# Calculations of Number of Moles, Molecules and Atoms

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### Schematic Diagram for Mole Calculations:

Where, m = Given mass, M = Molar mass

v = Given volume, V = Molar volume = 22.4 dm3

n = Number of moles

Number of atoms  = Number of molecules  × Atomicity

#### Conversions:

From To Factor
kg g × 103
mg g × 10-3
μg g × 10-6
metric ton kg × 103
metric ton g × 106
cm3 dm3 × 10-3
m3 dm3 × 103
litre dm3 × 1

#### Example – 1:

• Calculate the number of moles of following.
•  7.85 g of Fe (at. mass 56)

Given mass of Fe = 7.85 g

Fe is a monoatomic molecule. Hence molecular mass of Fe = Atomic mass of Fe = 56 g

Number of moles of Fe = Given mass of Fe / Molecular mass of Fe

Number of moles of Fe  =  7.85 g / 56 g = 0.1402

Number of moles of Fe = 0.1402

• 7.9 mg of Ca (at. mass 40)

Given mass of Ca =7.9 mg = 7.9 × 10-3 g

Ca is a monoatomic molecule. Hence molecular mass of Ca = Atomic mass of Ca = 40 g

Number of moles of Ca = Given mass of Ca / Molecular mass of Ca

Number of moles of Ca = 7.9 × 10-3 g / 40 g = 1.975  × 10-4

Number of moles of Ca = 1.975  × 10-4

• 1.46 metric tons of Al (at. mass 27)

Given mass of Al = 1.46 metric tons = 1.46 × 103 kg = 1.46 × 103 × 103  g = 1.46 × 106  g

Al is a monoatomic molecule. Hence molecular mass of Al = Atomic mass of Al = 27 g

Number of moles of Al = Given mass of Al / Molecular mass of Al

Number of moles of Al = 1.46 × 106  g / 27 g = 5.41  × 104

Number of moles of Al = 5.41  × 104

• 65.5 mg of C (at. mass 12)

Given mass of C = 65.5 mg = 65.5 × 10-3 g

Al is a monoatomic molecule. Hence molecular mass of C = Atomic mass of C = 12 g

Number of moles of C = Given mass of C/ Molecular mass of C

Number of moles of C = 65.5 × 10-3 g / 12 g = 5.46 × 10-3

Number of moles of C  = 5.46 × 10-3

#### Example  – 2:

• Calculate the number of moles and number of molecules of following.
• 0.032 mg of methane

Molecular mass of methane (CH4) = 12 × 1 + 1 × 4 = 12 + 4 = 16 g

Given mass of CH4 = 0.032 mg = 0.032 × 10-3 g = 3.2 × 10-5 g

Number of moles of CH4 =   n  =  Given mass of CH4 / Molecular mass of CH4

n = 3.2 × 10-5 g / 16 g = 2 × 10-6

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 2 × 10-6 × 6.022 × 1023

Number of molecules = 1.2044 × 1018

Number of moles of C  = 5.46 × 10-3 and Number of molecules = 1.2044 × 1018

• 6.4 × 10-2 kg of sulphur dioxide

Molecular mass of methane (SO2) = 32 × 1 + 16 × 2 = 32 + 32 = 64 g

Given mass of SO2 = 6.4 × 10-2 kg = 6.4 × 10-2 × 103 g = 64 g

Number of moles of SO2 =   n  = Given mass of SO2 / Molecular mass of SO2

n = 64 g / 64 g = 1

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 1 × 6.022 × 1023

Number of molecules = 6.022 × 1023

Number of moles of SO2 = 1 and Number of molecules =6.022 × 1023

• 0.065 mg of water

Molecular mass of water (H2O) = 1 × 2 + 16 × 1 = 2 + 16 = 18 g

Given mass of H2O = 0.065 mg = 0.065 × 10-3 g = 6.5  × 10-5 g

Number of moles of H2O =   n  = Given mass of H2O / Molecular mass of H2O

n  = 6.5  × 10-5 g / 18 g = 3.611  × 10-6

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 3.611  × 10-6 × 6.022 × 1023

