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Density Lab
Ed. Fall 2021
Names: Joanna Maciag, Teresa, Sarah
Group #:____________
Density & Statistics
Student outcomes:
By the end of this experiment, students will be able to:
● Estimate the volume of a liquid using a graduated cylinder
● Determine the mass of a substance using a balance
● Define density
● Calculate the average density for a solid or liquid based upon the substance’s mass and volume
● Calculate a percent error between experimental and literature values for a property
● Calculate a standard deviation between replicate measurements for values
● Define accuracy and precision
● Relate percent errors and standard deviations to precision and accuracy
Introduction:
Density:
Density is defined as the mass of a substance per given volume of substance, where the mass is the
amount of substance in terms of weight and volume is the amount of substance in terms of space
occupied. The density of a substance is calculated using equation 1 below:
𝑚𝑎𝑠𝑠
Equation 1: 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑣𝑜𝑙𝑢𝑚𝑒
The density of a substance can be experimentally determined by measuring the mass in grams (g) and
the volume in milliliters (mL) to calculate the density in units of grams/milliliter (g/mL). The mass of a
substance can be obtained by weighing a substance using a balance or scale. The volume of a substance
is obtained based upon the state (solid v. liquid) and shape of the substance. The volume of a liquid is
measured using a syringe or graduated cylinder. The volume of a regularly shaped object (cube, cylinder
etc.) can be simply measured using a ruler and volume calculated using the formula for volume for the
respective shape. The volume of an irregularly shaped solid can be measured by using volume
displacement. Volume displacement is the difference between the volume of water in a graduated
cylinder with the object being measured and the volume of the water in a graduated cylinder without
the object being measure. For example, if there is 15 mL of water in a graduated cylinder to start and a
glass marble is added causing the volume to increase to 18 mL, the volume of the marble is 3 mL.
Data Analysis, Accuracy and Precision:
When obtaining experimental data within the laboratory, the best experimental design includes taking
multiple measurements of the same variable to perform statistical calculations to provide measurable
insight into experimental success or failure. When considering statistics, the most basic of values to
obtain to determine success or failure would be averages, percent errors and standard deviations. The
mean or average (µ) of a data set is calculated by adding all of the values in the data set and dividing
them by the number of values. The standard deviation (σ) of a set of values determines how much the
individual trials vary from the average. When calculating standard deviation, the lower the value the
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closer the values are to one another whereas a higher standard deviation would indicate a large
variability in the measurements. The equation for standard deviation is seen in equation 2 below:
𝑁
∑
Equation 2: 𝜎 = √ 𝑖=1
(𝑥𝑖 −𝜇)2
𝑁
In equation 2 above, N is the number of values, xi is each value from the population and µ is the mean.
Lastly, percent error determines how much an experimentally calculated value differs from a known
literature value. The equation for percent error is seen in equation 3 below:
Equation 3: 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟 =
|𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑙𝑖𝑡𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒|
𝑙𝑖𝑡𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒
𝑥 100
Percent errors below 1% state that an experimentally calculated value is the same as the literature
value. Percent errors greater than 10% indicate a large difference between a known and experimental
value or a high degree of error.
When considering statistics, the values obtained can help determine if the experimental results are
accurate or precise. Accuracy refers to how close a measured value is to a known value, whereas
precision refers to how close a set of data values are to one another, or the ability to be reproducible.
When considering experimentation, results that are both accurate and precise show good technique.
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Pre Lab Questions:
1) What information do you need to solve for density?
The information needed solve for density is the mass of a substance and the volume of a
substance.
2) adapted from Harper College Virtual Chemistry Labs: Density (College, 2020)
The images below represent the data obtained to calculate the density of a metal bolt.
Figure 1: Mass and volume data for a metal bolt
Using the data for the bolt above, calculate the density for the bolt. (Show your work)
Using the data from the figure given the calculations we got are
Mass: 63.34g
Volume: 42mL
Density: m/v
D: 63.34g/ 42mL
3) Your group performs a lab to calculate the density of olive oil and obtains an average of 0.97
g/mL. You research literature values and discover the expected density of olive oil is 0.92 g/mL.
What is the percent error of your group’s experimental results?
Percent error= |0.97g/mL – 0.92g/mL| / 0.92g/mL x 100
Percent error= 5.43g/mL
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4) In your own words, briefly describe the steps to the scientific method.
First, we must make an observation and then we ask a question. After that, we gather
information and form a hypothesis. Then we test the hypothesis and make a conclusion. After
we’ve made the conclusion we report and evaluate.
Procedure:
Overview:
In this experiment you will be exploring density using the scientific method. In the first part of the
experiment, you will explore how density can be used to determine the identity of a substance. In this
section your group will create a hypothesis regarding the identity of an unknown liquid based upon
observations of the physical properties of the liquid. You will then determine the density of the
unknown liquid and percent error to determine if your hypothesis was correct or incorrect.
