**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

R.D = __mass of substance__

mass of equal volume of water

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

Mass of empty bottle = m_{1}

Mass of bottle + sand = m_{2}

Mass of bottle + sand + water = m_{3 }

_{ }Mass of bottle + water only= m_{4}

Mass of sand = m_{2} – m_{1}

Mass of water added to sand = m_{3} –m_{2}

Mass of water filling the bottle = m_{4} – m_{1}

Mass of water having the same volume as sand = (M_{4}-M_{1}) – (M_{3}-M_{2})

Relative density = __Mass of sand__

_{ } Mass of equal volume of water

R.D = __m _{2} – m_{1} __

(m_{4 }– m_{1}) – (m_{3 }-m_{2 })

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**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

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**Determination of R.D of Liquid**

mass of empty density bottle = m_{1 }

mass of bottle filled with water = m_{2}

mass of bottle filled with liquid = m_{3}

R.D of liquid = __m___{3}__ – m___{1}

m_{2} – m_{1}

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 = 0.00016m^{3}

Density = __Mass (m__) = __0.4 = __ 2500kgm^{3}

Volume (V) 0.00016

Example – Calculate the volume in m^{3} 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 = 658cm^{3 }= 6.58 x 10-4 m^{3}

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

m_{1}, mass of empty bottle = 15.0g

m_{2}, 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

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**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.

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## 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.
- 5kg1m b. 0.24kg1m c. 1.50kg/m.

- What is the height of a cylindrical iron if the density is 7900kg/m
^{3}? The mass is 700kg and the radius is 0.1m.- 918m b. 2.819m c. 3.418m.

- Density is defined as the ratio of mass to——-
- Pressure b. area c. volume

- Relative density is the ratio of mass of a substance to——
- 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 .

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**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

See also