Density: Connecting Mass and Volume
Students calculate and compare density to explain why equal-sized samples of different substances can have different masses.
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Mass and Volume Review
Mass and volume describe different properties of matter. Mass is the amount of matter in an object and is commonly measured in grams or kilograms. A balance measures mass. Volume is the amount of space an object occupies. Solid volume is often measured in cubic centimeters, while liquid volume is often measured in milliliters. One milliliter equals one cubic centimeter. Objects with the same volume do not always have the same mass because they may be made of different substances. For example, imagine two cubes that are each 2 centimeters on every side. Each cube has a volume of 8 cubic centimeters. If the wooden cube has a mass of 5 grams and the metal cube has a mass of 22 grams, the equal-sized metal cube contains more mass in the same amount of space.
Density as a Ratio
Density compares an object's mass with its volume. It tells how much mass is packed into each unit of volume. Calculate density by dividing mass by volume: density equals mass divided by volume. Common units include grams per cubic centimeter for solids and grams per milliliter for liquids. Suppose a metal sample has a mass of 5.4 grams and a volume of 2 cubic centimeters. Its density is 5.4 divided by 2, or 2.7 grams per cubic centimeter. This means each cubic centimeter of the metal has 2.7 grams of mass. A wood sample with the same 2-cubic-centimeter volume might have a mass of only 1.2 grams. Its density is 0.6 gram per cubic centimeter, so it is less dense than the metal.
Measuring Regular Objects
The volume of a regularly shaped object can be calculated from its dimensions. For a rectangular prism, multiply length by width by height. Measure each dimension with a metric ruler and record it in centimeters. For example, a metal block is 5 centimeters long, 3 centimeters wide, and 2 centimeters high. Its volume is 5 times 3 times 2, which equals 30 cubic centimeters. If a balance shows that the block's mass is 81 grams, its density is 81 divided by 30, or 2.7 grams per cubic centimeter. Keep units with every measurement and calculation. Measure from the ruler's zero mark, look straight at the scale, and record dimensions carefully. Even a small measurement error can change the calculated volume and density.
Finding Volume by Displacement
An irregular object, such as a rock, may not have dimensions that fit a simple volume formula. Its volume can be measured by water displacement. First, pour water into a graduated cylinder and read the bottom of the curved meniscus at eye level. Next, lower the object completely into the water without splashing. Subtract the initial water level from the final water level. For example, if the water begins at 50 milliliters and rises to 68 milliliters, the rock's volume is 18 milliliters. Because 1 milliliter equals 1 cubic centimeter, the rock's volume is also 18 cubic centimeters. If its mass is 45 grams, its density is 45 divided by 18, or 2.5 grams per cubic centimeter. Make sure no air bubbles cling to the submerged object.
Calculating and Comparing Density
To compare densities, measure each sample's mass and volume, divide mass by volume, and use the same units. Consider two equal-sized samples that each have a volume of 100 cubic centimeters. Sample A has a mass of 80 grams, so its density is 80 divided by 100, or 0.8 gram per cubic centimeter. Sample B has a mass of 270 grams, so its density is 2.7 grams per cubic centimeter. Sample B is denser because it has more mass in the same volume. Density is a characteristic property of a substance. A larger sample of the same pure substance usually has more mass and more volume, but the mass-to-volume ratio remains the same. When comparing results, check that measurements are accurate and that density answers include units such as grams per cubic centimeter.