wash your hands before leaving.