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# Mole Concept

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#### Mole Concept - Lesson Summary

Mole:  Mole is the measurement in chemistry. It is used to express the amount of a chemical substance.
One mole is defined as the amount of substance of a system which contains as many entities like, atoms, molecules and ions as there are atoms in 12 grams of carbon - 12".

Avogadro number:  The number of the particles present in one mole of any substance is equal to 6.022x1023. This is called avogadroâ€™s number or avogadroâ€™s constant.

Number of particles in 1 mole:
1 mole of hydrogen atoms represents 6.022 × 1023 hydrogen atoms.
1 mole of hydrogen molecules represents 6.022 × 1023 hydrogen molecules.
1 mole of water molecules represents 6.022 × 1023 water molecules.

Atomic mass:  The atomic mass of an element is the mass of one atom of that element in atomic mass units or (u).

Atomic mass unit (amu):  1/12th of the mass of an atom of carbon-12 is called atomic mass unit. It is a unit of mass used to express atomic masses and molecular masses.

Molar mass:  The molar mass of an element is equal to the numerical value of the atomic mass. However, in case of molar mass, the units change from â€˜uâ€™ to â€˜gâ€™. The molar mass of an atom is also known as gram atomic mass.
For example, the atomic mass of carbon =12 atomic mass units. So, the gram atomic mass of carbon = 12 grams.

Molecular mass of the molecule:  The sum of the atomic masses of all the atoms in a molecule of a substance is called the molecular mass of the molecule.

Molecular mass - calculation: Generally we use relative atomic masses of atoms for calculating the molecular mass of 1 mole of any molecular or ionic substances.
Example: Molecular mass of H2SO4
Atomic mass of Hydrogen = 1
Atomic mass of sulphur = 32
Atomic mass of oxygen = 16
Molecular mass of H2SO4 = 2(Atomic mass of Hydrogen) + 1 (Atomic mass of sulphur) + 4 (Atomic mass of oxygen)
= 2×1 + 32 + 4× 16 = 98 u.

Calculation of molecular mass of hydrogen chloride:
Atomic mass of hydrogen + Atomic mass of chlorine = 1 + 35.5 = 36.5 u.

Formula unit mass:
The formula unit mass of a substance is the sum of the atomic masses of all atoms in a formula unit of a compound. The term â€˜formula unitâ€™ is used for those substances which are made up of ions.
Formula unit mass of NaCl: 1 X Atomic mass of Na + 1 X Atomic mass of Cl
1x23 +1 x 35.5 = 58.5 atomic mass units.

Formula unit mass of ZnO:
= 1 X Atomic mass of Zn + 1 X Atomic mass O
= 1 X 65 + 1 X 16 = 81 u.

Avogadro's number, number of particles and moles - conversion formulae:

Number of moles (n) = Given number of particles (N) / Avogadro number (N 0)
Example: Find the number of moles present in 24.088X10 23 particles of carbon dioxide
1 mole of carbon dioxide contains 6.022x10 23
Solution: The number of moles (n ) = Given number of particles (N) / Avogadro number (N 0).
= 24.088X10 23 / 6.022x10 23
= 4 moles.
Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N 0)
Example: Calculate the number of atoms in 48g of Mg
Solution: Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N 0).
= 48/24 X 6.022x10 23
= 12.04 X10 23 atoms.
Number of molecules (n) = Given mass (m) / Molar mass (M) x Avogadro number (N 0)
Example: Calculate the number of molecules in 3.6 g of water
Solution: The molecular weight of H 2O = 18
18g of water - 6.022x10 23 molecules
3.6g of water - 6.022x10 23 X 3.6/18
= 1.206 X 10 22 molecules.
Number of particles (n) = Number of moles of particles (n) x Avogadro number (N 0)
Example:  Calculate the number of atoms in 0.5 moles of carbon
Solution: Number of atoms = 0.5 X 6.022x10 23
= 3.0115 atoms

Extra problems:

1) Calculate the number of moles in 12g of oxygen gas
Ans: 32g of oxygen gas = 1 mole
12g of oxygen gas = ?
= 12 X 1 / 32 =  0.375 mole.

2) Calculate the number of moles present in 14g of carbon monoxide .
Ans: 28g of CO = 1 mole
14g of CO = ?
= 14 X 1 / 28 = 1/2 = 0.5 mole.

3) Find the mass of 5 moles of aluminium atoms?
Ans: Atomic mass of aluminium atom = 27g
5 moles of aluminium atoms = 5 X 27g = 135 g.

4) Calculate the molar mass of sulphur.
Ans: Sulphur is a poly atomic molecule. It is made up of 8 sulphur atoms.
Atomic mass sulphur atom = 32 g.
Molar mass of sulphur = 8 X 32 = 256 g.

5) Calculate the mass of 0.2 mole of water molecules.
Ans: 1 mole of water molecules = 18g
0.2 mole of water molecules = ?
= 0.2 X 18 / 1 = 3.6 g.

