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

Mole Concept Explained: Class 10 Science Notes on Atoms and Molecules

Mole Concept

Introduction to the Mole Concept

So far we discussed about matters in terms of individual atoms and molecules. Atomic mass units provide a relative scale for the masses­ of the elements. Since the atoms have such small masses, no usable scale can be devised to weigh them in the calibrated units of atomic mass units. In any real situation, we deal with ­macroscopic samples containing enormous number of atoms­. Therefore, it is convenient to have a special unit to describe a very large number of atoms. The idea of a ‘unit’ to denote a ­particular number of objects is not new. For example, the pair (2 items) and the dozen (12 items), are all familiar units. Chemists measure atoms and molecules in ‘moles’. So, you can now understand that ‘mole’ denotes a number of particles.

In the SI system, the mole (mol) is the amount of a substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in exactly 12 g (or 0.012 kg) of the carbon-12 isotope. The actual number of atoms in 12 g of carbon-12 is determined experimentally. This is called Avogadro’s Number (N_A), named after an Italian scientist Amedeo Avogadro who proposed its significance. Its value is 6.023 × 10²³. So one mole of a substance contains 6.023 × 10²³ entities. Thus, 5 moles of oxygen molecules contain 5 × 6.023 ×10²³ molecules.

Mole Concept: The study of the collection of particles by using mole as the counting unit, in order to express the mass and volume of such unit particles in a bulk of matter is known as mole concept.

Calculating the Number of Moles

The number of moles of a substance can be calculated by various means depending on the data available, as follows:

• Number of moles of molecules.
• Number of moles of atoms.
• Number of moles of a gas (Standard molar volume at STP = 22.4 litre).
• Number of moles of ions.

Figure 7.3: Mole Concept Relationships

Note: STP-Standard Temperature and Pressure (273.15 K, 1.00 atm)

Mole of atoms:

One mole of an element contains 6.023 × 10²³ atoms and it is equal to its gram atomic mass.

i.e., one mole of oxygen contains 6.023 × 10²³ atoms of oxygen and its gram atomic mass is 16 g.

Mole of molecules:

One mole of matter contains 6.023 × 10²³ molecules and it is equal to its gram molecular mass.

i.e., one mole of oxygen contains 6.023 × 10²³ molecules of oxygen and its gram molecular mass is 32 g.

Molar volume:

One mole of any gas occupies 22.4 litre or 22400 ml at S.T.P. This volume is called as molar volume.

Calculation of number of moles by Different modes

Number of moles = Mass / Atomic Mass

Number of moles = Mass / Molecular mass

Number of moles = Number of Atoms / 6.023 × 10²³

Number of moles = Number of Molecules / 6.023 × 10²³

Figure 7.3: Mole Concept Summary