Density: Concise quick Introduction 1

Contents

Finding density involves determining the mass of a substance contained it it’s unit volume. It is usually represented by rho (ρ) and it’s SI Unit is kilogram per cubic meter, that is; (kgm^-3)

A common unit of density is grams per cubic centimeter (gcm^-3). This unit is very common in day to day measurements.

Finding density of some substances in a concise illustration

general Formulae for ρ

The general expression of density is given as:

$$ \rho = \frac{\text{mass m} } {\text{volume V}} $$

we can use symbols alone to write expressions about it when solving problems involving density.

$$\rho = \frac{m}{V}$$

We should be able to convert densities expressed in Kilogram per cubic meter(kgm^-3) into grams per cubic centimeter (gcm^-3). In many cases, conversion from on unit of measurement to another is usually necessary. Let say we want to change 1kgm^-3 into grams per cubic centimeter (gcm^-3) . 1kgm^-3 means that:

$$1 kgm^{-3} = \frac{1 kg}{1m^3}$$

Now we convert 1 kg into grams remembering that, 1 kg =1000 grams and 1 cubic meter into cubic centimeters;

remembering that 1m³ = 1000000 cm³

hence 1 kgm^-3 = 0.001 gcm^-3

if 1 kgm^-3  = 0.001 gcm^-3 
   y kgm^-3 =  1 kgm^-3
cross multiplying:

$$ 1 \ kgm^{-3} \times 1 \ gcm^{-3} = y \times 0.001 \ gcm^{-3} $$

then dividing by 0.001 gcm^-3 on both sides:

hence 1 gcm^-3 is equivalent to 1000 kgm^-3

Example

The density of a substance in a lab is expressed as 5g/cm³. Express it in it’s SI Unit.

solution

The SI unit of ρ is kilogram per cubic meter. We thus change grams into kilograms and cubic centimeter into cubic meter.

expressing in terms of grams and cubic centimeters:

$$5gcm^{-3} = \frac{5g}{1 \ cm^3} $$

1 000,000 cm³ = 1 m³ hence :

$$1 \ cm^3 = \frac{1}{1000,000}m^3$$

hence

=5000 kgm^-3

Practice Questions on density

A glass block measures 180mm by 80 mm by 20 mm. It’s mass is 280 g. Find it’s density in SI Units.
A certain metal has it’s density given as 1.9gcm-3. If 50000 kg of such metal was purchased by a company. what volume did it occupy?
A rectangular tank measures 12.5 m long 10.0 wide and 2.0m high. Calculate the mass of water in the tank when it is full.( ρ of water = 1000 kgm^-3 ) (3mks)
The figure below shows the reading of a measuring cylinder before and after a stone of mass 20g has been immersed in it. Determine the ρ of the stone (3mks)

5. The water level in a burette is 30 cm³. If 55 drops of water fall from the burette and the average volume of one drop is 0.12cm³, what is the final water level in the burette? (3mks)

6. (a) Given the following:

Mass of solid = 13.6 g
Volume of water before solid is immersed = 3.1 cm³
Volume of water after solid is fully immersed= 9.9cm³

Calculate the density of the solid. (3mks)

b)An empty density bottle has a mass of 10g. When completely filled with water its mass becomes 34g and its mass when completely filled with an acid is 30g. What is the density of the acid? (4mks)

7. A block of glass of mass 187.5g is 5.0cm long 2.0 cm thick and 7.5cm high. Calculate the density of the glass in kgm^-3. (3mks)

8. A density bottle has mass of 0.785 kg when empty and 1.125kg when full of water. Calculate the volume of water in the bottle giving your answer in litres.(take ρ of water as 1000kg/m³)

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