Lab 1 procedures / Chemistry B1A / Summer 2015
By Kenward Vaughan and Mike Daniel
Types of error
What limits a measurement? From where do errors arise? Are your measurement results
trustworthy and reproducible? Can your results be used by others in their research?
These are very real, important questions for a scientist. The terms precision and accuracy
accompany these questions. You should assimilate them into your consciousness when you enter
the lab!
So what are some sources of error? Generally we break these into
Two broad categories:
Systematic error – This error can result from a person repeating a mistake, such as reading a
water level in a graduated cylinder incorrectly due to lack of training, or an instrument poorly made
such as a ruler where the zero end of the ruler is not cut off at the proper place. Systematic errors
usually push the results in the same direction, such as your liquid volumes measured in a
graduated cylinder are always low because your eye is always above the liquid level.
Random error - Random errors are always present and are caused by unpredictable variations in
the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental
reading. Random errors are attributed to chance and have a random distribution. These errors can
be estimated by comparing many measurements, and reduced by averaging measurements.
Additionally, error itself can be characterized by the concepts of accuracy and precision.
Accuracy - How close to the real/accepted value is the measurement? This obviously is not always
known. It is established by repeated measurements using accepted procedures and standard
materials by experienced researchers. An example where the value is known is the calibration of a
balance. An object with a known mass is placed on the balance. If the balance does not give the
correct answer, it must be adjusted to be accurate, to give the accepted value of the standard
mass. Experimental error is a measure of accuracy.
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
|
𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
| 𝑋 100% = 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟
Here the difference between an experimentally measured value and the accepted value is
calculated and compared to the size of the accepted value. The smaller the error is, the more
accurate the data is. Absolute value is used so this is always a positive number.
Precision - How sensitive is the measuring instrument and how consistent is the measurement?
Sensitive here refers to the scale used for the measurement. Length measurements made with a
meter stick with only decimeter markings (10 dm = 1 m) can be made no better than estimating
between the decimeter marking. If you estimate between decimeters you estimate to 0.1 dm which
is to the centimeter level (a tenth of a decimeter). A 2nd meter stick with millimeter markings is good
to estimates of a tenth of a millimeter. The 2nd meter stick is 100 times more sensitive (and hence
more precise) than the first decimeter marked ruler. Precision is a measure of consistency, the
closer your answers are together, the more precise your measurements. Deviations are the
difference between an experimental measurement and the average measurement, and average
absolute deviation is the average of deviations and it is one measure of precision.
𝑑𝑖 = |𝑉𝑖 − 𝑉𝑎𝑣𝑔 |
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The smaller the average difference or deviation is, the closer each measurement is to all the other
measurements, and the more precise the measurements. Another measure of precision that is a bit
more complicated to calculate is the standard deviation. The average absolute deviation (or
average deviation) is less than or equal to the standard deviation.
Procedure
First you will compare the accuracy and precision from measuring the volume of water with beakers
and a 100 mL graduated cylinder. Then you will use the density of aluminum to calculate the
thickness of aluminum foil, and measure the foil thickness directly, and compare the two numbers.
Start recording data on page 5.
A. Note, some beakers do not have volume marks on them. You will need to use either your
100 mL or your 150 mL beaker with volume marks on it. Fill your plastic water bottle with
distilled water. You will use this to supply water for your experiment. Weigh the empty dry
beaker and record the mass. Using the volume marks on the beaker, add enough water to
have 20 mL in the beaker. Weigh the beaker with 20 mL of water. Add more water so the
beaker contains about 40 mL of water. Continue in 20 ml increments, recording each step,
till you have weighed a total of 100 mL of tap water in a beaker. Using a thermometer,
measure the temperature of the water. Pour out the water and weigh the empty container.
Repeat the procedure with a 100 mL graduated cylinder.
B. Look up the density of water at the temperature you measured in the CRC Handbook of
Chemistry and Physics. The density calculations can be done after you finish parts D.
