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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 avogadro’s number or avogadro’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 ‘u’ to ‘g’. 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 ‘formula unit’ 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 – 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
∴ 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 – 2 Al+3ions
3 X 1020 molecules contains – 2 X 3 X 1020
= 6 X 1020 Al+3 ions
∴ 0.051 g of Al2O3 contains 6 X 1020 Al+3 ions.

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