The concept of density.

Figure below Shows two identical flasks one filled with water to 250cm

^{3}mark and the other filled with kerosene to the same 250cm^{3}mark, when measured in electronic balance the flask filled with water is found to be heavier than that filled with kerosene why? The answer is in finding the mass per unit volume of kerosene and water in respective flasks.
Mass per unit volume of water is 250g/ 250cm

^{3}this is 1g/cm^{3}.
Mass per unit volume of kerosene is 200g/ 250cm

^{3}this is 0.8g/cm^{3}.
The results 1g/cm

^{3}and 0.8g/cm^{3}are the densities of water and kerosene respectively.*Therefore the density of a substance is the mass per unit volume of a given substance*

*.*

The SI unit of density is kilogram per meter cubic (kg/m

^{3}) also gram per centimeter cubic (g/cm^{3}). The symbol for density is rho (ρ) ρ=mass/volume.**Example 1.**

A block of ice with volume 5.5m

^{3}has a mass of 5060kg find the density of ice.
Solution

Volume of block=5.5m

^{3}
Mass of block=5060kg

Density=mass /volume

=5060/5.5m

^{3}.
=920kg/m

^{3}.
The density of ice is 920kg/m

^{3}.**Example 2.**

A silver cylindrical rod has a length of 0.5m and radius of 0.4m,find the density of the rod if its mass is 2640kg.

Solution

Mass of cylinder=2640kg

Volume of cylinder= πr²h

=3.14 x 0.4

^{2}x 0.5
=0.2512m

^{3}
Density=mass/volume

=10509kg/m

^{3}.**Example3.**

A stone has a mass of 112.5g.when the stone totally immersed in water contained in measuring cylinder displaced water from 50cm

^{3}to 95cm^{3}.find the density of the stone.
Solution

Mass of the stone=112.5g

Volume of stone=95cm

^{3}-50cm^{3}=45cm^{3}
Density=mass/volume

=2.5g/cm

^{3}.**Example 4.**

Beaker
contain 262.5cm

^{3}of a certain liquid weigh 410g,if the mass of an empty dry beaker is 200g,find the density of the liquid.
Solution

Mass
of liquid=410g-200g=210g

Volume
of liquid=262.5cm

^{3}.
Density=mass/volume

=0.8g/cm

^{3}.

__DENSITY BOTTLE__
The density bottle
(pycnometer) consists of ground glass stopper with a fine hole through it.

The function of the
fine hole in a stopper is that, when the bottle is filled and the stopper is inserted,
the excess liquid rises through the hole and runs down outside the bottle, by
this way the bottle will always contain the same volume of whatever the liquid
is filled in provided the temperature remains constant.

density bottle

the
bottle is used to measure density and relative density, relative density is
comparison of one density to another, thus a density of a given volume of a
substance to a density of equal volume of referenced substance, for example a
ratio of a density of a given volume of
substance to a density of an equal volume of water, this is referred to a relative
density of a given substance or Specific gravity of a given substance. The term
specific gravity is used when the reference substance is water.

**Measurement of density of liquid by relative density bottle**
ü The mass of bottle is found when dry and
empty

ü The bottle is then filled with the liquid
density is to be determined

ü The stopper is then inserted causing the
liquid to overflow

ü The bottle is dried up by using blotting
paper

ü The mass of the liquid and the bottle is
found

ü Density is found from the collected data

Mass
of empty bottle=m

_{1}g
Volume of liquid
in the bottle=V

mass of bottle
and the liquid=m

_{2}g
mass of liquid
only=(m

_{2}-m_{1})g
density= mass /volume

density=
. (m

_{2}-m_{1})g/V
The
volume of the bottle is known, usually 25ml, 30ml or 50ml

**Example 1**

A
30ml density bottle was filled with kerosene and found to weigh 86g.if the mass
empty dry bottle was 62g, find the density of kerosene.

Solution

Mass of empty
bottle=62g

Mass of bottle and
kerosene=86g

Mass of kerosene
only=86g-62g=24g

Density= mass /volume

=24g/30ml

=0.8g/cm

^{3}.

