3: LAB 3 - EXPLORING DENSITY
- Page ID
- 506131
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The purpose of this experiment is to:
-
Determine the density of water.
-
Determine the density of an unknown liquid and infer its identity from a table of listed densities.
-
Calculate the densities of regularly shaped and irregularly shaped solids.
INTRODUCTION
Density is defined as the amount of material present in a given volume. Every substance has a unique density value at a certain temperature, regardless of the amount of material present. (This is known as an intensive property.) For example, 25.0 mL and 50.0 mL of water should have a 1.00 g/mL density at room temperature because the mass-to-volume ratio is the same. Due to this nature, density can be used to infer the identity of an unknown substance.
In part of this activity, you will learn to experimentally determine water density. You will repeat the procedure with an unknown liquid and be asked to infer the unknown liquid’s identity using a table of density values. Procedures to calculate the density of regularly and irregularly shaped solids will also be explored, providing a comprehensive understanding of density.
5.0 mL of water was added to a graduated cylinder with a mass of 20.175 g. The combined mass of the graduated cylinder and water was 25.180 g. Using this information, determine the experimental density of water.
Solution
To find the mass of water, we subtract the mass of the empty graduated cylinder from the combined mass of the graduated cylinder and the water, as shown below:
Mass of water = 25.180 g - 20.175 g = 5.005 g
The density can be found by dividing the mass by the volume:
Density = 
= 
= 1.0 
Note: According to rules for multiplication and division, we round the answer to two significant digits because the measurement with the fewest significant digits (5.0 mL) has two significant digits.
Using different volumes of water, experimental densities were found to be 0.98 , 0.99 , and 0.99 
. Calculate the average density and percent error.
Solution
To find the average, we add up each value and divide the sum by the total number.
Average Density = 
= 0.99
The percent error can be calculated using the following equation:
Percent Error = 
x 100
Where E is the experimental average density and T is the theoretical density value of water. This is an absolute value, meaning that even if the answer is negative, it is recorded as a positive value.
Using the average shown above and the true density of water, which is 1.0 g/mL, and multiplying the answer by 100, the percent error can be calculated as:
Percent Error = 
x 100 = 0.01 x 100 =1%
The smaller the percent error, the closer the experimental value is to the true value.
A rectangular block having a mass of 45.250 g was shown to have a length of 2.75 cm, a width of 3.50 cm, and a height of 1.25 cm. Using this information, determine the density.
Solution
First, we need to find the volume of the rectangular block:
Volume = (2.75 cm) x (3.50 cm) x (1.25 cm) = 12.0 cm3
To find the density, we divide the mass by the volume, as follows:
Density = 
= 3.77 
A rubber stopper weighing 10.130 g was added to 30.0 mL of water in a 100-mL graduated cylinder, raising the cylinder's volume to 36.5 mL. Using this information, calculate the density of the rubber stopper.
Solution
First, find the volume of the rubber stopper.
36.5 mL - 30.0 mL = 6.5 mL
To find the density, we will divide the mass by volume.
Density = 
= 1.6 
(or 1.6 
)
- Wear chemical splash goggles throughout the experiment.
- Gloves are provided if you wish to wear them.
- Dispose of all chemicals in the appropriate waste container (as indicated during the experimental procedure).
- Be sure all glassware is clean and all equipment is returned to its proper place.
- Clean the lab benches and check the laminated sheets to ensure all equipment is in your lab drawer before leaving the lab.
- Remember, safety is paramount in the laboratory. Always wash your hands immediately upon leaving the lab to ensure you don't carry any chemicals.
EQUIPMENT *AND CHEMICALS NEEDED
Milligram balance
10 mL graduated cylinder
100 mL graduated cylinder
Centimeter ruler
Rectangular block
Rubber stopper
Deionized water
Cyclohexane
Amyl alcohol
Unknown liquid
* Images of equipment needed in this lab are in the appendix (the equipment may differ slightly or be subject to changes; follow your instructor’s directions).
