Required Practical 1: Measuring Density

Section 1 of 9Principle and apparatus

Density

Density mass ÷ volume, so two measurements are needed — the mass m and the volume V of the sample.

The method used to find the volume depends on whether the sample is a regular solid, an irregular solid or a liquid.

Apparatus and resolution:

• 30 cm ruler — measures lengths up to 30 cm with a resolution of 1 mm.
• Vernier callipers — measure lengths up to about 15 cm with a resolution of 0.1 mm.
• Micrometer — measures lengths up to about 3 cm with a resolution of 0.01 mm.
• Digital balance — measures mass with a resolution of 0.01 g.
• Eureka (displacement) can and measuring cylinders — measure volumes of irregular solids and liquids.

Section 2 of 9Regular solid

1

Place the object on a digital balance and record its mass.

2

Measure its dimensions (length, width, height or radius) with a ruler, Vernier callipers or a micrometer, chosen to suit its size.

3

Repeat the measurements at several places and take an average.

4

Calculate the volume from the dimensions: cuboid V = length × width × height, cylinder V = πr²h (r is half the diameter), sphere V = 4/3 πr³.

5

Calculate the density using ρ = m/V.

Section 3 of 9Irregular solid by displacement

1

Find the mass of the object on a balance.

2

Fill a eureka can with water until it is just below the spout and place an empty measuring cylinder under the spout.

3

Lower the object carefully into the can so that it is fully submerged and no water splashes.

4

Measure the volume of displaced water in the measuring cylinder; this equals the volume of the object.

5

Repeat, average, then calculate ρ = m/V.

Alternative

• Alternative place the object in a measuring cylinder containing a known volume of water and measure the rise in level.
• Volume of the object = final reading − initial reading.

A floating object must be pushed under with a thin rod, or a heavier object attached, so that it is fully submerged.

Section 4 of 9Liquid

1

Place an empty measuring cylinder on a digital balance and record its mass (or press tare to zero it).

2

Pour in the liquid and read its volume at the bottom of the meniscus with the eye level with the liquid.

3

Record the new mass of the cylinder with the liquid.

4

Mass of liquid = mass of cylinder with liquid − mass of empty cylinder.

5

Repeat, average, then calculate ρ = m/V.

• A graph of mass against volume for different volumes is a straight line through the origin and its gradient is the density.

Section 5 of 9Sources of error and improvements

Sources of error and improvements

Systematic error

• Systematic error a balance with a zero error gives all masses too high or too low.
• Zero the balance before every measurement, including after removing the cylinder when measuring a liquid.

Random error

• Random error the main cause is the measurement of length.
• Take repeat readings and calculate an average.

Air bubbles on a solid in water make the measured volume too large.

A meniscus read with the eye above or below the level gives a parallax error.

Wet surfaces add to the measured mass.

Dropping the object into the can causes splashing and an incorrect volume.

A larger sample, a narrower measuring cylinder and a more sensitive balance improve reliability.

Section 6 of 9Safety

Glassware

• Glassware handle measuring cylinders and cans carefully to avoid breakage.

Electrical safety

• Electrical safety do not pour water into a measuring cylinder while it is on the digital balance, because of the risk of electric shock.

Spills

• Spills stand during the experiment so you can react quickly to spills.

Section 7 of 9More from the specification

1Gravimetric density measurement on Earth

• Gravimetric density measurement on Earth weighing displacement volumes under local gravitational acceleration on Earth establishes accurate material densities.

2Density Formula and Units

• Density ρ is defined as mass per unit volume of a material (ρ = m / V), typically measured in kilograms per cubic metre (kg m⁻³) or grams per cubic centimetre (g cm⁻³).

3Measuring Density of Regular and Irregular Solids

• Regular solid volumes are determined by geometric measurement,
• whereas irregularly shaped objects are submerged in a displacement can to determine displaced fluid volume.

4Mass vs Weight and Gravitational Field Strength

• Mass is the amount of matter in an object (kg),
• whereas weight is the downward gravitational force acting on it,
  • (W = mg in newtons)
• where g is gravitational field strength.

5Upthrust and Archimedes' Principle

• Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force (upthrust) equal to the weight of fluid displaced by the object.

6Weight

• Gravitational force on a mass.

7Upthrust

• Upward force exerted by a fluid.

8Variable

• A factor that can change in an investigation.

9Gravitational field

• Region where mass experiences gravitational force.

10Field strength

• G = F_g/m.

11Independent variable

• The variable deliberately changed, here time

12Dependent variable

• The variable measured, here temperature

Section 8 of 9Key terms

Term	Meaning
Displacement method	Finding a volume from the rise in liquid level when an object is submerged.
Eureka can	Overflow vessel used to collect displaced liquid.
Meniscus	Curved liquid surface; read at its lowest point.
Tare	Resetting a balance to zero with a container on it.
Zero error	A reading shown when the true value is zero.
Resolution	Smallest change an instrument can detect.

Section 9 of 9Exam technique

1

Forgetting to subtract the mass of the container — the mass of the liquid is the difference between the two readings.

2

Using the final water volume as the volume of the object — the volume is the difference between final and initial readings.

3

Reading the meniscus from the top or at an angle — read the bottom of the curve at eye level.

4

Not fully submerging the solid or ignoring air bubbles — both give a wrong volume.