6) Which has greater number of atoms, 100g of sodium or 100g of iron?
Atomic mass of Na = 23 u, Fe = 56 u.
Ans: 1 mole of substance contains the number of particles =  Avagadro's constant.
1 mole of Na = 23g
23g of Na contains - 6.023 X 10 23 atoms
100g of Na Contains - ?
= 100 X  6.023 X 10 23/23
= 4.3 X  6.023 X 10 23 atoms.
1 mole of Fe =  56g
56g of Fe contains - 6.023 X 10 23 atoms
100g of Fe contains - ?
= 100 X 6.023 X 10 23/ 56
= 1.78 X  6.023 X 10 23 atoms
Therefore, 100g of Na has greater number of atoms than 100 g of Fe.

7) How many atoms of oxygen are present in 300 grams of CaCO3?
Ans: Molecular mass of calcium carbonate = 40 + 12 + 3 X 16 = 40 + 12 + 48 = 100g
1 mole of Calcium carbonate contains â€“ 3 mole of oxygen atoms.
100 g of calcium carbonate contains - 3 X 6.023 X 10 23 atoms
300g of calcium carbonate contains - ?
= 300 X 3 X 6.023 X 10 23/100
= 54.207 X 10 23 oxygen atoms.

8) The mass of one atom of an element 'A' is 2.65 X10-23 g.  Calculate its atomic mass and name the element.
Ans: The mass of one atom of an element A = 2.65 X10-23 g
We know that 1 mole of an atom = 6.023 x 1023 atoms
1 mole of an atom = Its atomic weight
Mass of one atom of an element = 2.65X10-23 g
Mass of 6.023 x 1023 atoms of an element A = 2.65X10-23 X6.023 x 1023
= 15.69 g

The element is oxygen.

9) Calculate the number moles of magnesium  in 0.478g of magnesium ?

Ans: Molecular weight of magnesium =24g

24g of magnesium = 1 mole

0.478g of magnesium = ?

= 0.478 X 1/24 = 0.019 mole.

10) In which of the following cases the number of hydrogen atoms is more ? Two moles of HCl or one mole of NH3.

Ans: Calculation of number of  hydrogen atoms present in 2 moles of HCl
1 mole of  HCl contains 6.023X1023 molecules of HCl
2 moles of HCl contains 2 X 6.023X1023 =  12.046X1023 molecules of HCl
1 molecule of HCl contains 1 hydrogen atom
12.046X1023 molecules of HCl contains12.046X1023 hydrogen atoms
Calculation of number of hydrogen atoms present in 1 mole of NH3
1 mole NH3 Contains 6.023X1023 molecules of NH3
1 molecule of NH3 contains 3 atoms of hydrogen
6.023X1023 molecules of NH3 contains 3X 6.023X1023 atoms of hydrogen
= 18.069 X1023 atoms of hydrogen
Number of hydrogen atoms present in 2 moles of HCl = 12.046X1023
Number of hydrogen atoms present in 1 mole of NH3 = 18.069 X1023
Therefore, numbers of hydrogen atoms are more in 1 mole of NH3.

11) Find the number of oxygen atoms in 88g of CO2?

Ans: Molar mass of CO2 = 44 g/mol
Number of moles of CO2 present in 88g of CO2 = 88g/44g mol-1
= 2 moles
1 mole of CO2 contains 2 moles of Oxygen atoms.
2 moles of CO2 contains 4 moles of Oxygen atoms
1 mole of oxygen contains 6.023 X 1023 atoms of oxygen
4 moles of oxygen contains = 4 X 6.023 X 1023
= 24.092 X 1023
= 2.4092 X 1024 atoms of oxygen

Therefore, 88g of CO2 Contains 2.4092 X 1024 atoms of oxygen.

12) Calculate the number of water molecules contained in a drop of water weighing 0.06g ?

Ans: 18g of water = 1 mole
0.06 g = ?
= 0.06/18 = 3.33 X 10-3 mole of water
1 mole of water contains - 6.022X1023 molecules of water
3.33 X 10-3 mole of water contains -----?
= 6.022X1023 X 3.33 X 10-3
= 2 X 1020 molecule of water
âˆ´ 0.06g of water contains 2 X 1020 molecules of water.

13) Find the number of aluminium ions present in 0.051g of aluminium oxide(Al2O3).

(Atomic masses: Al= 27u;O= 16u)

Ans: Molecular weight of Al2O3 = 102 g
102 g of Al2O3 contains 6.022X1023 molecules
0.051g of Al2O3 contain X number of molecules
X = 0.051 X 6.022X1023 /102 = 0.003 X 1020
X = 3 X 1020
1 molecule of Al2O3 contains â€“ 2 Al+3ions
3 X 1020 molecules contains â€“ 2 X 3 X 1020
= 6 X 1020 Al+3 ions
âˆ´ 0.051 g of Al2O3 contains 6 X 1020 Al+3 ions.