EXPERIMENTAL PROCEDURE
Part A: Sink or Float.
1. Add 2.0 mL of water and 2.0 mL of cyclohexane to a 10-mL graduated cylinder. Record your observations in the data sheet. Based on the table of density values (see part C), determine which liquid forms the top layer and which forms the bottom layer. Pour the contents of the graduated cylinder into the non-halogenated waste container. Wash and dry the graduated cylinder before moving on to step 2.
2. Add 2.0 mL of water and 2.0 mL of amyl alcohol to a 10-mL graduated cylinder. Record your observations in the data sheet. Based on the table of density values (see part C), determine which liquid forms the top layer and which forms the bottom layer. Pour the contents of the graduated cylinder into the non-halogenated waste container. Wash and dry the graduated cylinder before moving on to part B.
Part B: Density of Water
1. Using a milligram balance, determine the mass of an empty 10-mL graduated cylinder. Record this value in each of the three trials in the data table. (Remember, when recording mass from a milligram balance, write down the exact number being read by the balance.)
2. Add between 1.0 mL and 10.0 mL of deionized water to the graduated cylinder and write the exact volume of water used in trial one on the data sheet. (Remember to record volume from a graduated cylinder to the tenth decimal point.)
3. Obtain the combined mass of the graduated cylinder and the water. By subtracting the mass of the empty graduated cylinder from the combined mass, you can find the added mass of water. Record these values in trial 1 of the data sheet.
4. Calculate the density of water by dividing the mass by volume. Record your density value to 2 or 3 significant digits, depending on the amount of water you added. Write this value under trial 1 of the data sheet.
5. Repeat steps 2 - 4 two more times, using a different volume of water in each trial.
6. Calculate the average density of water by adding up the densities from the three trials and dividing that value by 3.
7. Calculate the percent error using the following formula: Percent Error = 
x 100
where E is the experimental average density calculated in step 6, and T is the theoretical density value of water. This is multiplied by 100 to get a percent. This is an absolute value, meaning that even if the answer is negative, it is recorded as a positive value.
Part C: Density of an Unknown Liquid
Liquid |
Density |
|---|---|
|
Water |
1.00 g/mL |
|
Methanol |
0.791 g/mL |
|
Ethanol |
0.789 g/mL |
|
Isopropyl alcohol |
0.786 g/mL |
|
Amyl alcohol |
0.805 g/mL |
|
Cyclohexane |
0.779 g/mL |
|
Methylene chloride |
1.33 g/mL |
Repeat part B (steps 1-6) using the unknown liquid. Be sure the graduated cylinder is completely dry before beginning. After each trial, pour the contents of the graduated cylinder into the non-halogenated waste container. Then, based on your average density and the densities in the table below, provide a possible identity for the unknown liquid.
Part D: Density of a Rectangular Block
1. Using a milligram balance, obtain the mass of a rectangular block. Be sure to record the block color used in the data table.
2. Using a centimeter ruler, measure the rectangular block's length, width, and height. Record your values to the hundredth of a decimal point.
3. Calculate the volume of the rectangular block to the appropriate number of significant digits using the following formula:
V = (length) x (width) x (height)
The volume will be expressed in units of cm3. (Note: 1 cm3 = 1 mL)
4. To find the density of the rectangular block, divide the mass by volume.
Part E: Density of a Rubber Stopper
1. Obtain the mass of a rubber stopper. Record the mass of both trials in the data table.
2. Fill a 100 mL graduated cylinder with 50.0 mL of water, and record this as the initial volume in trial 1.
3. Carefully add the rubber stopper to the water in the cylinder (avoid spilling out any water when the stopper is added). Record the new volume of water in the cylinder as the final volume in trial 1.
4. By subtracting the initial volume of water from the final volume of water, we can find the volume of the rubber stopper. (This is an application of Archimedes' Principle, which states that an object will displace a volume of water equal to its volume. We can use this principle to determine the volume of an irregularly shaped object, such as a rubber stopper.) Record the volume of the rubber stopper in trial 1.
