2-1
Experiment2
Measurement and the Metric System
Objectives
1. To become acquainted with physical measurement techniques (both direct and indirect methods).
2. To learn how to read and record data to the proper number of significant figures.
3. To become familiar with the metric system.
4.
To practice unit conversions involving met1i.c units.
Discussion
Measurements are basic to any scientific pursuit. A measurement has both a magnitude (numerical value)
and a unit. Metric and S.I. units are used in the sciences.
In our daily lives, approximations of temperature, distance, etc. are often sufficient. In the laboratory,
however, measurements must be more accurate to be of any value. Due to inexact tools and faulty
observations, measurements are subject to error; they are never absolutely exact . .Most measurements are
made from a scale. Data should generally be recorded to one decimal place beyond what is calibrated on
the scale. This requires estimating '1between the linesrr to determine the last digit. For more detail and
practice with measurements see, the section titled Measurement in your chemistry 4 supplement.
Measurements are typically performed several times during any particular experiment. Each time a
measurement or set of measurements is made, the measurement (or set of measurements) is called a trial.
Three is typical (and the minimum) number of trials performed in an experiment. Since each
measurement has some uncertainty, the average results from the trials is considered the experimental
result. To illustrate, the average mileage for a Ford 1998 F-150 pickup truck was determined by
''experimentation." Three sets of data were collected during .January 1999.
Trial
Date
#
Miles Traveled
(mi)
Gallons Used
(gal)
Gas Mileage
or :MPG)
(mil~g-al,
'.J..
1/13/99
362.1
22.589
16.03
2
1116/99
346.7
20.184
17.18
3
1/17/99
363.2
21.410
16.96
Average m:i/gal
16.72
The result of this experiment - the experimental value - is 16.72 l\/IPG. A curious scientist and consumer
would want to know how dose this value is to the estimate made by the Environmental Protection Agency
(EPA). The EPA s estimate for the mileage for this vehicle is 17.00 MPG. One way to show how close the
experimental value is to the EPA estimate is to determine the difference between the two values. The next
question is; do you subtract the EPA estimate from the experimental value, or vice versa? The convention
is to subtract the accepted value (the EPA estimate) from the experimental value. Thus the difference can
be calculated as follows:
1
Experimental Value
Accepted Value
=
Difference
16.72 l\1PG
17.00 :NIPG
=
- 0.28 :MPG
The difference, - 0.28 .MPG, gives three pieces of information. First it gives the !(direction" that the
experimental result is off from the EPA estimate, that is negative, this means that the experimental value
is smaller than the accepted value. Second it gives the magnitude of the difference between. the two l\/IPG
values, 0.28. Finally, it gives the units. The difference between the experimental result and the accepted
value is a good way to compare an experimental value with an accepted value, however, it is not the best
way to express the error in an e~--periment.
To illustrate. assume that the 1V1PG for an economv car was determined bv its owner to be 32.22 l\1PG and
the EPA estimate is 32.50 JMPG. Given these two ;alues we have:
·
Ex-perimental Value
Accepted Value
=
Difference
32.78 lVIPG
32.SOMPG
=
0.28 MPG
Notice that the magnitude of the difference in each "experiment" is 0.28 IvlPG. Although these two
differences are the same, the difference for the F-150 tvIPG is more significant than the difference for the
economy car. This is because 0.28 is a larger percentage of the accepted value of 17.00 MPG for the F-150
than that for the economy car. The percent error is a better way to express an error relative to an accepted
value.
The percent error is a way to express bow close an experimental result is to the accepted value and in what
"direction" that result is off relative to the accepted value. The percent error is calculated using the
following formula:
Percent Error ... Experimental Value - Accepted Value x 100
Accepted Value
Shown in the table below is a comparison of percent error and a simple difference calculation. Notice that
the percent error for the :F-150 is greater than that for the economy car.
Automobile
Experimental MPG
EPA MPG
Difference
Percent Error
F-150
Economy
16.72
32.78
17.00
32.50
- 0.28
+0.28
- 1.6%
-i-0.86%
The experimental result may be greater than, less than or equal to (rarely) the accepted value. This leads
to percent errors that may be positive, negative .or zero.
ln this experiment, linear dimensions, masses, volumes and temperatures will be measured. These
quantities can be easily measured using common equipment. Often two measurements are combined in
order to define a new quantity. For example, the mass divided by the volume of a given sample of matter
defines density, a physical property characteristic of a given substance. Some of your results will be
compared to accepted values by calculation of percent errors. You will be expected to calculate percent
errors for many of the experiments that you perform in this course.
:-3
Procedure
A. Densitv of a Liquid
Weigh a drv 50 mL graduated cylinder on the ele<..'tronic balance. "Masses should be recorded to the nearest
hundredth of a gram (0.0X g) when using the electronic balance. Add about 15 mL of distilled water, from
a squeeze bottle, to the graduate and determine the volume to the nearest tenth of a milliliter (0.X mL).
