Chapter 1. Analysis of Density

Experiment 2
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Safety Precautions

  • Chemical splash goggles, gloves, and apron must be worn at all times.

Materials List

  • metals: copper, brass, aluminum
  • polyvinyl chloride (PVC) and Pyrex glass

Objectives

After completing this project, you will be able to:

  • calculate the density of a substance from measurements of its mass and volume

Introduction

Buoyancy and Density

There are a number of methods for determining a material’s density. The most widely applicable method takes advantage of buoyancy. According to the principle of buoyancy, any object immersed in water is pushed upward (“buoyed”) by a force equal to the weight of the water displaced by the object. Consequently, if a steel ball with a volume of one gallon is suspended by a wire and lowered into a tank of water, the ball will be buoyed by a force equal to the weight of one gallon of water. If you were holding the wire with your hands, you would feel that the ball was less heavy when suspended in the water because of the buoying force. This is also the reason why it is easier to lift a person in a pool of water than in the air.

Since a body of water pushes upward on an immersed object, there must be an equal force pushing down on the water. (Remember equal and opposite forces in physics.) Indeed, if you place a container of water on an electronic balance and lower a massive object into the water, you will find that the apparent mass of the water increases. The mass increase will equal the mass of water displaced by the object. Knowing the mass increase, you could determine the volume of the object also, using the density of water. Knowing the volume of the object and the object’s mass, you can calculate the object’s density.

For example, one way to estimate the percent fat in a person’s body is to measure the person’s average density using buoyancy and then use this average density in the Brozek formula.1 To do so, the person is suspended above a tub of water by a machine that measures their weight. The weight is determined when the body is suspended in air and when it is fully submerged. Consider a person whose mass (by weighing) is 64.05 kg in air and 2.84 kg in water. The mass of water displaced by the body is:

and the apparent mass of the tub of water increased by 61.21 kg, the mass of displaced water, when the body was submerged. The volume of the displaced water can be found using the density of water [0.9982 g/mL or 0.9982 kg/L at 20°C]

The volume of the person’s body must have been 61.32 L. To determine the person’s average density (d), simply divide their mass (in air) by their volume (remember d = m/V).

Introduction of this average density into the Brozek formula gives a rough estimate of the person’s percent fat.

Physically fit females and males typically have percent body fat in the ranges 21–24% and 14–17%, respectively. Thus, a percent body fat value of 23% indicates either a physically fit female or a male of average fitness.

1R.W. Johnson. (1996) Fitting Percentage of Body Fat to Simple Body Measurements. J. Stat. Ed. 4 (1) http://www.amstat.org/publications/jse/v4n1/datasets.johnson.html (accessed Sept. 9, 2009).

Procedure: Density Determinations

  1. Have your laboratory notebook preliminary outline approved by your teaching assistant.
  2. Work in pairs.
  3. Obtain a sample of one of the materials listed in Table 2-1 (see Data Report Sheet).
  4. Bring into the weighing room one of the materials, a thin piece of wire, and a 250 mL beaker containing about 100 mL of tap water.
  5. Place the beaker on an electronic balance. Tare the reading to zero.
  6. Suspending the material from a piece of thin wire, lower it into the water until it is completely submerged, but not touching the bottom of the beaker. You want to submerge as little of the wire as possible. Some have found bending the wire into a small hook aids this effort. The mass reading now corresponds to the mass of water displaced by the material. Record this value in Table 2-1.
  7. Allow the material to rest on the bottom of the beaker and release the wire. The mass reading is now the mass of your sample. Record this value in Table 2-1.
  8. Return to your lab bench, pour out the water, and dry the beaker, wire, and sample.
  9. Repeat Steps 1–6 with each of the other materials listed in Table 2-1.
  10. Calculate the volume of each sample using the mass of displaced water and the density of water at 20°C (0.9982 g/mL). Fill your calculated values into Table 2-1.
  11. Calculate the density of each material and fill in your calculated values in Table 2-1.
  12. Have your teaching assistant verify our completion of this experiment by signing the data report sheet. Rip off and hand in the data report sheet for grading.