Measurements of Mass, Volume and Density
Prelab
Name____________________________________
Total_______/10
1. What is the purpose of this experiment?
2. Determine the number of significant figures in the following measurements.
a) 0.00913
b)
4.2860
c) 5.77
d) 31.00
3. a) What is the rule for significant figures when adding or subtracting measurement values?
b) What is the rule for significant figures when multiplying or dividing measurement values?
4. Define accuracy and precision.
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Measurements of Mass, Volume and Density
In this experiment you will measure the mass of an object with two different kinds of balances
and calculate the volume of liquid that is delivered from a transfer pipet. You will also
determine the density of an object.
Introduction
Many experiments require some type of measurement, and are often simple measurements of
mass and volume. The validity of an experiment is dependent on the reliability of these
measurements. A measurement’s reliability is usually considered in terms of its precision.
Precision is the closeness of the agreement between successive measurements of the same
quantity. The dispersion in a set of measurements is usually expressed in terms of the standard
deviation, whose symbol is s. You are going to be asked to determine the standard deviation for
some of your data. The standard deviation measures how close the data are clustered around the
mean. The smaller the standard deviation, the more closely the data are clustered around the
mean and the more precise your measurements are. After a quantity has been measured in an
experiment, it may be necessary to use that measurement in a subsequent calculation. If you use
a hand calculator for the arithmetic, eight or more digits may appear in the answer. It is up to
you to decide how many of these digits are significant. IT IS YOUR RESPONSIBILITY TO
KNOW THE RULES FOR SIGNIFICANT FIGURES BEFORE YOU START THIS
EXPERIMENT.
You will have to practice using an analytical and top loader balance and then a transfer pipet so
you can gain confidence to perform this experiment. Next, you will measure the mass of a flask
four times on each balance. The precision of the measurements will be examined when you
determine the correct number of significant figures in the mean mass of the flask. You will then
add water to the flask from a filled 5-mL pipet, and then measure the mass of the flask and water.
You will repeat this process three more times. After calculating the mass of the water that was
delivered each time from the pipet, you will calculate the volume of each addition from the mass
and density of water. You will then determine the correct number of significant figures in the
mean volume. This number will allow you to appreciate the precision that you have achieved
with the pipet.
You will have to measure volume using a graduated cylinder. A graduated cylinder is used to
measure an approximate volume of a liquid. When water or an aqueous solution (a solution
containing water) is added, the upper surface of the liquid in the graduated cylinder will be
concave. This concave surface is called the meniscus. The bottom of the meniscus is used for
all measurements. To avoid error, your eye should always be level with the meniscus when you
are measuring the volume. Using the graduated cylinder gives you the ability to measure the
volume to only one decimal place.
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Procedure
Part I: Using the Balance
1. Obtain about 100 mL of distilled water in a beaker. Allow the beaker and water to sit
on the laboratory bench while you are learning to use the balances and the pipet for parts II
and III. The water should come to the temperature of the laboratory during that time.
2. Obtain a thermometer and a 50-mL Erlenmeyer flask with a rubber stopper.
3. Use the SAME top loader balance throughout the experiment.
4. Place the rubber stopper in the Erlenmeyer flask. Tare the top loader balance. Measure and
record the combined masses of the flask and stopper.
5. Use tissue paper or paper towel to remove the stoppered flask from the pan of the balance.
This is used because some balances are sensitive enough to detect the oils from your
fingerprints and you will be weighing the flask on the analytical balance in step 8.
6. Bring your balance to the zero position again. Measure and record the mass of the
stoppered flask once again.
7. Repeat steps 5 and 6 until you have measured the mass four times.
8. Calculate the mean (average) mass. The differences between the measured masses and the
mean should be very small. If you are unsure of your results, consult your laboratory
instructor.
9. Repeat steps 3-8 with the analytical balance. Be sure to use the SAME balance throughout
the experiment.
Part II: Using the Pipet
Be sure to use the SAME BALANCE for ALL measurements.
1. Obtain a 5 mL pipet.
2. Practice using the pipet with distilled water (not the water you have set aside) until
you are comfortable with the technique. You should plan on using the same analytical
balance and the same pipet throughout the experiment.
3. Using the thermometer, note the temperature of the laboratory and of the distilled
water that you have set aside. When the temperatures are identical or very nearly
identical, you can begin. Record the temperature to the nearest degree.
4. Measure and record the mass of the empty stoppered flask again using the ANALYTICAL
BALANCE. Use tissue paper/paper towel as you did before.
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5. Remove the flask from the balance, using tissue paper. Pipet exactly 5 mL of the
room-temperature water into the flask without touching the flask with your fingers.
