Density and Pressure » Practical: Measuring Density

The plan: measure mass, measure volume

This is a practical you need to know for the exam. You may not have a laboratory at home, so this lesson describes each method step by step. Learn the steps well enough to write them out yourself.

The idea is always the same. You measure the mass directly, you measure the volume directly, then you use density = mass ÷ volume from the lesson Density. The mass is the easy part: it always comes from a balance. Only the way you find the volume changes.

Key terms:

• Balance: electronic scales with a flat pan on top. You place the object on the pan and read its mass in grams from the screen.
• Measuring cylinder: a tall, narrow container with a volume scale marked up its side, usually in cm³.
• Meniscus: the curved surface of a liquid in a narrow container. Water curves down in the middle.
• Callipers: an instrument with two jaws that close on an object to measure its length more finely than a ruler can.
• Displacement: pushing water out of the way. An object under water displaces a volume of water equal to its own volume.
• Resolution: the smallest change that an instrument can show.

Method 1: a regular solid

A regular solid has a shape with a volume you can calculate, such as a cuboid.

1. Check that the balance reads zero with nothing on it. Place the block on the balance and record its mass.
2. Measure the length, width and height of the block with a ruler. For a small block use callipers.
3. Measure each side in two or three different places and work out a mean, in case the block is not perfectly even.
4. Calculate the volume: length × width × height.
5. Calculate the density: mass ÷ volume.

Method 2: a liquid

You cannot put a liquid straight onto a balance, so you weigh it inside a measuring cylinder and take away the mass of the cylinder.

1. Place the empty, dry measuring cylinder on the balance. Record its mass.
2. Pour in some of the liquid. Stand the cylinder on a flat bench.
3. Read the volume. Put your eye level with the liquid surface and read the scale at the bottom of the meniscus.
4. Place the cylinder and liquid on the balance. Record the total mass.
5. Mass of liquid = total mass − mass of empty cylinder.
6. Calculate the density: mass of liquid ÷ volume of liquid.

Method 3: an irregular solid

A pebble has no length, width or height to measure. Instead you find its volume by displacement of water. Always measure the mass first, while the object is dry. A wet object has water clinging to it, so its mass reading would be too large.

Using a measuring cylinder:

1. Place the dry object on the balance and record its mass.
2. Part fill a measuring cylinder with water and record the volume.
3. Tie the object to a thin thread and lower it gently until it is completely under water.
4. Record the new volume.
5. Volume of object = second reading − first reading.
6. Calculate the density: mass ÷ volume.

Using a displacement can: this is a can with a spout near the top. It is useful when the object is too big to fit inside a measuring cylinder.

1. Place the dry object on the balance and record its mass.
2. Fill the can until water runs out of the spout, then wait until the dripping stops.
3. Put an empty measuring cylinder under the spout.
4. Lower the object in gently on a thread until it is completely under water.
5. When the dripping stops, read the volume of water in the measuring cylinder. This equals the volume of the object.
6. Calculate the density: mass ÷ volume.

Results, repeats and the calculation

Draw the results table before you start, with a heading and a unit for every column. Here are the results for a pebble of mass 46.8 g. The student dried the pebble and repeated the volume measurement three times.

Try	Water level at the start in cm3	Water level with the pebble in cm3	Volume of pebble in cm3
1	50	68	18
2	50	69	19
3	50	67	17

Repeating shows up any reading that does not fit, and the mean is closer to the true value than a single reading is likely to be. For a liquid, you can repeat with different volumes. The density should come out the same each time.

Resolution and sources of error

No measurement is perfect. Each instrument can only show changes down to its resolution, so choose the instrument with the finest resolution that suits the job.

Instrument	Typical resolution
Ruler	1 mm
Callipers	0.1 mm
Balance	0.1 g or 0.01 g
100 cm3 measuring cylinder	1 cm3

Resolution matters most when the quantity is small. A volume of 4 cm³ read on a scale with 1 cm³ divisions could easily be wrong by a large fraction. To improve this, use the narrowest measuring cylinder the object fits into, because its scale divisions are smaller.

Working safely

• Wipe up spilled water or oil straight away, so that nobody slips.
• Glass measuring cylinders are tall and fall over easily. Keep them away from the edge of the bench, and do not pick up broken glass with bare hands.
• Lower solids in on a thread. A dropped metal block or stone can crack the glass or land on your foot.

Exam-style question

A student wants to find the density of a small brass key. The key has an irregular shape.

(a) Describe how the student should measure the mass and the volume of the key. [5 marks]

(b) The mass of the key is 33.6 g. The water level in the measuring cylinder rises from 30 cm³ to 34 cm³ when the key is added. Calculate the density of the key. Give the unit. [3 marks]

(c) The measuring cylinder has a resolution of 1 cm³. Suggest one way the student could measure the volume more accurately using the same measuring cylinder and other identical keys. Give a reason for your answer. [2 marks]