In the second part of this experiment you will explore how the size of an object affects density. Here you
will create a hypothesis regarding the relationship between density and the size of a metal rod. You will
then determine the average density of four different sized metal rods as well as the standard deviation
of the four densities. You will then use the data to determine if your hypothesis regarding how size
affects density is correct or incorrect.
Lastly you will explore how the statistical calculations of percent error and standard deviation relate to
accuracy and precision of measurements.
Part 1: How can we use density to determine the identity of a substance?
1. Obtain the test tube assigned to your group containing a ~5-10 mL volume of an unknown liquid.
Pour the unknown liquid in a clean & dry small beaker (30 or 50 mL beaker) from your group’s
drawer.
2. Using your sense of smell and sight, complete Table 1 below with your group’s observations. To
observe thickness you can tilt the test tube or use a disposable pipette to draw up a small volume and
empty the volume back into the test tube to see how easily it moves.
Table 1: Observations of Unknown Liquid
Unknown Number:
Color of Unknown Liquid: Clear
Scent of Unknown Liquid: Unknown
Is the liquid thick or thin? Thin
3. In the space provided for Hypothesis I, create a hypothesis (prediction) about the identity of the
unknown liquid based upon your observations recorded in Table 1. The possible identities of your
unknown liquids and their corresponding densities can be seen in Table 2 below.
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Table 2: Densities of Liquids
Liquid
Density (g/mL)
Hexane
Ethanol
Milk
Olive Oil
Ethylene Glycol
Water
0.659
0.791
1.028-1.035
0.918
1.109
0.998
Hypothesis I:
We predict that the unknown substance is Ethanol. We say this because the
substance is thin and it matches the number on the last graph and the
substance has no smell.
4. Using the thermometer in your drawer, measure the temperature of the room & record this value in
the proper location in Table 3.
5. Obtain a clean 10 mL syringe (ensure the graduation marks and volumes are legible). Using your
group’s assigned balance, weigh the empty syringe in grams to the thousandths decimal place (0.000
g). Record the dry weight of the syringe in Table 3.
6. Use the 10 mL syringe to draw up a volume (any volume is appropriate) of your unknown liquid.
Measure volume of the liquid to the nearest tenth decimal place (0.0 mL) and record in your Table 3
for Trial 1.
7. Weight the syringe now containing a volume of unknown liquid to the thousandths decimal place.
Record the mass of the syringe with the liquid in Table 3 for Trial 1.
8. Empty the syringe of unknown liquid back into your small beaker of liquid.
9. Repeat steps 6-7 with three more volumes of the same unknown liquid to complete Table 3 for trials
2, 3, & 4. (the volume doesn’t have to be the same for each trial)
Table 3: Raw Data
Temperature of the Room
Mass of Dry/Empty
syringe (g)
25.0c*
7.744g
Trial
Volume (mL0
1
6.8mL
Mass of syringe with
liquid (g)
14.702g
2
6.8mL
14.788g
3
6.8mL
14.750g
4
6.8mL
14.773g
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10. Dispose of the liquid in the Waste container labeled for Density Lab specifically for Chemistry 109. If
you can not identify the proper container, ask your instructor or TA. DO NOT dispose of this liquid in
the sinks.
11. Take the volumes from Table 3 and copy them into the Transformed Data Table 4 below.
12. Using the Mass of the Dry/Empty Syringe and the Mass of the syringe with the unknown liquid
column, calculate the mass of the volume of liquid inside the syringe for Trials 1-4. Record this in
Table 4 below.
13. Using the volumes and masses of the liquids, calculate the density of your unknown liquid for each of
the trials. Record your values in Table 4.
Table 4: Transformed Data of Unknown Liquid
Trial
Volume (mL)
1
2
3
4
6.8mL
6.8mL
6.8mL
6.8mL
Net Mass of Volume
of Liquid (g)
6.959g
7.044g
7.006g
7.029g
Density (g/mL)
1.0g/mL
1.0g/mL
1.0g/mL
1.0g/mL
14. Calculate the average density of the unknown liquid. Show work below.
Calculation for average density of the unknown liquid:
1.0+1.0+1.0+1.0=4,0
4.0/4= 1
15. Calculate the percent deviation between your average density (experimental value) and the literature
value for the density of your predicted liquid (density listed in Table 2). See Equation 3 from the
Introduction. Show work below.
Calculation for percent error:
1.05mL - 0.791g/mL / 0.791g/mL x 100 = 26.42g/mL
16. Form a conclusion regarding your hypothesis based upon your results. Your conclusion should state
whether your group accepts or rejects your Hypothesis I and the reasoning behind your group’s
decision. Your reasoning should reference the calculations.
Conclusion:
We rejected the hypothesis because the amount of density was larger than we thought.
17. Clean and return your original unknown liquid test tube and 10 mL syringe.
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Part 2: How does the size of an object affect density?
