Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material.A material's density is defined as its mass per unit volume.
Density:
Suppose we measure the masses of three metal blocks with identical dimensions (i.e. identical volumes)
Three metal blocks with the same volumes but different masses.
Three metal blocks with the same volumes but different masses.
Given that the masses of the blocks are 5.4g, 18.0g and 15.6g respectively and that the blocks are all the same size, what explains their different masses?
In closer investigation we see that the three blocks are made from different metals.
This suggests that there is a property of matter that relates its masses and volumes. This property is called density.
Definition;
Density is the mass of an object per unit volume.
Density (r) = mass (m) of substance
Volume(v) of the same substance.
Density (r) = mass (m) of substance
Volume(v) of the same substance.
(r) = m
V
The SI unit is kilometre per Cubic metre(kg/m3)
Other units are grams per cubic centimetre (gcm3)
V
The SI unit is kilometre per Cubic metre(kg/m3)
Other units are grams per cubic centimetre (gcm3)
Substance
|
Density (g/cm3
|
Solids
| |
Aluminium
|
2.7
|
Copper
|
8.3
|
Gold
|
19.3
|
Iron
|
7.8
|
Lead
|
11.3
|
Ice (00c)
|
0.92
|
Liquids
| |
Sea water
|
1.3
|
Water (40c)
|
1.000
|
Water (200c)
|
0.998
|
Gasoline (petrol)
|
0.700
|
Gases (at standard conditions)
| |
Air
|
0.0013
|
Carbon dioxide
|
0.001977
|
Hydrogen
|
0.000090
|
Helium
|
0.000178
|
Density of regular solid:
The density of a regular object can be obtained by calculations once its mass and volume have been measured. It is found by dividing its mass by its volume.
Example
Using the table of densities. Calculate the mass of glass that has the same volume as 5.4g of aluminiu
Solution
r of aluminium = 2.7g/cm3
Mass of aluminium = 5.4g
From the formula: r = m
V
Mass of aluminium = 5.4g
From the formula: r = m
V
V= m
r = 5.4 = 2cm3
r = 5.4 = 2cm3
Volume is 2cm3
Note: that this is also the volume of glass.
Note: that this is also the volume of glass.
- Glass has a density of 2.5 g/cm3 and a volume of 2cm3
- Mass of glass = Volume x density.
= 2.5g/cm3 x 2cm3
= Mass of glass = 5g
= Mass of glass = 5g
Density of an irregular solid:
The density of an irregular solid can be obtained by:
- Measuring its mass using a triple beam balance digital balance.
- Determining the volume through the displacement and immersion method including eureka can and measuring cylinder.
- Dividing the mass by volume obtained.
The density of an irregular solid,
r= mass of an irregular solid
Volume of displaced water
Volume of displaced water
Example
An irregular solid X has a mass of 50g when it is totally immersed in water of volume 60cm3; the final water volume reads 70cm3. Calculate the density of the irregular solid X.
An irregular solid X has a mass of 50g when it is totally immersed in water of volume 60cm3; the final water volume reads 70cm3. Calculate the density of the irregular solid X.
Solution:
Mass of the solid = 50g
Initial volume of water V1= 60cm3
Final volume of water V2= 70cm3
Volume of water displaced = V2-V1
Volume of the solid = Volume of water displaced
But, density = mass = 50g
Volume 10cm3
Volume 10cm3
Density = 5g/cm3
Density of insoluble granules:
Determine the density of small insoluble particles such as sand and grain also possible. One technique involves using a density bottle.
The following are the steps followed when using a density bottle to measure the density of insoluble granules. For this explanation, we shall make use of sand.
- Measure the mass of the empty density bottle with its stopper. Record as M1.
- Add a small amount of sand to the bottle, replace the stopper and measure the mass again. Record M2.
The difference between M2 and M1 gives the mass of the sand.
Mass of sand = M2-M1 - Fill the bottle with water and replace the stopper (wipe off any water that collets on top of the stopper)
Measure the mass again and record as M3
The difference between M3 and M1 given the mass of water added to the bottle.
Mass of water = M3 – M1 - Since the density of water is 1g/m1 the volume of water in m.1 added to the bottle is equal numerically to the mass of water in grams.
Volume of water in ml= Mass of water in grams - Since the only materials in the bottle are the water and the sand, the sum of their volumes must be equal to the volume of the bottle.
Volume of sand = volume of bottle – volume of water - Calculate the density of this sand by dividing its mass by its volume
Density of sand = Mass of sand
Volume of sand
The density of stone and the lead shots can be obtained by dividing their masses by the volume of the water displaced.
Volume of sand
The density of stone and the lead shots can be obtained by dividing their masses by the volume of the water displaced.
