Measuring Liquid Volume and Density

Liquid volume is measured with graduated glassware such as measuring cylinders, and density is the mass of a substance divided by its volume, calculated as density = mass ÷ volume. In brief: read the volume at the bottom of the meniscus with your eye level with the liquid surface; if 50.0 mL of a liquid has a mass of 39.5 g, its density is 0.790 g/mL, which matches ethanol.

Volume and density are two of the most frequent measurements in a chemistry lab. This article explains how to choose and read glassware, how to find the density of a liquid and of an irregular solid, gives a table of reference densities, works through several calculations, describes the history of Archimedes’ discovery and lists common reading errors.

Which glassware measures liquid volume?

For a single measurement of a volume, choose the smallest cylinder that can hold the volume, because it has finer divisions and gives a smaller error.

How do you read a meniscus?

1. Place the cylinder on a flat surface, or hold it vertically.
2. Bring your eyes to the same level as the liquid surface to avoid parallax error.
3. Water and most solutions curve downward, forming a concave meniscus. Read the bottom of the curve.
4. Mercury curves upward (convex), so you read the top of the curve.
5. Estimate one digit beyond the smallest division. If the divisions are 1 mL apart, you can estimate to 0.1 mL.

What is density and how is it measured?

Density (symbol ρ) is mass per unit volume: ρ = m ÷ V. The usual units are g/cm³ or g/mL for liquids and solids, and g/L or kg/m³ for gases. Because 1 mL equals 1 cm³, the two units are the same size. Density is an intensive property, so a drop of ethanol and a liter of it have the same density at the same temperature.

To measure the density of a liquid:

1. Weigh a dry, empty measuring cylinder.
2. Add a measured volume of liquid, and record the volume.
3. Weigh the cylinder with the liquid.
4. Subtract to find the mass of the liquid and divide by its volume.

Densities of common substances

How do you find the volume and density of an irregular solid?

Regular solids have volumes given by formulas, such as length × width × height for a block. For an irregular solid, use water displacement: record the starting volume of water in a cylinder, lower the solid in so that it is fully submerged, record the new volume and subtract. The solid must not dissolve or react with the water, and it must be fully covered. Float materials can be pushed under the surface with a thin wire.

Worked examples

1. Density of a liquid. An empty cylinder has a mass of 62.35 g. With 50.0 mL of a liquid, it has a mass of 101.85 g. The liquid has a mass of 101.85 − 62.35 = 39.50 g. Its density is 39.50 ÷ 50.0 = 0.790 g/mL, which is close to ethanol.
2. Irregular metal piece. The water level rises from 25.0 mL to 35.0 mL when a metal piece with a mass of 27.0 g is added. Volume = 35.0 − 25.0 = 10.0 mL. Density = 27.0 ÷ 10.0 = 2.70 g/cm³, so the metal is probably aluminum.
3. Finding mass from density. What is the mass of 250 mL of mercury? m = ρ × V = 13.5 × 250 = 3,375 g, or 3.38 kg. A glass of mercury is very heavy, which is why it is not handled casually.
4. Finding volume from mass. What volume does 100.0 g of glycerol occupy? V = m ÷ ρ = 100.0 ÷ 1.26 = 79.4 mL.
5. Will it float? Oil with ρ = 0.92 g/mL on water (0.998 g/mL): the oil is less dense, so it floats.

How does temperature affect density?

Most substances expand when heated, so their density falls. The density of water at 4 °C is 0.99997 g/mL, at 20 °C is 0.99820 g/mL and at 80 °C is 0.97182 g/mL. Because of this, precise volumetric glassware is calibrated at a specific temperature, usually 20 °C, and volumes of liquids should be measured at that temperature. Water is unusual, as its maximum density is at about 4 °C and not at its freezing point.

Who discovered the principle of density?

According to a story told by the Roman writer Vitruvius, Archimedes was asked to test whether a crown was pure gold. By measuring the volume of water displaced when the crown was immersed, and comparing it with that of an equal mass of gold, he could detect a lighter metal mixed in. The details of the story are uncertain, but the principle of volume measurement by displacement is real and still taught. The concept of density as an identifying property was developed in the 17th and 18th centuries.

Which mistakes are common?

Mistake 1: Reading the meniscus from above or below

Look at the level, not down or up at the liquid, to avoid parallax error.

Mistake 2: Using a beaker for accurate measurement

Beaker markings are only approximate. Use a graduated cylinder or better.

Mistake 3: Forgetting to subtract the mass of the container

The density needs the mass of the liquid alone.

Mistake 4: Ignoring trapped air bubbles on a submerged solid

Bubbles add to the displaced volume and make the volume appear larger. Tap gently to release them.