Introduction to Measurement

Description

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If you count the number of chairs or people in an ordinary sized room, you will probably get exactly the right answer. But if you measure the length of a page of paper with a ruler, your answer will have a small margin of uncertainty. That is, numbers read from measuring instruments do not give the exact measurements in the sense that an integer number is exact when you count objects. Every measurement is to some extent uncertain.

Moreover, if another person measures the length of the same piece of paper, he or she will probably get a different answer from yours. Does this mean that the length of the page has changed? Hardly! Then can you possibly find the length of the page without any uncertainty in your measurement?

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Be certain to exercise care when using the instruments.

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Number a piece of paper, use a handout supplied, or a page in your lab notebook, from 1 to 16. Various stations have been set up around the room and at each one you are to take a measurement. Instructions will be given to you at the lab station. Record the result of each measurement on the paper, in a table like the one shown. When you have completed the entire series of measurements, record your results on the board along with those of your classmates. Do not talk about your results or how you got them until everyone has finished.

Suggested Stations:

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Name ___________________________ Class ________

Teacher__________________________

DoChem 009 Introduction to Measurement

Data Table

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Purposes

• To practice a variety of measurement techniques.
• To recognize variations in data.
• To learn the correct usage of the terms precision, accuracy, and error in measurements.

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(per class)

• 16 index card, 3" x 5"
• timer or classroom clock
• string or wire
• meter stick (1 mm calibration)
• meter stick (1 cm calibration)
• thermometer (-10 to 110 °C)
• water in 100-mL beaker
• 30 mL lemon juice in 100-mL beaker
• 30 mL salt water in 100-mL beaker
• pH paper
• laboratory table
• water in a 1L volumetric flask
• several coins
• stopwatch
• wire
• plastic disc (checker piece, etc.)
• vernier caliper
• large ice cubes
• laboratory balance
• metal weights
• spring scale
• barometer
• hydrometer
• rubber tubing
• metric ruler (30 cm long, 1 mm calibration)
• water in a 50-mL graduated cylinder

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• The list included above suggests typical stations that may be used for this experiment. Anything that is available that gives students practice with instrument manipulation is appropriate. This experiment is meant to provide an overview of measurement.
• Write instructions for each measuring assignment on individual index cards. For example:

• Use the meter stick to determine the length of this piece of string.
• Put some tap water into the beaker. Find the temperature of the water.
• Use one card (i.e., one assignment) for each lab station that you wish to set up. Place the card, along with the required equipment or supplies, at each lab station or desk. One recommendation is to put one card on each side of a large lab table. Adapt this to your particular laboratory setting.
• Have the students number a data sheet (with as many numbers as there are stations), find a place to start in the lab, take the measurement stated, and, on cue from you, move to the next lab station to take the next measurement. In other words, the students walk through the lab stopping at each "index card" and recording each measurement.
• To keep students moving at a regular pace, use a timer or clock and signal to them at regular time intervals. Two minutes per station is usually sufficient.
• The classroom lecture area can be set up with stations, but this experiment is best done in a spacious laboratory.
• Since this lab is an introductory overview, and because one of its purposes is to expose lab errors, tell students to make the "best" measurements they can, to be as precise as they think they can be.
• Opaque tape (such as masking tape) can often be used to cover selected calibration marks on a meter stick so that only larger calibration units are visible. For example, covering the millimeter marks at the edge of the meter stick will still permit the centimeter calibration marks to be visible.
• After the students are finished, class measurements should be compiled and printed for the students to see. This can be done as a tally on the chalkboard or as a ditto/xerox sheet. These results then become the basis for closure discussion.

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Teacher preparation: 1 hour (first time)

Class Time: 40 to 50 minutes

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Possible exposure to mercury if mercury thermometers are used.

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Be certain that the students exercise care when using the instruments. When mercury thermometers are used, be prepared to clean up a mercury spill. (Have a commercial mercury spill kit available.)

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Save the index cards for future use. If any chemicals are used, be certain to select ones which pose little or no hazard, and which can be disposed of at the sink.

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• To measure something is to find the numerical value of one of its properties. The results of quantitative measurements are called values. Units are the quantities that have been defined for making measurements. In the SI system, for example, the meter is a unit of length. If the speed of a car is measured, the units of the result could be meters/second or miles/hour, or any of several other units.
• Conscious and careful attention to units is important in working problems as well as being necessary for communication. Even the simplest measurements contain uncertainty. In order to discuss measurements, three terms are often used:

• Accuracy - The closeness with which an experimental result approaches the true value.
• Precision - The closeness with which several measurements of the same quantity agree.
• Error - The difference between the true value and the experimental result.

• It is possible to have an experiment which is quite precise but still contains large errors, that is, has poor accuracy. The precision of a result is only an indication of the agreement of the measurements, not of whether the results were close to the true value.
• Errors that result from experimental equipment or faulty technique are called systematic errors. Such an error would result, for example, if a calibration mark were missing from a buret. At one station, students are asked to measure the diameter of a rubber tube. Some will measure the outside diameter and others the inside diameter. This classroom "trick" gives an opportunity for the introduction of a discussion of systematic errors.
• In addition to systematic errors, there are always random errors -- the inescapable uncertainty of the measurements themselves, regardless of what the true value is. These are the result of the necessary human or machine judgment of the relationship between the measured property of the measured object versus the calibration of the measuring instrument. There is always judgment, for example, about where the edge of the paper is compared to the markings on the measuring ruler.
• Systematic errors always err in the same direction. On the other hand, random errors are just as likely to be as positive as negative. As a result, random errors tend to cancel when an average of several measurements of the same object is reported. Computer data collection is excellent for averaging random errors, but systematic errors must be detected in the laboratory and corrected at the source of the errors.
• There is always uncertainty except when counting small numbers of discrete, individual units such as coins, people, or automobiles.

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Students may enter the class' data directly into a worksheet of a spreadsheet computer program. See EXPT 134 for suggestions.

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20-30 minutes the next day.

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• measurement
• length
• time
• temperature
• pH
• rate
• accuracy
• precision
• error
• error in measurement
• mass
• volume
• weight
• density

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