__Determination of densities of granules and sand__
To
find the density of sand or granules such as lead shots a density bottle is
used as follows

1. Find the mass of empty dry density bottle

**m**_{o}
2. Put some granules and find the mass

**m**_{1}_{ }=( mass of empty bottle + mass of granules)
3. Pour water in the bottle until it is full
and find mass

**m**_{2}_{ = }( mass of bottle + mass of granules + mass of water on top of granules)
4. Find the mass of bottle filled with water
only

**m**=( mass of bottle + mass of water)_{3 }
The mass of sand = (m

_{1}-m_{0}) g
Mass of water above the
sand = (m

_{2}-m_{1}) g
Mass of water filling
the bottle = (m

_{3}-m_{0}) g
Since
density of water is 1g/cm³

Volume
of sand = [(m

_{1}+m_{3})-(m_{o}+m_{2})]/1g/cm³
= [(m

_{1}+m_{3})-(m_{o}+m_{2})] cm³^{}
Density=mass/volume

*Example 1*
Given
the data below find the density of granules

Mass
of empty dry density bottle =18g

Mass
of density bottle and granules=131g

Mass
of density bottle and granules together with water on top =171g

Mass
of density bottle full of water=68g

**RELATIVE DENSITY**

*Relative density of a substance is the ratio of the density of substance to the density of water.*

*Or*

*Relative density of a substance is the ratio of mass of any volume of substance to the mass of an equal volume of water.*

*Example***1**

**To measure relative density of liquid by density bottle**

ü
Find
mass of empty bottle –m

_{0}
ü
Find
mass of bottle and liquid-m

_{1}
ü
Empty
the bottle and rinse it with water

ü
Fill
the bottle with water and find mass m

_{2}
Mass of liquid= (m

_{1}-m_{0})g
Mass of equal volume of water= (m

_{2}-m_{0})g
Since
comparison of density is done with water (referenced substance) the other name
of the ratio is

*specific gravity*of a given substance. Because the density of water is 1g/cm³.Relative density has no units it is simply a number or ratio.

*Example*
The
mass of density bottle is 19g when dry and empty, 45g when filled with water
and 40g when full of liquid x. calculate the density of the liquid x.

*Determinations of relative density by eureka can method*
ü Find the mass m₀ g of solid

ü Fill the eureka can and let water overflow until last drop

ü Place under the spout of overflow can a
clean dry beaker of mass m₁ g.

ü Lower the solid slowly with thin thread
until it is totally immersed

ü Obtain the mass of water that overflow
from the eureka can and the beaker itself m₂ g.

The
volume of water overflows into a beaker is equal to the volume of solid

Mass of solid = m₀ g

Mass of beaker and water=m₂ g

Mass of beaker=m ₁g.

Mass of water only = (m₂-m₁)g

EXAMPLE

A
certain piece of metal has a mass of 282.5 g,if when the block was totally
immersed in overflow can displaced water in a beaker of mass 20 g.if the mass of
water and the beaker was 45 g,find the relative density of the metal.

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ReplyDeleteA density bottle weighs 3.4N when empty, 5N when filled with water and 6.4N when filled with a substance 'A'. Calculate the density of the substance 'A'.

Take weight in air devide by upthrust in water.

DeleteR.d = ml -mo

Delete__ -------

MW - mo

6.5- 3.4

---------

5.0- 3.4

=3.1

---

1.6

=2.1

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ReplyDeleteDensity Bottle = 3.4N .....(1)

ReplyDeleteDensity Bottle + Water = 5N ..(2)

Mass of Water = 5N-3.4N

= 1.6N

Mass of Substance A

= 6.4N- Empty Bottle

= 6.4N- 3.4

= 3.0N

Relative Density =

Mass of substance / Mass of water

= 3.0N/1.6N

= 1.875N

Density of Substance = 1.875N

Weight of empty bottle = 3.4N

DeleteWeight of bottle+Water = 5N

Weight of bottle+liquid A = 6.4N

R.D= Wa-Wb /Ww-Wb

= 6.4-3.4/5-3.4

= 1.875N

Density of liquid A

= R.D * Density of water

= 1.875*1000

=1875kg/m3

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Ans is 50/(50-35)=3.3

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ReplyDeleteA piece of iron weighs 250N in air and 200N in a liquid of density 1000kg/m3. Calculate the volume of iron

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ReplyDeleteA bottle full of water has a mass of 45g, when full of Mercury its mass is 360g if the mass of empty bottle is 20g when empty calculate density of mercury

ReplyDeleteMass of bottle + water = 45g

DeleteMass of bottle + mercury = 360g

Mass of emty-dry bottle = 20g

Mass of water only = 45g - 20g

= 25g

Mass of mercury only = 360g-20g

= 340g

Relative Density = Density of substance/density of water.

Where Density of water = 1.0g/cm^3

R.D = 340g/25 = 13.6

But R.D = density of substance/density of water

Therefore 13.6 = density of substance/density of water.

Density of substance = 13.6X1.0g/cm^3

= 13.6g/cm^3

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ReplyDeleteA fluid having a relative density of 0.8 is mixed with 10 kg of water. Determine the mass of the mixing fluid if the mixture has relative density 0f 0.9.

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( Mass of bottle filled with water + Sand (outside the bottle) = 78.79g

( Mass of bottle + water + sand (inside the bottle) = 75.66g

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