1. Obtain 4 metal rods from the instructor or TA. The 4 metal rods will be made of the same metal,
however they must be different sizes.
2. In the space provided for Hypothesis II, create a hypothesis about how you think the size of the
metal rod will affect the density of the metal rod.
Hypothesis II:
The bigger the metal rod is the density gets bigger as well.
3. Using the ruler found in your drawer, measure the length of each of the dry metal rods in cm to
the tenths place (0.0). Record the lengths in Table 5 below.
4. Using your group’s assigned balance, weigh each of the dry metal rods. Record their masses in
Table 5.
5. Obtain a 50mL graduated cylinder. If you do not have one in your drawer, obtain one from the
TA to borrow for the day.
6. Put ~20mL of water in the cylinder. Record the volume of water in the cylinder to the tenths
place (0.0) in Table 5.
7. Slide one of the metal rods into the graduated cylinder (don’t drop the rod, slide it down the side
of the cylinder).
8. Measure the new volume of water with the rod to the tenth decimal place (0.0 mL) and record in
your Table 5.
9. Gently pour the water out of the cylinder into the sink and remove the rod from the cylinder.
10. Repeat steps 6-9 for the remaining 3 metal rods.
Table 5: Raw Data for Metal Rods
Rod
Number
1
Length of
Rod (cm)
4.0cm
Mass of Rod
(g)
14.274g
Volume of water w/o Rod
(mL)
20mL
Volume of water with the
Rod (mL)
26.0mL
2
3.7cm
12.482g
20mL
25.0mL
3
3.1cm
10.735g
20mL
24.0mL
4
2.5cm
8.365g
20mL
23.0mL
11. Take the masses of the metal rods from Table 5 and rewrite them in the mass of rod column in
Table 6.
12. Using the volume of the water without the rod values and the volume of water with the rod
values, calculate the volume of the rods. Record these volumes in Table 6.
13. Using the volumes and masses in Table 6, calculate the density of each of the rods. Record your
values in Table 6.
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Table 6: Transformed Data for Metal Rod Densities
Rod
Number
1
2
3
4
Volume of rod
Mass of rod
Density
6.0mL
5.0mL
4.0mL
3.0mL
14.274g
14.482g
10.735g
8.365g
2.3g/mL
2.4g/mL
2.6g/mL
2.7g/mL
14. Calculate the average density of the metal rods. Show your work in the space provided.
Average Density Calculation:
2.3+2.4+2.6+2.7= 10/4
=2.5
15. Calculate the standard deviation of the densities calculated. Show your work in the space
provided.
Standard Deviation Calculation:
18. Form a conclusion regarding your hypothesis based upon your results. Your conclusion should state
whether your group accepts or rejects your Hypothesis II and the reasoning behind your group’s
decision. Your reasoning should reference the calculations.
Conclusion:
We reject our conclusion because as we said, the density gets bigger as the metal rods get bigger.
We said this because usually when you have an amount of liquid and add something bigger each
time then the liquid rises. But the hypothesis was rejected because the density got smaller as the
rods got bigger.
19. Dry the metal rods and return to the TA. If your group borrowed a 50 mL graduated cylinder, return
it to the TA.
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Post Lab Questions:
1) Consider the definition of accuracy. Which of the data analysis calculations performed would be
best to determine if your results obtained are accurate, standard deviation or percent error?
Explain.
With knowing the definition of accuracy, the percent error would be the right thing to get the
results. Percent error involves less factors to input. The literature value is also almost always
given in the question. For standard deviation, this is a more complex formula. If you put one
thing wrong then the whole answer will be incorrect.
2) According to your answer to post lab question 1 and the corresponding results, were your
result(s) accurate? Explain.
The results were not accurate for the rods since they all had different density values. For the
liquid in part one, the results were accurate because the density values were close to the known
and were consistent throughout.
3) Consider the definition of precision. Which of the data analysis calculations performed would be
best to determine if you were precise, standard deviation or percent error? Explain.
In table 6, the results of the rod density and volume show precision since they are not exact but,
close enough of an amount. For example the average density was 2.5g/mL while rod #1 has a
density of 2.3g/mL. These values are not exact but they are close to one another.
4) According to your answer to post lab question 3 and the results corresponding to your choice,
was your group precise? Explain.
Our group was precise since the average density for the rods were not the exact amount for
each rod but they were close in value.
5) Provide a reason for why it is critical for a nurse to be both accurate and precise in providing
medication dosages.
Accuracy is important in nursing when giving medical dosages because they need to ensure the
right amount is given to the patient. Precision is important in medical dosages to be aware of
certain factors that may affect the patient through a medical dosage.
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6) Provide an example of how a nurse can be accurate with dosages, but not precise.
The nurse can be accurate by measuring the dosages exactly to the known values of dosage
amount.
7) Provide an example of how a nurse can be precise with dosages, but not accurate.
For precision, the nurse can look at the data values for a patient and see how close they are to
one another in order to determine the correct amount .
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