C. Get a piece of aluminum foil about 20 cm long. Measure its length and width with the
greatest precision possible using a meter stick. Fold the aluminum foil enough times so you
can fit it on the balance to measure its mass. From the density of aluminum and its area
(length X width), you can calculate its thickness. Clearly record all of your data and clearly
show your calculation.
D. The use of a Micrometer Screw Gauge will be demonstrated. This will be used to measure
your folded aluminum foil. The thickness of n layers of aluminum foil divided by the number
of layers will equal the thickness of 1 layer of foil. Calculate an experiment error assuming
the Micrometer Screw Gauge produces an accepted value.
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Graph 1 – This shows the parts expected in your graph. It should include both axis labeled
with units, a title of y versus x and your (not your instructor's) name.
Mass versus Beaker Measured Volume of
Water / Daniel
30
25
M = 0.9578 V - 0.1634
Mass / g
20
15
10
5
0
0
5
10
15
20
25
30
Volume / mL
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Page left blank
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Lab 1 – Measurements
Name______________________________________
Chemistry B1A / Summer 2015
Partner’s Full Name_____________________________
Complete pages 5-9 and attach your two graphs attached to the back. Turn in 1 week after
the lab is done. Please answer with complete sentences and show your work for
calculations.
The first two questions can be answered after lab.
1. Describe the difference between accuracy and precision.
2. If you misread a gasoline pump so that you measured the volume of gasoline dispensed in liters
instead of gallons, would your error be a (circle answer)
a) systematic error or a
b) random error?
Explain.
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3. Water Volume measured by a beaker and a graduated cylinder, mass of water, and density.
_____mL Beaker
100 mL Graduated Cylinder
A. Mass of Empty Container
/g
B. Mass of container + 20
mL of water/g (°C)
C. Mass of container + 40 mL
of water/g
D. Mass of container + 60 mL
of water/g
F. Mass of container + 80 mL
of water/g
G. Mass of container + 100
mL of water/g
H. Mass of 20 mL of water /g
I. Mass of 40 mL of water /g
J. Mass of 60 mL of water /g
K. Mass of 80 mL of water /g
L. Mass of 100 mL of water /g
M. Mass of empty wet
container
N. Temperature of Water / ℃
O. CRC Reference Density of
Water / g/cm3
Edition _________________
P. Density of 20 mL of water
g/cm3
Q. Density of 40 mL of water
g/cm3
R. Density of 60 mL of water
g/cm3
S. Density of 80 mL of water
g/cm3
T. Density of 100 mL of water
g/cm3
U. Average Density of water
g/cm3
V. Average Deviation of
Water Density (calculated
below) g/cm3
W. Percent Error compared
to CRC Reference Density
(calculated below)
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4. Average deviation was discussed on page 1. Show the five absolute values of the difference
between the average density of water measured with a beaker and each measurement of water
density. Use these numbers to calculate the average deviation of density measured with a beaker.
Record your calculations below. Calculate the average deviation of water density measured with
a 100 mL graduated cylinder. You do not need to show your calculations for this second average
deviation. Record your two average deviations in the table above.
Record Calculated Results below
Density Deviation for 20 mL of
water
“
40 mL “
“
60 mL “
“
80 mL “
“
100 mL “
Average Deviation /mL
5. Experimental Error was discussed on page 1. Show your work calculating the experimental error
for the average water density measured using a beaker and using a 100 mL graduated cylinder.
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6. Use your data to discuss which calculated density was more precise.
7. Use your data to discuss which calculated density was more accurate.
8. Graph in the landscape mode, the mass of water versus the volume of water measured with a
beaker, similar to that shown above. Determine the best fit equation of line from this data. The
slope of this line is an average value of the density. Record the equation of your line below. Make a
similar graph using the 100 mL graduated cylinder data, and record the equation below. Using
these density measurements, discuss which data set, the beaker data or the graduated cylinder
data, is more accurate.
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9. Report below your aluminum measurements and calculations. You should have a calculated
value for the thickness of aluminum foil, and a measurement of the thickness. Clearly label your
work.
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