Using tissue paper/paper towel, replace the stopper to prevent evaporation.
6. Bring your balance to the zero position. Measure and record the combined mass of the
water and the stoppered flask.
7. Remove the flask from the balance. Do not pour out the first sample. Pipet another
5 mL sample into the flask. The volume of the water in the flask should now be 10 mL.
Replace the stopper and repeat step 6.
8. Repeat until four samples of water have been delivered to the flask and the final
volume is 20 mL.
9. Calculate the mass of water that was delivered each time from your pipet. These
masses should be approximately identical.
10. Calculate the volume of each sample from the mass and density of water. Use Table 1
to find the density that corresponds to your recorded temperature.
Part III: Determining the Density of an Object
1. Using your graduated cylinder, measure 40-50 mL of water from your beaker in Part I and
leave it in the graduated cylinder. Record this measurement to the nearest 0.1 mL.
2. Take one of the objects from the samples that are given and find its mass on the
analytical balance.
3. Place that same object in the graduated cylinder with the water in it. Make sure that
the object is completely submerged in the water. If the object is not completely
submerged, repeat steps 1and 2 being sure to dry the object and adding more water in
the graduated cylinder. Avoid splashing any water out of the graduated cylinder or cracking
the bottom of the graduated cylinder.
4. Record the level of the water with object in the graduated cylinder. The difference
between this measurement and the measurement in step 1 is the volume of the object.
5. Using the same object that has been dried well, measure the length, width and height of the
object to the nearest 0.01 cm.
6. Calculate the volume of the object using the measurements determined in step 5.
7. Calculate the density of the object (g/mL and g/cm3) using the correct number of
significant figures.
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Table 1 Density (g/mL) of Water at Various Temperatures (o C)
Temp.
Density
Temp.
Density
Temp.
17
18
19
20
21
0.9988
0.9986
0.9984
0.9982
0.9980
22
23
24
25
26
0.9978
0.9976
0.9973
0.9971
0.9968
27
28
29
30
31
Density
0.9965
0.9962
0.9959
0.9956
0.9953
Example I: How to Calculate a Standard Deviation
You obtain the following measurements: 15.2654, 15.2657, 15.2658 and 15.2655. In the
following calculations, each individual measurement from above will be represented using the
symbol xi and the mean (the average of these values) will be given the symbol x .
s=
∑d
2
i
N −1
Σ means “the sum of”
di = xi - x
N = the number of measurements
x = 15.2656
xi
15.2654
15.2657
15.2658
15.2655
s=
di2
di (xi – x )
-0.0002
0.0001
0.0002
-0.0001
0.00000004
0.00000001
0.00000004
0.00000001
0.00000010 = Σ di2
0.00000010
= 0.000183 = 0.0002
4 −1
When you report a value, it is the mean (average) value that is reported along with the standard
deviation to show the precision of the measurements which contributed to the mean value.
Therefore, the value reported for this example would be 15.2656 ± 0.0002.
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Results
Part I
Using the Analytical Balance
Mass of the stoppered
flask (g)
____________ ____________ ____________ ____________
Mean mass (g) ____________
Calculation:
Using the Top Loader Balance
Mass of the stoppered
flask (g)
____________ ____________ ____________ ____________
Mean mass (g) ____________
Part II
Using the Pipet
Temperature (o C) __________
Density of water (g/mL) __________
Addition No.
Mass after
addition (g)
1
2
3
__________
__________
__________
__________
Mass before
addition (g)
__________
__________
__________
__________
Mass of water
in flask (g)
__________
__________
__________
__________
Volume of water
delivered each
time (mL)
__________
__________
__________
__________
Mean volume (mL) __________
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4
Calculations (Part II):
Part III
Determining the Density of an Object
Mass of the object (g) __________
Volume after adding object (mL) __________
Volume before adding object (mL) __________
Volume of object (mL) __________
Volume of object (cm3) __________
(using the equation V = hπr2 )
Diameter of object (cm) ____________
Radius of object (cm) __________
Height of object (cm) __________
Density of the object (g/mL) __________
Density of the object (g/cm3) ____________
Calculations:
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Questions
1 a. Calculate the standard deviation (look at example on page 5) for the measured mass
of the empty stoppered flask. (Pick the values where there is a greater difference
between the measurements.)
b. Based on your standard deviation from part a, report the mean value for the
average mass of the flask and give the precision of this value. (Ex. Your mean
value is 10.12, and your standard deviation is 3.0 x 10-2. You would report your
mean mass as 10.12 ± 0.03.)
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