5. To find the density of the rubber stopper, divide the mass by the volume, and record this value in trial 1 of the data table.
6. Repeat steps 2-5 using a different initial volume of water.
7. Calculate the average density of the rubber stopper.
PRE-LAB QUESTIONS
Name:____________________________________
- Explain how density can be used to infer the identity of an unknown.
- An unknown liquid has a mass of 10.750 g and a volume of 11.5 mL. Calculate the density.
- A rectangular block has a mass of 60.001 g. Using a centimeter ruler, the dimensions were determined as follows:
length = 2.30 cm
width = 5.60 cm
height = 1.11 cm
Using this information, determine the density of the rectangular block.
- How can density be used to explain why solids float or sink when placed in liquids?
DATA AND OBSERVATIONS
Name: _________________________Lab Partner(s): ______________________________
Part A: Sink or Float.
1. When water and cyclohexane were mixed, which liquid formed the top layer?
2. When water and amyl alcohol were mixed, which liquid formed the top layer?
Part B: Density of Water
Trial 1 |
Trial 2 |
Trial 3 |
|
|---|---|---|---|
|
Mass of Empty Graduated Cylinder |
|||
|
Mass of Graduated Cylinder and Water |
|||
|
Mass of Water |
|||
|
Volume of Water |
|||
|
Density of Water |
Show calculations for the density of water for each trial:
Trial 1:
Trial 2:
Trial 3:
Average density of water (show calculation):
Percent error (show calculation):
Part C: Density of an Unknown Liquid
Unknown Liquid Number or Letter =
Trial 1 |
Trial 2 |
Trial 3 |
|
|---|---|---|---|
|
Mass of Empty Graduated Cylinder |
|||
|
Mass of Graduated Cylinder and Unknown |
|||
|
Mass of Unknown |
|||
|
Volume of Unknown |
|||
|
Density of Unknown |
Show calculations for the density of the unknown liquid for each trial:
Trial 1:
Trial 2:
Trial 3:
Average density of unknown liquid (show calculations):
Possible identity of unknown liquid (from table):
Part D: Density of a Rectangular Block
Unknown rectangular block Number or Letter:
Color of Block:
Mass of rectangular block =
Length of rectangular block =
Width of rectangular block =
Height of rectangular block =
Volume of rectangular block (show calculations):
Density of rectangular block (show calculations):
Part E: Density of a Rubber Stopper
Trial 1 |
Trial 2 |
|
|---|---|---|
|
Mass of rubber stopper |
||
|
Initial volume of water |
||
|
Final volume of water |
||
|
Volume of rubber stopper |
||
|
Density of rubber stopper |
Show calculations for the density of the rubber stopper for each trial:
Trial 1:
Trial 2:
Average density of rubber stopper (show calculations):
POST LAB QUESTIONS
- When 2.0 mL of water and 2.0 mL of an unknown liquid were added to a 10-mL graduated cylinder, water was shown to form the top layer. Using the table of densities in part C of the experiment, propose an identity for the unknown liquid.
- List three potential sources of error for part B (density of water) and part C (density of unknown liquid) of this experiment.
- In addition to density, what other properties could have been used to support the identity of the unknown liquid?
- You are given a rectangular block that someone insists is gold. The block has a mass of 74.376 g and the following dimensions:
length = 1.50 cm; width = 2.75 cm; height = 2.01 cm
Part A: What is the density of the rectangular block?
Part B: Based on the density, could the block be gold? If not, what could it be? (Note: You will need to search for the density of gold.)
- A rectangular sheet of aluminum foil, having a mass of 0.250 g, has a length of 5.75 cm and a width of 8.20 cm. If the density of aluminum is 2.70 g/cm3, find the aluminum foil's height (or thickness).
Please click here to access the Pre-Lab, Data Tables, and Post-Lab in Word or PDF format. Complete them and upload according to your instructor's instructions.