1 mole of aluminium oxide, Al₂O₃ = 2  x 27 + 3 x 16 = 102 u = 102 g
102 g Al₂O₃ has = 6.023 x 10²³ Al₂O₃ molecules
0.051  g Al₂O₃ has = \(\frac { 6.023\times { 10 }^{ 23 } }{ 102 } \)
= 3.01 x 10²⁰ Al₂O₃ molecuels
1 molecule of Al₂O₃ gives = 2Al⁺⁺⁺ ions
Hence 0.051 g Al₂O₃ gives = 2 x 3.01 x 10²⁰ Al⁺⁺⁺ ions
=6.023 x 10²³ aluminium ions.

23 gram atomic unit or 23 gram sodium (1 mole) = 6.022 x 10²³ atoms
100 gram atomic unit or 100 gram sodium (1 mole) = \(\frac { 6.022\times { 10 }^{ 23 }\times 100 }{ 23 } =2.617\times { 10 }^{ 24 }\)atoms
again 56 gram atomic unit or 56 grams iron (1 mole) =  6.022 x 10²³ atoms
100 gram atomic unit or 100 grams iron = 1.075 x 10²³ atoms
Thus 100 g of carbon has more atoms than 100g of iron.

Number of atoms in 23 g of sodium =6.022 x 10²³
Number of atoms in 11.5 g of sodium = \(\frac { 11.5 }{ 23 } \times 6.022\times { 10 }^{ 23 }\)
=3.011 x 10²³ atoms
Number of atoms in 40 g of calcium = 6.022 x 10²³
Number of atoms in 15 g of calcium = \(\frac { 6.022\times { 10 }^{ 23 }\times 15 }{ 40 } \)
=2.25 x 10²³ atoms.
Therefore, 11.5g of sodium has more number of atoms than in 15g of calcium

Number of atomes in 1 mole or 24 g Mg = 6.022 x 10²³
Number of atoms in 6 g Mg = \(\frac { 6 }{ 24 } \times 6.022\times { 10 }^{ 23 }\)
= 2.5 x 10²³ atoms
Now 6.022 x 10²³ number of atoms in grams of sodium = 23 g
2.5 x 10²³ number of atoms in grames of sodium = \(\frac { 23\times { 2.5\times 10 }^{ 23 } }{ 6.022\times { 10 }^{ 23 } } \)
= 9.548 x 10^-1 g.

(a) Carbon dioxide
(b) Elements: Carbon and oxygen.Valency of oxygen is -2 and carbon is +4 in CO
(c) Number of moles in 44 g CO = 1
Number of mole in 360 g CO = \(\frac { 360 }{ 44 } \) = 8.18 moles
(d) Number of molecules CO in 44 g = 6.022 x 10²³
Number of molecxules of CO in 88 g = \(\frac { 88 }{ 44 } \times 6.022\times { 10 }^{ 23 }\)=12.044 x 10²³

1 mole = atomic mass = 6.022 x 10²³ atoms
Now mass of one atom of M = 3.05 x 10^-22
Now mass of 6.022 x 10²³ atoms of M =  3.05 x 10^-22 x  6.022 x 10²³ g = 183.7 g
Mass of 1 mole or atomic mass of M = 183.7 g
This could be tungeten (W)

(a)Molar mass of nitrogen = 14 g
5.6 gh of nitrogen = \(\frac { 5.6 }{ 14 } \)= 0.4 mole
(b) 28 g nitrogen = 6.0222 x 10²³ molecules.
5.6 g of nitrogen = 2.15 x 10²² molecules
(c) 14 g of nitrogen =  6.0222 x 10²³ atoms.
5.6 g of nitrogen =  4.30 x 10²² atoms.

1 u = 1/12th of 1 atom of C-12
1 mole C-12 = 12 gram
12 gram C-12 = 6.022 x 10²³ atoms
or  6.022 x 10²³ atoms of C-12 = 12 grams
One atom of C-12 = \(\frac { 12 }{ 6.022\times { 10 }^{ 23 } } \)g
1 u = \(\frac { 12 }{ 6.022\times { 10 }^{ 23 } } \times \frac { 1 }{ 12 } \)
= 1.660302 x 10^-24 gram.

1 u = 1/12th of 1 atom of C-12
1 mole C-12 = 12 gram
12 gram C-12 = 6.022 x 10²³ atoms
or  6.022 x 10²³ atoms of C-12 = 12 grams
One atom of C-12 = \(\frac { 12 }{ 6.022\times { 10 }^{ 23 } } \)g
1 u = \(\frac { 12 }{ 6.022\times { 10 }^{ 23 } } \times \frac { 1 }{ 12 } \)
= 1.660302 x 10^-24 gram.

Utility of mole concept:
(i) Form the number of moles of a substance, we can calculate the number of elementary particles because the number of moles of a substance is directly proportional to the number of elements particles.
(ii) One mole of a gas occupies 22.4 litres at S.T.P
(iii) One mole of any gas under the same conditions of temperature and pressures occupies the same volume
(iv) One mole is equal to molecular mass in grams which is equal to 6.022 x 10²³ atoms, molecules, ionsetc.Thus, we can calculate absolute masses of atoms and molecules.

(i) According to Dalton's atomic theory, matter is invdivisible, i.e which cannot be divided.But now it is known that under special circumstances, atoms can be divided into still smaller particles called electrons, protons and neutrons.
(ii) Dalton's atomic theory fails to explain why substances like charcoal, graphite and diamond have different properties when all these substances are made up the same type of atoms, called carbon atoms.
(iii) Dalton's atomic theory postulated that all the atoms of the same element have exactly the same mass.It is now known that isotopes are atoms of the same element but have different masses.
(iv) It is known that some atoms called isobars have same masses but these belong to different elements.whereas Dalton's atomic theory says that atoms of different atoms have different masses.

According to dalton's atomic theory, each element consists of atoms which are similar have same weights.Further atoms of one element combine with atoms of another element to form compounds.Let us suppose that x atoms of element A combine with y atoms of element B and the compound formed is AxBy.If  'a' stands for the atomic mass of A and 'b' for that of b. then
Percentage of A in the compound=\(\frac { ax\times 100 }{ ax+by } \)
Percentage of B in the compound=\(\frac { by\times 100 }{ ax+by } \)
Now a and b are fixed x and y are also fixed whole numbers according to atomic theory.Therefore. percentage of A and B in the compound is also constant.This shows that the composition of various elements in a compound is also fixed.This is the law of constant proportion.

50 g of 10% lead nitrate means the solution contains 5 g lead nitrate and 45 g water.Similarly, 50 g of 10% sodium chloride means the solution contains 5 g sodium chloride and 45 g water.
Thus total contents before reaction = 5+5+90 = 100 g
After reaction, amount of water = 90 g
Amount of precipitate= 6.83 g
Since according to law of conservation of mass, the total mass of reaction mixture = 100 g
Amount of sodium nitrate = 100-90-6.83 = 3.17g