Measurement of Density
Description
Several measuring techniques are applied to determine the density of an object. The concept of density is explored. Archimedes' principle is introduced, and a Cartesian diver is demonstrated.
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Precautions
Do NOT drop the metal cylinders into the graduated cylinders. The glass graduated cylinders break easily.
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Procedure
- Part I-Direct Measure
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- Measure the diameter and length of the metal cylinder to the precision permitted by the measuring instrument.
- Determine the mass of a metal cylinder to the nearest 0.01g and record.
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- Part II-Volume by Archimedes' Principle
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- Suspend the metal cylinder from the hanger of the centigram balance with a thread. Record the mass of the metal cylinder to the nearest 0.01 g.
- Attach a platform support to the centigram balance. Place a 250-mL beaker which has been filled three-fourths full of water on the platform. Adjust the position of the platform support and the 250-mL beaker so that the metal cylinder suspended from the thread is completely submerged. Be sure that the metal cylinder does not touch the beaker.
- Record the mass of the cylinder suspended in the beaker of water to the nearest 0.01 g.
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- Part III-Volume by Water Displacement
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- Place about 25 mL of water in a 50-mL graduated cylinder. Record the volume of the water to the nearest 0.2 mL.
- Slide the object gently into the graduated cylinder without splashing any of the water. Record the volume of the water with the object to the nearest 0.2 mL.
- Part IV-Demonstration of Cartesian Diver. (Demonstration or experiment.)
- Fill a 2-L clear, colorless plastic soda bottle with tap water. Place 750 mL of tap water in a 1-L beaker. Place a medicine dropper in the beaker. Squeeze the rubber bulb to expel enough air such that the dropper floats, bulb-up with a vertical posture in the water, without sinking.
- Remove the dropper and place the dropper in the soda bottle. Cap the bottle. Squeeze. Observe the result.
- Account for the result.
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Handout
Name ___________________________ Class ________
Teacher__________________________
DoChem 011 Measurement of Density
Table I. Density by Direct Measurement
mass of cylinder (g) =
diameter of cylinder (cm) =
height of cylinder (cm) =
calculated volume of cylinder (cm3) =
calcuated density of cylinder (g/cm3) =
Table II. Density by Archimedes' Principle
- mass of cylinder in air =
- mass of cylinder in water =
- mass of water displaced by the cylinder =
- density of water =
- volume of water displaced =
- volume of cylinder =
- density of cylinder (g/cm3) =
Table III. Volume by Water Displacement
- volume reading of water plus cylinder =
- volume reading of water =
- volume of water displaced =
- volume of cylinder =
- mass of cylinder =
- density of cylinder =
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- Questions
- Calculate the volume of the metal cylinder from its measured diameter and height.
- Calculate the density of the cylinder from the mass determined in Part I and the volume calculated in Question 1. D = m/V.
- Determine the difference between the apparent mass of the metal cylinder in air and its apparent mass in water from Part II. Record this as the mass of water displaced.
- Assume that the density of water at room temperature is 1.00 g/mL. Calculate the volume of water displaced by the cylinder in Part II.
- Calculate the density of the metal cylinder from the data collected in Part II.
- Determine the volume of water displaced by the metal cylinder in Part III. This is accomplished by subtracting the volume of the water alone from the total volume of the water and the metal cylinder combined.
- Using the mass of the metal cylinder recorded in Part I, and the volume by water displacement from Question 3, calculate the density of the metal cylinder.
- The densities of several common metals are listed below. Compare your experimental density with these values. If possible, identify the metal with which the cylinder is made.
- Which method gave the most accurate value for the volume of the metal cylinder in this experiment. Explain.
- Which measurement limited the accuracy in each case?
- Osmium metal, the densest element, has a density of 22.5 g/mL; while hydrogen gas, the least dense element, has a density of 0.00009 g/mL (at 0°C and 760 torr). Calculate the volume that 1.0 g of each element would occupy.
- Explain how Archimedes' Principle could be used to determine the density of an aqueous solution.
Reference Data
| Element |
density, g/cm3 |
| Iron |
7.86 |
| Copper |
8.92 |
| Aluminum |
2.7 |
| Lead |
11.34 |
| Tin |
7.31 |
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Handout Makeup
Name ___________________________ Class ________
Teacher__________________________
DoChem 011 Measurement of Density
- Watch the movies and answer the questions using the data below.
Table I-Direct Measure
- Mass of cylinder = 16.21 g
- Diameter of cylinder = 0.9 cm
- Height of cylinder = 8.8 cm
- Volume of cylinder = 5.6 cm3
- Density of cylinder = 2.9 g/cm3
Table II-Volume by Archimedes' Principle
- Mass of cylinder in air = 16.20 g
- Mass of cylinder in water = 10.00 g
- Mass of water displaced by the cylinder = 6.20 g
- Density of water = 1.00 g/cm3
- Volume of water displaced by the cylinder = 6.20 cm3
- Volume of cylinder = 6.20 cm3
- Density of cylinder = 2.61 g/cm3
Table III-Volume by Water Displacement
- Final reading of water and cylinder = 31.2 mL
- Initial reading of water only = 25.0 mL
- Volume of water displaced = 6.2 mL
- Volume of cylinder = 6.2 mL
- Mass of cylinder = 16.21 g
- Density of cylinder = 2.6 g/mL
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- Questions
- Calculate the volume of the metal cylinder from its measured diameter and height.