Now measure the mass of the graduate containing the liquid. From the data, calculate the mass of the
distilled water in the graduated cylinder and compute the density of distilled water. Record the
temperature of the water to the nearest tenth of a degree Celsius (0.X °C). Use the table on page 2-4 to find
an accurate value of the density of distilled water at your experimental temperature. Repeat the same
experiment using approximately 30 mL and then 45 mL of distilled water.
B. Density of a Solid
Obtain a copper metal cylinder and an unknown metal cylinder from the stockroom. Record the sample
number that is stamped on the unknown. metal cylinder. Determine the mass of the cylinder using the
electronic balance (O.OX g). Place about 30 mL of water in a 50 mL graduate and record the volume (O.X
mL). Tilt the graduate and gently slide the copper cylinder into the water; avoid splashing and spilling.
Record the new volume and use the data to calculate to volume of the copper cylinder. Calculate the
density of the copper cylinder, and using the theoretical density of copper calculate the percent error.
Determine the density of the unknown metal cylinder in the same manner that you used for the copper
cylinder. After calculating the density of the unknown metal, obtain the theoretical density from the
instructor.
C. Indirect Determination of the Thickness of One Sheet of Paper and the Mass ofl.00 Square
Centimeter of One Sheet of Paper
Obtain a packet of paper from the middle of the lab. Be sure to· record the color and tare weight of the
packet. Using a platform balance, determine the mass (0.0X g) of the packet (250 sheets) of paper
provided. Measure the thickness, length, and width of the packet in centimeters (0.0X cm). Do the
calculations and unit conversions indicated on the data and calculations table.
D. Indirect Determination of the Mass and Volume of One Drop of Water:
Using the electronic balance, determine the mass (0.0X g) of a dry, 10 mL graduated cylinder._ Now add 60
drops of distilled water and record the volume (O.OX mL). Weigh the graduate containing the 60 drops of
water. Do the calculations and unit conversions indicated on the data and calculation table.
E. Introduction to the Metric Svstem
l. Obtain from the stockroom or your instructor a ruler that has at least a 1/16 inch scale on one edge and
a centimeter scale on the other edge.
2. Measure each of the five lines on page 2-7 with each scale.
a. Measure a line in centimeters; being careful to estimate the open space between the scale marks.
b. Measure the same line in inches; being careful to estimate the open space. It is often more reliable
to record English length data as a sum to be performed on your calculator. A typical reading and
conversion to decimal notation is:
r---------
r-------------------,
Fractional ' 4"
3/4 11
+
Decimal
Decimal
1
0.75"
4"
1_ - -
0.75'1
+
- - -
-
-
~- -
- -
- - -
-
.,. - ..:
Certain "digits" give an
unlimited number of
significant figures.
0.5/16"
:
0.03125" :
+
0.03 11
·-----r--~
=
4.78 11
Uncertain (doubtful) "digitsu give a limited number
of significant figures. The doubtful digit here
limits the decimal answer to the hundredths place
Experiment 2
Name: ____________________________________
MEASUREMENTS AND THE METRIC SYSTEM
A. Density of a Liquid
Total Mass of the
Cylinder and its
Content
Empty 50-mL Graduated
Cylinder
Mass of
Water
Volume of
Water
Density of
Water
0.00 g
0.0 mL
--------------
Graduated Cylinder with
Approximatively 15 mL
Graduated Cylinder with
Approximatively 30 mL
Graduated Cylinder with
Approximatively 45 mL
Average Density of Water
(from the three measurements) __________________
Accepted Density = 0.998 g/mL
Percent Error
(Show work.)
__________________
D. Indirect Determination of the Mass and Volume of One Drop of Water
Mass of the Dry Graduated Cylinder
___________ g
Number of Drops of Water Added
___________ drops
Mass of the Graduated Cylinder with Water
___________ g
Volume of Water
___________ mL
Mass of Water
___________ g
Volume of One Drop of Water
___________ mL/drop = ___________ µL/drop
Mass of One Drop of Water
___________ g/drop = ___________ µg/drop
B. Density of a Solid
Unknown Metal
Cylinder Number:
Copper Cylinder
Sample
Trial 1
Trial 2
8.96 g/cm3
8.96 g/cm3
Trial 1
Trial 2
Mass of the metal
cylinder
Initial volume: volume of
water alone in the
graduated cylinder
Final volume: combined
volume of water and the
metal cylinder submerged
Volume of the metal
cylinder
(show work)
Density of the metal
cylinder
(show work)
Accepted density
Percent error
(show work)
NOT GIVEN
NO CALCULATION IS REQUIRED