Science Focus Topic 6 Notes: Density | Print |

When we talk about density, it's usually mass density we're referring to. The mass density of an object is simply it's mass divided by it's volume.
Density depends on the weight of the individual atoms and molecules making up the object, and how much space there is between them. Density also depends on whether the object is solid, filled with airpockets, or something in between.

Densities are often given in terms of specific gravity. Specific gravity of a substance is defined as the ratio of the mass of a given volume of substance, at a certain temperature, to the mass of an equal volume of water at the same temperature.The specific gravity of an object or a material is the ratio of its density to the density of water at 4' C (this temperature is used because this is the temperature at which water is most dense). Very dense substances such as lead and gold have densities 10 - 20 times larger, whereas gases, which are less dense, have densities around 1 kg / m3, or about 1/1000 of water. Gold has a specific gravity of 19.3, aluminum 2.7, and mercury 13.6. These values are at standard temperature and pressure; objects will change size, and therefore density, in response to a change in temperature or pressure.

Density is the mass of a substance divided by its volume. This changes as temperature changes, therefore, any stated density should be accompanied by the appropriate units in which it was determined, together with the temperature at which it was determined.

Key Concepts to be covered:

  • Predict changes in liquid density that results from temperature changes and from change in concentration.
  • Predict changes in buoyant force that result from changes in fluid density.
  • Density is the amount of mass of a certain substance. p. 80
  • When comparing the 'heaviness' of substances, the masses of equal volumes of those substances are needed. p. 80
  • As density increases, buoyant force increases. p. 80
  • Density can be affected by heat.
  • Most fluids increase density as temperature decreases, except for water, which reaches its maximum density at 4oC p. 85

In terms of marine fuel quality, density is a very important characteristic. When used with viscosity the density is useful to predict the ignition quality of the fuel.

Measurement of Density

There are physical characteristics of a substance that help identify the substance. One of these characteristics is density. Density (whose symbol is the lowercase letter d) is defined as mass per unit volume. Density is calculated by dividing the mass of an object by its volume. This is shown in equation form, as follows:

Density = mass/volume

(Note the difference in units in the formulas of the density of a solid and liquid.)
The unit for cubic centimeters is cm3
For milliliters is mL.
solids: d = grams/cubic centimeters
liquids: d = grams/milliliters
(Table 2-5 p. Approximate Densities of Common Matcrials)

After measuring the mass of a regularly shaped object, use a formula to determine its volume. For example, to obtain the volume of a rectangular solid, multiply the length by the width by the height. (Volume = Length x Width x Height)

One way to determine the volume of an irregular object is to measure its mass in air and then in water, subtract the second measurement from the first, and divide by the density of water.

Another way to determine the volume of an irregularly shaped object is to submerge the object in a full container of water. The volume of the object equals the volume of water that overflows, (ie. that it displaces)

To determine the volume of an object that floats, first attach a metal sinker to the object.
Next, submerge the metal sinker and measure the over-flow.
Then submerge the object and measure the total overflow.
The volume of the object equals the difference between the measurements.

Density Calculations (Memory Method)

This simple equation will help you figure out how to solve density problems:


Simply cover up whichever value you need to calculate and the other two are shown in their proper placement, be it to multiply or to divide.

For example: cover up the M. This leaves you with d/V (ignore the fact that it is in the de-nominator). Density times volume will give you mass. You can also check it out by way of the units: (g / cm3) x cm3 cancels out the volume unit leaving grams, the desired unit for mass.

Practice Calculation Problems:

1) A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?

2) Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder weighs 306.0 g. From this information, calculate the density of mercury.

3) What is the weight of the ethyl alcohol that exactly fills a 200.0 mL container? The density of ethyl alcohol is 0.789 g/mL.

4) A rectangular block of copper metal weighs 1896 g. The dimensions of the block are 8.4 cm by 5.5 an by 4.6 cm. From this data, what is the density of copper?

5) A flask that weighs 345.8 g is filled with 225 mL of carbon tetrachloride. The weight of the flask and carbon tetrachloride is found to be 703.55 g. From this information, calculate the density of carbon tetrachloride.

6) Calculate the density of sulfuric acid if 35.4 mL of the acid weighs 65.14 g.

7) Find the mass of 250.0 mL of benzene. The density of benzene is 0.8765 g/mL.

8) A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weighs 1587 g. Front this inforination, calculate the density of lead.

9) 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49. 10 mL mark, From this information, calculate the density of iron.

10) What volume of silver metal will weigh exactly 2500.0 g. The density of silver is 10.5 g/CM3.

Answers to the Practice Density Problems


A hydrometer is a device that uses buoyancy to measure density directly p. 82 ... Activity 2-1 and 2-2

Hydrometers are calibrated in g/ml, by making marks that indicate the levels at which the instrument floats in different fluids. p.83

The higher the hydrometer floats, the higher the density of the liquid.

A liquid can exert a buoyant force making objects (solids, liquids or gases) float, p. 14 Activities 2-6/2-7 /2-8

Density depends, in part, on the concentration of the solution (how much solute is dissolved in a certain solvent) the more concentrated the solution. the more dense it is, Pages 789 819 82,, 85

Ships can float because they contain large volume of air. The overall density of the ship is less dense than water, so it floats.

Archimedes' Principle
An object that is partly or completely submerged in a fluid
will experience a buoyant force
equal to the weight of the fluid the object displaces.

According to legend, it is said that Archimedes, a Greek inventor, who lived in the third century, discovered his principle after noticing that his bath overflowed when he got into it. He ran through the streets naked, shouting "Eureka!" ("I've got it!"). With this principle, he helped to prove that the King's goldsmith had tried to cheat him by putting silver into a gold crown. Archimedes also made discoveries in hydrostatics (science of stationary fluids), geometry, and mechanics (science of machines).

Practical Applications

The buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. p. 82

Using a hydrometer to measure density directly is important in industrics such as plastics.

Making candy

Oil Refining

Hot-Air Balloons p. 83