Density of a liquid:
The density of a liquid can also be calculated if its mass and its volume are known. Thus, the density of a liquid can be determined through the following steps:-
- Measure the empty beaker M1
- Using a bundle, run out a known volume (V) of the liquid into a beaker and measure the mass.
- Record it as M2
- Subtract M1 from M2 to get the mass of the liquid i.e. mass of liquid = (M1-M2) g
- Calculate the density of the liquid by dividing mass obtained in (iii) by the known volume of liquid.
Hence, density of liquid = Mass of liquid
Known volume of liquid
Known volume of liquid
Example
In an experiment to determine the density of liquid Y. Hassan a form I student came out with the following results.
Mass of beaker Y= 25cm3
Mass of empty beaker = 500g
Mass of beaker + liquid Y = 600g
Mass of liquid = ( 600-500)g = 100g
Density of liquid = M = 100g
V 25cm3
Density of liquid = 4g/cm3
V 25cm3
Density of liquid = 4g/cm3
NB: the density of kerosene can be calculated using the formula.
M2-M1
20
20
RELATIVE DENSITY
Relative density is the number of times a substance is denser than water.
Definition;
Relative density of a substance is the ratio of the substance’s density to the density of water.
Hence, relative density = Density of a substance
Density of water
Relative density of a substance is the ratio of the substance’s density to the density of water.
Hence, relative density = Density of a substance
Density of water
R.D = has no SI Unit
Example
An object has a density of 7glcm3, calculate its relative density R.D.
An object has a density of 7glcm3, calculate its relative density R.D.
Solution:
R.D = Density of a substance
Density of water
Density of water
= 7g/cm3
7g/cm3
7g/cm3
R.D = 7
NB: In SI Units, the density of water is 1000kg/m3 more often, the 1g/cm3 is used.
Example 3
A piece of copper metal of volume 5.1cm3 has a mass of 41.6g calculate the relative density of copper.
A piece of copper metal of volume 5.1cm3 has a mass of 41.6g calculate the relative density of copper.
Solution;
Mass of the piece of copper = 41.6g
Volume of the piece of copper = 5.1cm?
Mass = 41.6g = 8.16g/cm3
Volume 5.1cm3
Volume 5.1cm3
R.D = density of substance
Density of water
Density of water
= 8.16g/cm3
g/cm3
g/cm3
= 8.16
- Relative density of copper = 8.16
Determination of relative density of a liquid:
Relative density of a liquid can be determined by using relative density of a bottle. This bottle has a volume of 25cm3 or 50cm3
Relative density of a liquid can be determined by using relative density of a bottle. This bottle has a volume of 25cm3 or 50cm3
Procedure for determining relative density of a liquid:
- Find the mass of an empty bottle, M0
- Fill the bottle with the liquid
- Dry the bottle using a bottling paper.
- Find the mass of bottle + liquid record as M1
- Empty the bottle and use with clean water
- Finally fill it with water and find the mass, M2
Hence, mass of liquid = (M1-M0)g
Mass of an equal volume of water = (M2-M0)g
Mass of an equal volume of water = (M2-M0)g
- Relative density
= Mass of substance
Mass of an equal volume of water.
Mass of an equal volume of water.
R.D = M1-M0
M2 – M0
M2 – M0
The relative density of cooing oil can be obtained by:
- Finding the mass of cooking oil, (M2-M1)g
- Finding the mass of an equal volume of water (M3-M1)g
- M2-m1 is the relative density of cooking oil.
M3-m1
The narrow hole in the stopper enables air to escape from the bottle when it is being filled with liquid.
Example
In an experiment to determine the relative density of liquid x, form physics students obtained the following results after various measurement.
Mass of an empty relative density bottle = 15g.
Mass of bottle + liquid x = 35g
Mass of bottle + water = 40g
Mass of bottle = 25cm3
Calculate;
- The density of water in kg/m3
- The density of liquid x in kg/m3
- the relative density of liquid x
Solution;
- Mass of water = 25g
- Volume of water = 25m3
Density of water = 25g = 1g/m3
25cm3
25cm3
In kg/m3, density of water = 1000kg/m3
b) Mass of liquid x = 20g
Volume of liquid x = 25cm3
Density of liquid x = 20g = 0.8 kg/m3
25cm3
25cm3
In kg/m3, density of liquid = 800 kg/m3
C) relative density of liquid x = 800kg/m3
1000cm3
1000cm3
- R.D = 0.8
Density and relative density in everyday life:
Relative density has its applications in our everyday lives. These are the following;-
- It is used during the design of various structures of ship and planes.
A ship has to be hollow so as to float as this reduces its density. Materials used for building the parts of aeroplanes should be light e.g., aluminium - Relative density can be used in determining the density of unknown substance using knows density of another.
- Density is used by geologists and mineralogists to help them to determine the mineral content of a rock in other samples.
- It aids in the identification of gemstones
- Density is also considered during the design of swimming and diving
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