The Density of materials and the particle model of matter
Doc Brown's Physics Revision Notes
Suitable for GCSE/IGCSE Physics/Science courses or their equivalent
A simple experiment to determine the density of a material is described,
and how to use the formula for density to calculate density.
This section also looks at density from the point of view of a particle model of matter.
In everyday language, dense objects are described as 'heavy' and less dense objects as 'light', but this is not a correct scientific description of the object or the nature of the material.
What is density? and what is the formula for density?
Density is a measure of how compact a material is - it indicates how much space or volume a given mass occupies.
The greater the mass of material in a given volume, the greater the density of the material.
The density of a material depends on what it is made up of (atoms and their arrangement) and its physical state.
The density for a given material is the same whatever its shape or size for a given physical state.
The scientific symbol for density is the Greek letter rho (ρ)
The formula for density is: ρ = m ÷ v
DENSITY (kg/m3) = MASS (kg) ÷ VOLUME (m3)
Density units in physics are usually kg/m3.
However, in chemistry, density data is often quoted in g/cm3 because most quantitative measurements in a school/college chemistry laboratory are usually quoted in grams (g) and ml (cm3), so I've sometimes quoted both sets of units,
Its advisable to be able to convert mass and volume units e.g.
Density is very important property to know about a material
Experiments to determine the density of a material
All the apparatus needed for the different methods for measuring density is described below and illustrated in one big diagram via parts (1a), (1b), (2a) and (2b).
Simple experiments to measure the density of a solid material
(i) An irregularly shaped object
(ii) A regular shaped object
Calculation of density
Q1 Irregular shaped solid object
Q2 A regular solid block
Q3 A regular solid cylinder of an alloy has a diameter of 3.0 cm, a length of 12.0 cm and a mass of 750 g.
Simple experiments to determine the density of a liquid
To measure the density of liquid you need to weighed an accurately measured volume of the liquid.
(i) Using a measuring cylinder (2b)
(ii) Using a burette or pipette (both more accurate than a measuring cylinder) (2a) and (2b)
To calculate the density of liquid is no different from the calculations for a solid so I don't feel the need to add any more density calculations.
DENSITY and the particle model
The density of a material depends on the nature of the material eg air, water, wood or iron AND the physical state of the material, which is how the particles are arranged. We can use the particle model of matter to partly explain the differences in density between different materials, and in particular the difference in density between gaseous, liquid and solid state of specific substance. When explaining different density values, you must consider both the kinetic energy of the particles and the arrangement of the particles.
Applying the particle model to the different densities of the states of matter.
GASES: The particles have more kinetic energy than in liquids or solids and can move around at random quite freely. This enables the particles to spread out and fill all the available space giving a material a very low density compared to liquids and solids. With very weak forces of attraction between the particles there is no constraint on their movement - they can't club together to form a liquid or solid.
In a substance like air, the particles are widely spread out in the atmosphere giving air a very low density.
LIQUIDS: In liquids, the particles are close together, usually giving densities a bit less than the solid, but much greater than the density of gases. The forces between liquid particles are greater than those between gaseous particles and are strong enough so they are attracted close together leaving little free space. However, liquid particles still have enough kinetic energy to move around at random and create a little space and on average are spaced out just that little bit more than in solids, hence their slightly lower density than the solid.
SOLIDS: The strongest interparticle forces of attraction occur in solids where particles are attracted and compacted as much as is possible. The particles can only vibrate around fixed positions in the structure and do not have sufficient kinetic energy to break free and move around creating a little space like in liquids. The result is the highest density for the state of a specific material. Although liquid densities for a specific material are just a bit less than those of the solid, both the solid and liquid states have much greater densities than the gaseous or vapour state.
Heat Transfer and explaining physical changes and physical properties using a particle model
OCR A gcse 9-1 physics P1.1d Be able to define density. From measurements of length, volume and mass be able to calculate density. See also the investigation of Archimedes’ Principal using eureka cans. density (kg/m3) = mass (kg) / volume (m3) d = m/v P1.1e Be able to explain the differences in density between the different states of matter in terms of the arrangements of the atoms and molecules. P1.1f Be able to apply the relationship between density, mass and volume to changes where mass is conserved. You should be familiar with the structure of matter and the similarities and differences between solids, liquids and gases. You should have a simple idea of the particle model and be able to use it to model changes in particle behaviour during changes of state. You should be aware of the effect of temperature in the motion and spacing of particles and an understanding that energy can be stored internally by materials. P1.2a Be able to describe how mass is conserved when substances melt, freeze, evaporate, condense or sublimate. Use of a data logger to record change in state and mass at different temperatures. Demonstration of distillation to show that mass is conserved during evaporation and condensation. P1.2b Be able to describe that these physical changes differ from chemical changes because the material recovers its original properties if the change is reversed.
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