# Problems / Numericals based on Mole Concept (Atomic Mass/ Molar Mass/ Avogadro number)

Formulas in brief –

•  Mass = Molar mass x Number of moles
•  Number of moles = Given number of particles / Avogadro number
•  Number of particles = (Given mass / molar mass) x Avogadro number          (from 1 and 2)
•  If one carbon atom has a mass of 12 atomic mass units and one magnesium atom has a mass of 24 atomic mass units, then as a magnesium atom is twice as heavy as a carbon atom. It follows that this ratio will be maintained for any number of atoms.
• Equal masses of carbon and magnesium contain different numbers of atoms.

6 g of carbon contains 6 / 12 moles of carbon = 0.5 moles
6 g of magnesium contains 6 / 24 moles of magnesium =0.25 moles

• 1 mole = 6.022 x 1023atoms or molecules or formula units of that substance.

1 mole of water (H2O)contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms. It is a simple matter of multiplying the moles of the compound by the atoms or ions that make it up.

Problem based on formula no. – 1
Mass = Molar mass x Number of moles
Calculation of mass from mole of any fundamental unit like atom, molecule and vice – versa.

Note that if it is not mention atom or molecule before mole, it always means one mole of that substance in its natural form.

Example 1- How many grams are there in 5.5 mol of sulphur?

Solution – For converting mass into mole and vice versa, we always need the molar mass.
Molar mass of sulphur = 32.0 g mol–1
Number of moles of sulphur = 5.50 mol
Therefore, mass of sulphur (in grams)  = molar mass x number of moles

= 5.50 mol × 32.0 g mol–1= 176.0 g sulphur

Example 2- Calculate number of moles present in 64 g of oxygen.

Solution – Molar mass of oxygen = 32 g mol–1

Oxygen in natural form will be molecular oxygen, O2

Therefore, number of moles of oxygen = 64 g / 32 g mol–1  = 2.0 moles

Example 3- Calculate the number of moles present in 108 g of aluminium.

Solution –      Atomic mass of Al = 27gm

So,      27g of aluminium  = 1 mole of aluminium

Or, by using formula , Number of moles = given mass / atomic mass

Or,                      Number of moles = 1/27 x 108 =  4 moles of aluminium

Thus,  108g of aluminium  = 4 moles of aluminium

Example 4 – Calculate the mass of 0.5 mole of iron.

Solution –      Atomic mass of iron = 55.9 g

Mass of the 1 mole of iron = 55.9 g

Or, by using formula,  mass = atomic mass x number of moles

Mass of the 0.5 mole of iron = 55.9 x 0.5 g = 27.95 g

1. Atomic number (Z) of Iron, Fe is 26, Atomic mass 56.
Using the above information answer the following-
(a) 1 mole of iron weighs __________ grams.
(b) 7.4 moles of iron weighs ________________ grams.

2. 1 litre of an aqueous solution of NaCl contains 117g of the dissolved salt. Calculate the number of moles of the solute in the solution. (Na = 23u , Cl = 35.5)

3. Two bottles A and B contain 1000 ml. water solutions of 60g NaOH and 117g NaCl respectively. Which bottle has more concentrated solution?

Problem based on formula no. – 2
Number of moles = Given number of particles / Avogadro number
Calculation of mole from number of particles and vice – versa.

Example 5 – Calculate the number of moles of 24.088 x 1023 numbers of sodium atom.

Solution –      Given number of particles =  24.088 x 1023
Avogadro number =   6.022 x 1023
Number of moles = Given number of particles / Avogadro number
24.088 x 1023   / 6.022 x 1023

=  4 moles

Example 6 – Calculate the number of particles in 0.5 moles of N atom.

Solution –                              Number of moles =  0.5 moles
Avogadro number =   6.022 x 1023
Number of particles = Number of moles x Avogadro number
0.5 x 6.022 x 1023

=  3.011 x 1023

Atomic number (Z) of Iron, Fe is 26, Atomic mass 56.
Using the above information answer the following-
(a) 7.4 moles of iron contains ________________ atoms.
(b) 1.2 x 1024 atoms of iron would be _____________ moles of iron.

Problem based on formula no. – 3
Number of particles = (Given mass / molar mass) x Avogadro number
Calculation of number of particles from mass and vice – versa.

Example 7 – Calculate the number of molecules in 22 g of CO2

Solution –      Gram molecular mass or molar mass of CO2 = 44 g

Number of particles = (Given mass / molar mass) x Avogadro number                                   =  ( 22 g / 44 g ) x 6.022 x 1023 = 3.011 x 1023  molecules

Example 8 – Calculate the mass of 18.066 x 1023  molecules of SO2

Solution –      Gram molecular mass or molar mass of SO2 = 64 g
Mass = (Number of particles x molar mass) / Avogadro number
= (18.066 x 1023 x 64) /  6.022 x 1023

=  192 g

Example 9 – Calculate the mass of glucose in 2 x 1024 molecules.

Solution –     Gram molecular mass or molar mass of glucose = 180 g

Mass = (Number of particles x molar mass) / Avogadro number
= (2 x 1024  x 180) /  6.022 x 1023

=  597.8 g

Example 10 – How many atoms are there in 24 g of carbon?

Solution –        24 g of carbon = 24 / 12 moles = 2 moles

1 mole of atoms = 6.022 x 1023

Therefore 2 moles of carbon contains 2 x 6.022 x 1023 atoms = 1.204 x 1024 atoms.

Atomic number (Z) of Iron, Fe is 26, Atomic mass 56.
Using the above information answer the following-
(a) 1 gram of iron contains ________________ atoms.
(b) 1 atom of iron weighs _________________ grams.

Thus, One mole of oxygen stands for –
1.  6.022 x 1023 molecules of oxygen
2.  2 x 6.022 x 1023 atoms of oxygen
3. 1 gram molecule of oxygen
4. 2 gram atoms of oxygen
5. 32 grams oxygen

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QUIZ – Mole Concept and Stoichiometry – 1

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