- Calculate the density of the cylinder from the mass determined in Part I and the volume calculated in Question 1. D = m/V.
- Determine the difference between the apparent mass of the metal cylinder in air and its apparent mass in water from Part II. Record this as the mass of water displaced.
- Assume that the density of water at room temperature is 1.00 g/mL. Calculate the volume of water displaced by the cylinder in Part II.
- Calculate the density of the metal cylinder from the data collected in Part II.
- Determine the volume of water displaced by the metal cylinder in Part III. This is accomplished by subtracting the volume of the water alone from the total volume of the water and the metal cylinder combined.
- Using the mass of the metal cylinder recorded in Part I, and the volume by water displacement from Question 3, calculate the density of the metal cylinder.
- The densities of several common metals are listed on the following page. Compare your experimental density with these values. If possible, identify the metal with which the cylinder is made.
- Which method gave the most accurate value for the volume of the metal cylinder in this experiment. Explain.
- Which measurement limited the accuracy in each case?
- Osmium metal, the densest element, has a density of 22.5 g/mL; while hydrogen gas, the least dense element, has a density of 0.00009 g/mL (at 0 °C and 760 torr). Calculate the volume that 1.0 g of each element would occupy.
- Explain how Archimedes' Principle could be used to determine the density of an aqueous solution.
Reference Data
| Element |
density, g/cm3 |
| Iron |
7.86 |
| Copper |
8.92 |
| Aluminum |
2.7 |
| Lead |
11.34 |
| Tin |
7.31 |
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Teachers Guide
Purpose
To determine the density of a cylindrical solid.
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Materials
(per 10 students working in pairs)
- 10 cylindrical metal solid, 4-5 cm long
- 5 centigram balance
- 5 30-cm metric ruler read to 0.1-cm, or caliper
- 5 50-mL graduated cylinder
- 5 pieces of thread, each about 1 foot long
- 5 250-mL beaker
- 5 support stand, iron ring, watch glass
- 1 2-L colorless plastic soda bottle filled with water, and bottle screw-cap
- 1 dropping pipet (medicine dropper)
- 1 1-L beaker filled with water
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Lab Hints
- The metal cylinders may be made of metals such as copper, aluminum, or iron. The cylinders may be obtained from the physics teacher at your school. If they are not available from the physics teacher, purchase them at a local hardware store, or from scientific supply company.
- Consider placing a thin layer of paint on all of the cylinders to prevent them from being identified on the basis of color, luster, or oxidation. Each metal cylinder should be numbered.
- Most overhead beam balances have, as part of the pan hanger, hooks from which a specimen can be hung. If the balance lacks facilities for supporting a beaker of water, use a ring stand and ring. Many platform balances can be mounted on a vertical bar and specimens hung from a hook under the pan.
- There are two alternate methods for the performance of this experiment: 1) students may be assigned an unknown cylinder whose identity is determined by the calculation of its density; or 2) class data may be pooled to determine an accepted value for the density of a particular sample.
- The student should be urged to take special care to prevent the object being weighed in water from touching the beaker. Students may need to be coached in the determination of the volume of a cylinder from a measure of its diameter:
- V = πr2l = 0.25πd2l
- The method of volume determination may be discussed before or after the experiment has been performed.
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Time
Teacher preparation: 30 minutes
Class Time: 30 to 40 minutes
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Hazards
There are no unusual hazards in this experiment.
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Precautions
Provide for cleaning up spilled water. Caution students not to drop the metal cylinders into the graduated cylinders. The glass graduated cylinders break easily.
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Disposal
Save all materials for reuse.
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Presentation?
Presentation Question:
- What would happen if the water were replaced with concentrated salt water in this experiment?
- Using salt water would cause the weight to decrease still more in this experiment. Using a fluid less dense than water (vegetable oil, ethanol) would cause the weight to decrease less. The maximum weight would be observed in a vacuum. Air is not a massive fluid, so its effect is small (but measurable).
