Solved Problems: Atoms and Molecules | Chemistry & Science Guide

Solved Problems: Atoms and Molecules

Table of Contents

1. Calculation of molar mass
2. Calculation based on number of moles from mass and volume
3. Calculation of mass from mole
4. Calculation based on number of atoms/molecules
5. Calculation based on molar volume
6. Calculation based on % composition

I. Calculation of molar mass

Calculate the gram molar mass of the following.

1) H₂O        2) CO₂        3) Ca₃(PO₄)₂

Solution:

1) H₂O

Atomic masses of H = 1, O = 16

Gram molar mass of H₂O = (1 × 2) + (16 × 1)

= 2 + 16

Gram molar mass of H₂O = 18 g

2) CO₂

Atomic masses of C = 12, O = 16

Gram molar mass of CO₂ = (12 × 1) + (16 × 2)

= 12 + 32

Gram molar mass of CO₂ = 44 g

3) Ca₃(PO₄)₂

Atomic masses of Ca = 40, P = 30, O = 16.

Gram molar mass of Ca₃(PO₄)₂ = (40 × 3) + [30 + (16 × 4)] × 2

= 120 + (94 × 2)

= 120 + 188

Gram molar mass of Ca₃(PO₄)₂ = 308 g

II. Calculation based on number of moles from mass and volume

1) Calculate the number of moles in 46 g of sodium?

= 46 / 23

2 moles of sodium

2) 5.6 litre of oxygen at S.T.P

3) Calculate the number of moles of a sample that contains 12.046 × 10²³ atoms of iron ?

III. Calculation of mass from mole

Calculate the mass of the following

1) 0.3 mole of aluminium (Atomic mass of Al = 27)

Mass = No. of moles × atomic mass

So, mass of Al = 0.3 × 27

= 8.1 g

2) 2.24 litre of SO₂ gas at S.T.P

Molecular mass of SO₂ = 32 + (16 × 2) = 32 + 32 = 64

Mass = No. of moles × molecular mass

Mass = 0.1 × 64

Mass of SO₂ = 6.4 g

3) 1.51 × 10²³ molecules of water

Molecular mass of H₂O = 18

0.25 = mass / 18

Mass = 0.25 × 18

Mass = 4.5 g

4) 5 × 10²³ molecules of glucose ?

Molecular mass of glucose = 180

= (180 × 5 × 10²³) / 6.023 × 10²³

= 149.43 g

IV. Calculation based on number of atoms/ molecules.

1) Calculate the number of molecules in 11.2 litre of CO₂ at S.T.P

= 11.2 / 22.4

= 0.5 mole

Number of molecules of CO₂ = number of moles of CO₂ × Avogadro’s number

= 0.5 × 6.023 × 10²³

= 3.011 × 10²³ molecules of CO₂

2) Calculate the number of atoms present in 1 gram of gold (Atomic mass of Au = 198)

Number of atoms of Au = 3.042 × 10²¹ g

3) Calculate the number of molecules in 54 gm of H₂O?

Number of molecules of water = 6.023 × 10²³ × 54 / 18

= 18.069 × 10²³ molecules

4) Calculate the number of atoms of oxygen and carbon in 5 moles of CO₂.

1 mole of CO₂ contains 2 moles of oxygen

5 moles of CO₂ contain 10 moles of oxygen

Number of atoms of oxygen = Number of moles of oxygen × Avogadro’s number

= 10 × 6.023 × 10²³

= 6.023 × 10²⁴ atoms of Oxygen

1 mole of CO₂ contains 1 mole of carbon

5 moles of CO₂ contains 5 moles of carbon

No. of atoms of carbon = No.of moles of carbon × Avogadro’s number

= 5 × 6.023 × 10²³

= 3.011 × 10²⁴ atoms of Carbon

V. Calculation based on molar volume

Calculate the volume occupied by:

1) 2.5 mole of CO₂ at S.T.P

2) 3.011 × 10²³ of ammonia gas molecules

= 2 moles

Volume occupied by NH₃ = number of moles × molar volume

= 2 × 22.4

= 44.8 litres at S.T.P

3) 14 g nitrogen gas

Number of moles = 14 / 28

= 0.5 mole

Volume occupied by N₂ at S.T.P = no. of moles × molar volume

0.5 × 22.4

11.2 litres.

VI. Calculation based on % composition

Calculate % of S in H₂SO₄

Molar mass of H₂SO₄ = (1 × 2) + (32 × 1) + (16 × 4)

= 2 + 32 + 64

= 98 g