DENSITY & RELATIVE DENSITY

DEFINITION OF DENSITY

The density of a substance is the mass per unit volume of the substance.

Table of Contents

Density = mass of a given substance

Volume of the substance

Density is scalar quantity& measured in kgm-³(kilogram per cubic meter)

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Determination of Density

The determination of density involves the determination of a mass and a volume. The mass can be found by weighing. The density of a substance can be determined using a graduated density bottle.

Relative Density

Relative density is also known as specific gravity. Relative density of a substance is defined as the density of the substance per density of water.

R.D = Density of the substance

Density of water

R.D is also equal to the ratio weight of a substance to weight of an equal volume of water. As weight is proportional to mass

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R.D = mass of substance

mass of equal volume of water

Determination of R.D of Solid (e.g. Sand)

Mass of empty bottle = m₁

Mass of bottle + sand = m₂

Mass of bottle + sand + water = m₃

Mass of bottle + water only= m₄

Mass of sand = m₂ – m₁

Mass of water added to sand = m₃ –m₂

Mass of water filling the bottle = m₄ – m₁

Mass of water having the same volume as sand = (M₄-M₁) – (M₃-M₂)

Relative density = Mass of sand

Mass of equal volume of water

R.D = m₂ – m₁

(m₄– m₁) – (m₃-m₂)

EVALUATION

Differentiate between density & relative density
A glass block of length 100cm width 60cm and thickness 20cm has a mass of 4000g.

calculate the density of the glass

Determination of R.D of Liquid

mass of empty density bottle = m₁

mass of bottle filled with water = m₂

mass of bottle filled with liquid = m₃

R.D of liquid = m₃ – m₁

m₂ – m₁

Example – A glass block of length 10cm width 8cm and thickness 2cm has a mass of 400g. calculate the density of the glass.

Solution

l = 10cm = 0.1m, b = 8cm = 0.08cm, h = 2cm = 0.02m, m = 400g = 0.4kg

V = lbh = 0.1 x 0.08 x 0.02 = 0.00016m³

Density = Mass (m) = 0.4 = 2500kgm³

Volume (V) 0.00016

Example – Calculate the volume in m³ of a piece of wood of mass 500g and density 0.76 gcm-3

mass of the wood = 500g

density = 0.76gcm^-3

volume = ?

volume = mass / density= 500

0.76

volume = 658cm³= 6.58 x 10-4 m³

Example – An empty relative density bottle has a mass of 15.0g. when completely filled with water, its mass is 39.0g. what will be its mass if completely filled with acid of relative density 1.20?

solution

m₁, mass of empty bottle = 15.0g

m₂, mass of bottle + water = 39.0g

mass of acid = n – 15 . 0g

mass of water = 39.0 – 15.0g

= 24.0g

R.D = 1.20

R.D = n – 15.0g

39.0 – 15.0g

1.20 = n –15.0

24.0

n- 15.0= 1.20×24.0

n- 15= 28.8

n =28.8+15

n=43.8g

NB: The hydrometer is an instrument used to measure the relative density of liquids

EVALUATION

1. The volume of an object is 1.5x10m and its mass is 3.0×10 kg. Calculate its density.

2. A relative density bottle weighs 20g when empty, 80g when filled with water & 100g when filled with liquid. Find the relative density of the liquid.

WEEKEND ASSIGNMENT

Find the density of a substance, if the mass of the substance is 150,000g and the dimension is 20m by 10m by 500cm.
1. 5kg1m b. 0.24kg1m c. 1.50kg/m.
What is the height of a cylindrical iron if the density is 7900kg/m³? The mass is 700kg and the radius is 0.1m.
1. 918m b. 2.819m c. 3.418m.
Density is defined as the ratio of mass to——-
1. Pressure b. area c. volume
Relative density is the ratio of mass of a substance to——
1. Mass of 2an equal volume of water b. volume of a substance c. density
The S.I unit of density is ————- a. g1cm b. kg1m c.kg1m .

THEORY

Alcohol of mass 33.2g and density 790kg1m is mixed with 9g of water. What is the density of the resulting mixture?(density of water is 1g1cm ).
Define relative density of liquid