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Sample Data
Table I-Direct Measure
- Mass of cylinder = 16.21 g
- Diameter of cylinder = 0.9 cm
- Height of cylinder = 8.8 cm
- Volume of cylinder = 5.6 cm3
- Density of cylinder = 2.9 g/cm3
Table II-Volume by Archimedes' Principle
- Mass of cylinder in air = 16.20 g
- Mass of cylinder in water = 10.00 g
- Mass of water displaced by the cylinder = 6.20 g
- Density of water = 1.00 g/cm3
- Volume of water displaced by the cylinder = 6.20 cm3
- Volume of cylinder = 6.20 cm3
- Density of cylinder = 2.61 g/cm3
Table III-Volume by Water Displacement
- Final reading of water and cylinder = 31.2 mL
- Initial reading of water only = 25.0 mL
- Volume of water displaced = 6.2 mL
- Volume of cylinder = 6.2 mL
- Mass of cylinder = 16.21 g
- Density of cylinder = 2.6 g/mL
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Closure
- The volume of a solid that is fairly regular in form can be determined by measuring its linear dimensions and manipulating the dimensions in an appropriate manner. The volume of the metal cylinder is found by V=πr2l. However, measuring the dimensions of a solid of irregular shape could be very difficult. Archimedes developed a simple method for just such a determination. The volume of the liquid in which the solid is submerged is measured. The method is useful for cases in which the solid does not dissolve in the liquid. The solid is placed in the liquid and the volume is recorded. The increase in volume is equal to the volume of the solid itself. This method is known as measuring volume by displacement.
- V object = V final - V initial
- The mass of an object apparently depends on the medium in which it is weighed. This observation poses a dilemma since mass is an invariant property of matter. Mass determinations are usually made in the air. The air buoys up the object. The buoyancy effect of air is not a serious deduction to the apparent mass of an object unless the density is very low. The buoyancy of air is about one gram per liter of matter. This leads to an error of less than 0.1% for objects with a density greater than 1 g/cm3. However, an object whose mass is determined in water has a larger buoyancy factor. The density of water is approximately 1.0 g/cm3. The mass of an object determined in water will be significantly less than its apparent mass in air. The "true" mass of an object is determined by measuring its mass in a vacuum.
- An object will displace a volume of water equal to its own volume. The fluid in which an object is submerged changes the apparent mass of the object. The difference between the apparent mass of an object in air and water is equal to the mass of the fluid displaced.
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Closure?
Closure Questions:
- Calculate the volume of the metal cylinder from its measured diameter and height.
- Calculate the density of the cylinder from the mass determined in Part I and the volume calculated in Question 1. D = m/V.
- Determine the difference between the apparent mass of the metal cylinder in air and its apparent mass in water from Part II. Record this as the mass of water displaced.
- Assume that the density of water at room temperature is 1.00 g/mL. Calculate the volume of water displaced by the cylinder in Part II.
- Calculate the density of the metal cylinder from the data collected in Part II.
- Determine the volume of water displaced by the metal cylinder in Part III. This is accomplished by subtracting the volume of the water alone from the total volume of the water and the metal cylinder combined.
- Using the mass of the metal cylinder recorded in Part I, and the volume by water displacement from Question 3, calculate the density of the metal cylinder.
- The densities of several common metals are listed on the following page. Compare your experimental density with these values. If possible, identify the metal with which the cylinder is made.
- Which method gave the most accurate value for the volume of the metal cylinder in this experiment. Explain.
- Which measurement limited the accuracy in each case?
- Osmium metal, the densest element, has a density of 22.5 g/mL; while hydrogen gas, the least dense element, has a density of 0.00009 g/mL (at 0 °C and 760 torr). Calculate the volume that 1.0 g of each element would occupy.
- Explain how Archimedes' Principle could be used to determine the density of an aqueous solution.
Reference Data:
| Element |
density, g/cm3 |
| Iron |
7.86 |
| Copper |
8.92 |
| Aluminum |
2.7 |
| Lead |
11.34 |
| Tin |
7.31 |
Answers to Closure Questions:
- V = πr2h
- V = 5.6 cm3
- D = m/V
- D = 2.9 g/cm3
- m = mair - m water
- M = 6.20 g
- V = mD
- V = 6.20 cm3
- D = m/V
- D = 2.61 g/cm3
- V = V final - V initial
- V = 6.2 mL
- D = m/V
- D = 2.6 g/mL
- The metal has a density close to that of aluminum in the case of the sample data used here. Each student will respond according to their individual data.
- Determination of the volume by Archimedes' Principle produces a more accurate value for density in this case. The measures made have more precision in that part of the experiment.
- In each case, the measure of the volume limits the accuracy.
- Os 1.0 g (1 mL/22.5 g) = 4.4 x 10-2 mL
- H2 1.0 g (1 mL/0.00009 g) = 1 x 104 mL
- To find the density of an aqueous solution, measure the mass of a solid object in air; measure the mass of the same object in water; and measure the mass of the same object in the aqueous solution.
- D soln = ((mair - msoln)/(mair - m water) ) x D water
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Applications
- Archimedes' Principle may be used to determine the density of solutions.
- A very small dimension of a regularly shaped object may be determined using density and its other dimensions. For example, the thickness of a piece of aluminum foil could be determined from length, width, mass, and density.
- Archimedes' Principle leads to the concept of specific gravity. Specific gravity is the ratio of the mass of a sample compared to the mass of an equal volume of water.
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Computer Use
Students may enter the class' data directly into a worksheet of a spreadsheet computer program. See EXPT 134 for suggestions.
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Key Words
- density
- Archimedes' principle
- volume of a cylinder
- volume by displacement
- Cartesian diver
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