**
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.
The greater the mass of material in a given
volume, the greater the density of the material.
The scientific symbol for density is the
Greek letter rho (**ρ**)
The
formula for density is: **
ρ****
= m ****
÷ v**
**
DENSITY** (kg/m^{3}) **
= MASS** (kg) **/ VOLUME** (m^{3})
Density units in physics are usually kg/m^{3}.
However, in chemistry, density data is often
quoted in g/cm^{3} because most quantitative measurements in a
school/college chemistry laboratory are usually in grams (g) and ml (cm^{3}),
so I've quoted both sets of units, so don't get them muddled!
**
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**).
By some means you need to know the mass and volume of the material.
**
Simple experiments to measure the density of a solid material**
(i) **An irregularly shaped object**
Any lump of a solid material can be
accurately weighed on an electronic balance (**2b**)
(usually grammes, g).
**Don't forget to tare the balance
to zero before placing the object on it.**
If the solid is a lump with an irregular
shape (and insoluble in water!) you can use a Eureka can (displacement can) to
measure its volume.
The eureka can (**1a**)
is filled with water above the spout and any excess drains off into the
measuring cylinder.
Then empty the collection
measuring cylinder and place it under the spout again.
You then carefully lower the object into
the water attached to a very fine thread.
As the object enters the water, the water
level rises and a volume
of water equal to the volume of the object is displaced from the eureka can
down the spout and measured on
collection in the measuring cylinder (**1b**).
Only measure the volume when the spout
has stopped dripping, otherwise you won't measure the correct volume!
You cannot use this method if the object
has a density <1.0 g/cm^{3} (1000 kg/m^{3}), because it
floats on water and only partially displaces the water.
(ii) **A regular shaped object**
Again the block is weighed on the
electronic balance (**2b**).
If the material is a perfectly shaped
cube or rectangular block, you can then accurately measure the length,
breadth and height and calculate the volume (V = l x b x h).
**Calculation of density**
(i) Irregular shaped solid object
A stone weighing 27.2 g displaced 8.5 cm^{3}
of water (ml), calculate its density.
density of solid ρ
= m **÷** v,
ρ = 27.2 ÷ 8.5 = **
**__3.2 g/cm__^{3}
However, you may have to calculate the
density in kg/m^{3} and this is arithmetically a bit more awkward!
27.2 g = 27.2/1000 = 0.0272 kg
and 8.5 cm^{3} = 8.5 / 10^{6} = 8.5 x 10^{-6}
m^{3} (1 m^{3} = 10^{6} cm^{3})
ρ
= m **÷** v,
ρ = 0.0272 **÷**
(8.5 x 10^{-6}) = 0.0272 **÷** 0.0000085 = __3200 kg/m__^{3}
It might be handy to know that kg/m^{3}
is 1000 x g/cm^{3} !!! 3.2 x 1000 = 3200 !!!
(ii) A regular solid block
A block of iron had dimensions of 3.0 cm
x 5.0 cm x 12.0 cm and weighed 1.420 kg, calculate the density of iron.
Volume of block = 3 x 5 x 12 = 180 cm^{3},
volume = 180/10^{6} = 1.8 x 10^{-4} m^{3}
(0.00018)
density of solid ρ
= m **÷** v,
ρ = 1.42 **÷**
0.00018 = **7889**__ kg/m__^{3}
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**)
If you are only using 10 ml of liquid,
you should use a 10 ml measuring cylinder , a 50 ml measuring cylinder would
not be accurate enough.
A clean empty measuring cylinder is weighed on the
electronic balance (m1).
The liquid under investigation is poured
to a convenient **volume v** eg 50 cm^{3} (in a 50 ml measuring
cylinder for best accuracy)
Make sure the bottom of the liquid's meniscus rests exactly on
the 50 cm^{3} mark.
The measuring cylinder and liquid are
then reweighed (m2).
The difference between the weights gives
you the **mass m** of the liquid (m = m2 - m1)
density of liquid **ρ****
= m ÷ v**
(ii) **Using a burette or pipette** (both more
accurate than a measuring cylinder) (2a) and (**2b**)
Weigh a suitable container, eg a conical
flask or beaker, on the electronic balance (m1).
Carefully measure into the container an
accurately known **volume v** of the liquid under investigation.
You can use a burette (for any volume
from 10.00 to 50 cm3) or a 10.00/25.00 ml (25 cm^{3}) pipette.
In either case make sure the bottom of
the liquid's meniscus rests exactly on the calibration mark.
The container and liquid are reweighed
(m2) and the difference in weight is the **mass m** of the liquid (m = m2
- m1)
density of liquid **ρ****
= m ÷ v**
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.
Density of air in the atmosphere is 1.2
kg/m^{3}. Density of steam = 0.6 kg/m^{3}.
Hydrogen and helium are the 'lightest',
lowest density gases, ρ (H_{2})
= 0.10 kg/m^{3}, ρ
(He) = 0.17 kg/m^{3}
Carbon dioxide sinks in air because it is
'heavier', it has a higher density than air, density = 1.9 kg/m^{3}
(air is 1.2).
If you compress a gas, you force the
molecules closer together, same mass in smaller volume, so the density
increases.
**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.
Water has a density of 1000 kg/m^{3},
more than 1600 times more dense than steam!
Density of liquid air is 974 kg/m^{3},
see this sharply contrasts with gaseous air, which is over 800 times less
dense at 1.2 kg/m^{3}!
Hydrocarbon petroleum oil, typically has
a density of 820 kg/m^{3}, less dense than water, so it floats on
it!
Mercury atoms have a much greater atomic
mass than hydrogen, oxygen or carbon so liquid mercury has a density of 13
584 kg/m^{3}, that is more than 13 times more dense than water!
If you heat a liquid, increasing its
temperature, the particles gain kinetic energy and the collisions become
more frequent and energetic and this enables the particles on average to
spread out a bit more, increasing the liquid volume and lowering the
density.
**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.
Generally speaking the solid state
exhibits the highest density.
In a very dense material like iron, the
particles (iron atoms) are not only heavy, but very close together giving
the high density of 7870 kg/m^{3}.
Because of the particular crystal
structure of ice (ρ
= 931 kg/m^{3}), solid water is less dense than liquid water (ρ
= 1000 kg/m^{3}), so ice floats on water! Very unusual!
When dealing with insulating materials,
beware!, their densities are much lower than the 'bulk' solid because very
low density gases like air or carbon dioxide are trapped in them,
considerably lowering the overall density of the original solid material.
If you heat a solid, increasing its
temperature, the particles gain kinetic energy and the vibrations become
more energetic and this enables the particles on average to spread out a bit
more ('pushing' each other apart), increasing the solid volume and lowering
the density.
**
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