### DENSITY AND RELATIVE DENSITY

The concept of density.
Figure  below Shows two identical flasks one filled with water to 250cm3 mark and the other filled with kerosene to the same 250cm3 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.

The mass of the flask filled with water is 330g, and the mass of flask filled with kerosene 280g, the empty flasks were measured and found to be 80g therefore mass of water only is 250g and kerosene only is 200g.
Mass per unit volume of water is 250g/  250cm3 this is 1g/cm3.
Mass per unit volume of kerosene is 200g/ 250cm3this is 0.8g/cm3.
The results 1g/cm3 and 0.8g/cm3 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/m3) also gram per centimeter cubic (g/cm3). The symbol for density is rho (ρ) ρ=mass/volume.
Example 1.
A block of ice with volume 5.5m3 has a mass of 5060kg find the density of ice.
Solution
Volume of block=5.5m3
Mass of block=5060kg
Density=mass /volume
=5060/5.5m3.
=920kg/m3.
The density of ice is 920kg/m3.

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
=0.2512m3
Density=mass/volume
=10509kg/m3.

Example3.
A stone has a mass of 112.5g.when the stone totally immersed in water contained in measuring cylinder displaced water from 50cm3 to 95cm3.find the density of the stone.
Solution
Mass of the stone=112.5g
Volume of stone=95cm3-50cm3=45cm3

Density=mass/volume
=2.5g/cm3.

Example 4.
Beaker contain 262.5cm3 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=262.5cm3.
Density=mass/volume
=0.8g/cm3.

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=m1g
Volume of liquid in the bottle=V
mass of bottle and the liquid=m2g
mass of liquid only=(m2-m1)g
density= mass /volume
density= .(m2-m1)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/cm3.

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 mo
2.      Put some granules and find the mass  m1 =( mass of empty bottle + mass of granules)
3.      Pour water in the bottle until it is full and find mass m2 = ( 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)
The mass of sand  = (m1-m0) g
Mass of water above the sand    = (m2-m1) g
Mass of water filling the bottle  = (m3-m0) g
Since density of water is 1g/cm³

Volume of sand  =   [(m1+m3)-(mo+m2)]/1g/cm³
= [(m1+m3)-(mo+m2)] 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
A globe of steel has a mass of 12g and a volume of 15.2cm³,find its relative density.

To measure relative density of liquid by density bottle

ü  Find mass of empty bottle –m0
ü  Find mass of bottle and liquid-m1
ü  Empty the bottle and rinse it with water

ü  Fill the bottle with water and find mass m2

Mass of liquid= (m1-m0)g

Mass of equal volume of water= (m2-m0)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 mg 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 mg.
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 mg.

The volume of water overflows into a beaker is equal to the volume of solid
Mass of solid = mg
Mass of beaker and water=mg
Mass of beaker=m g.
Mass of water only = (m-m)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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8. I need someone to help me out with this question:
A 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'.

1. Take weight in air devide by upthrust in water.

2. R.d = ml -mo
__ -------
MW - mo
6.5- 3.4
---------
5.0- 3.4
=3.1
---
1.6
=2.1

9. Great job...

10. Density Bottle = 3.4N .....(1)
Density 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

1. Weight of empty bottle = 3.4N
Weight 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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11. This comment has been removed by a blog administrator.

12. A solid displaced 8.5cm3 of liquid when floating in a certain liquid and 11.5cm3 when fully submerged in the same liquid.The density of the solid is 0.8g/cm3.Determine (1)the upthrust on the solid when floating (2)The density of the liquid (3)The upthrust on the solid when fully submerged

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17. Please can someone help me with this question
The mass of the volume of a substance is 50g. The mass of the volume immersed in the water is 35g.
Find the relative density of the substance
Find the density of the substance
These were the only two parameters they gave in the question
So pls I need answers. Thank you.

1. Ans is 50/(50-35)=3.3

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19. Can someone help me with this question please
a 1000 centimeter cube vessel is filled with two liquids (l1, l2) of relative densities l1=0.75 and l2=1.85 if the relative density of the mixture was found to be 1.5, what volume of each liquid enters the mixture? assume there is no volume change when the liquids mix

20. Plz someone should work out this Vanessa question. Even me I have problem in it too. Density is mass/vol.but here vol.is not given

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22. A car a,moving with a velocity of 15ms travels in opposite direction to another car b,at a velocity of 35ms. Determine the relative velocity of a to b. Pls i need help thank you

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24. I need someone to help me with
A piece of iron weighs 250N in air and 200N in a liquid of density 1000kg/m3. Calculate the volume of iron

25. good evening all please someone should help me out with this problem, it goes... if R is the relative density of the solid, prove that d1 = R(d1-d2)

26. Can someone one help me this question: A piece of metal weighs 0.54N in air and 0.24N when immersed in water. Find
I. It's relative density
II. It's apparent weight in a liquid of density 1.2g/cm³

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28. Pls how can u measure the relative density of a kerosene using the relative density bottle

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32. This comment has been removed by a blog administrator.

33. 100g of water mixed with 60g liquid of density 1.2g/cm³.assume no change in volume. What is the average relative density of the mixture?

34. This comment has been removed by the author.

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36. A 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

1. Mass of bottle + water = 45g
Mass 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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43. Explain relative density in terms of mass

44. Explain relative density in terms of mass

1. Relative density is the ratio mass of the given substance yo the mass of equal volume of water

45. A relative density of a substance is 2.8.What is it's density?

1. Its density is equal to 2.8g/cm^3

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48. If R is the relative density of the solid, prove that d1=R(d1-d2)

49. If R is the relative density of the solid, prove that d1=R (d1-d2)

50. I need help,
A 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.
a. 12kg
b. 8kg
c. 4kg
d. 16kg

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55. Guys help me how can you find the volume of a density bottle

1. First find the mass of the substance of a bottle and second find the mass of an empty bottle

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59. Check the - and + in formula for sg of sand.to me there seems to be an error

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61. Find density of sand from the following information
( Mass of density bottle filled with water 70.64g
( Mass of bottle filled with water + Sand (outside the bottle) = 78.79g
( Mass of bottle + water + sand (inside the bottle) = 75.66g

62. determine the minimum volume of copper that must be attached to Cork of mass 25g so that the will just submerged in water. given that relatative density of copper is 9 and that of cork is 0.25

63. Plz can someone help me with this
Transform the equation R=d1÷d1-d2

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More solutions based on the calculation

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70. 360g of liquid A of density, 1.20g/cm³ were missed with 100g of liquid B of Density 1.00g/cm³ Showing your working, calculate
a) the volume of the mixture
b)the Density of the mixture

Pls I need help😭