Number of molecules = 2.174 × 1018

Number of moles of H2O = 3.611  × 10-6 and Number of molecules = 2.174 × 1018

• 500 mg of carbon dioxide

Molecular mass of methane (CO2) = 12 × 1 + 16 × 2 = 12 + 32 = 44 g

Given mass of CO2 = 500 mg = 500 × 10-3  g = 0.5 g

Number of moles of CO2 =   n  = Given mass of CO2 / Molecular mass of CO2

n  = 0.5 g / 44 g = 1.136 × 10-2

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 1.136 × 10-2  × 6.022 × 1023

Number of molecules = 6.843 × 1021

Number of moles of CO2 = 1.136 × 10-2  and Number of molecules = 6.843 × 1021

#### Example – 3:

• Calculate the number of moles, number of molecules and number of atoms of following.
• 1.1. × 10-4 kg of carbon dioxide

Molecular mass of CO2 =12 × 1 + 16 × 2 = 12 + 32 = 44 g

Given mass of CO2 = 1.1. × 10-4 kg = 1.1. × 10-4 × 103 g = 0.11 g

Number of moles of CO2 = Given mass of CO2 / Molecular mass of CO2

Number of moles of CO2 = 0.11 g / 44 g = 2.5 × 10-3

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 2.5 × 10-3 × 6.022 × 1023

Number of molecules of CO= 1.505 × 1021

Atomicity of CO2 is 3

Hence Number of atoms in CO2 = Number of molecules of CO2 × Atomicity of CO2

Hence Number of atoms of CO2 =  1.505 × 1021 × 3 = 4.515 × 1021

Number of moles  = 2.5 × 10-3 , Number of molecules = 1.505 × 1021  and Number of atoms =4.515 × 1021

• 4.25. × 10-2 kg of ammonia

Molecular mass of NH3 =14× 1 + 1 × 3 = 14 + 3 = 17 g

Given mass of NH3 = 4.25. × 10-2 kg = 4.25. × 10-2 × 103 g = 42.5  g

Number of moles of NH3 = Given mass of NH3 / Molecular mass of NH3

Number of moles of NH3 = 42.5 g / 17 g = 2.5

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 2.5  × 6.022 × 1023

Number of molecules of NH3 = 1.505 × 1024

Atomicity of NH3 is 4

Hence Number of atoms of NH3 = Number of molecules of NH3 × Atomicity of NH3

Hence Number of atoms in CO2 =  1.505 × 1024 × 4 = 6.020 × 1024

Number of moles  = 2.5, Number of molecules = 1.505 × 1024 and Number of atoms = 6.020 × 1024

• 0.4 g of helium gas.

Molecular mass of He =4 g

Given mass of He = 0.4 g

Number of moles of He = Given mass of He / Molecular mass of He

Number of moles of He = 0.4 g / 4 g = 0.1

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 0.1  × 6.022 × 1023

Number of molecules of He = 6.022 × 1022

Atomicity of He is 1

Hence Number of atoms of He = Number of molecules of He × Atomicity of He

Hence Number of atoms in He = 6.022 × 1022 × 1 = 6.022 × 1022

Number of moles  = 0.1, Number of molecules = 6.022 × 1022 and Number of atoms = 6.022 × 1022

• 5.6 cm3 of ammonia at STP.

Given volume of ammonia = 5.6 cm3 = 5.6 × 10-3 dm3

1 mole of ammonia at STP occupies 22.4 dm3 by volume.

Number of moles of NH3 = Given volume of NH3 / 22.4 dm3

Number of moles of NH3 = 5.6 × 10-3 dm3 / 22.4 dm3 = 2.5 × 10-4

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 2.5 × 10-4  × 6.022 × 1023

Number of molecules of NH3 = 1.5055  × 1020

Atomicity of NH3 is 4

Hence Number of atoms of NH3 = Number of molecules of NH3 × Atomicity of NH3

Hence Number of atoms of NH3 = 1.5055  × 1020 × 4 = 6.022 × 1021

Number of moles  = 2.5 × 10-4 , Number of molecules = 1.5055  × 1020 and Number of atoms =6.022 × 1021

• 5.6 dm3 of ammonia at STP.

Given volume of ammonia = 5.6  dm3

1 mole of ammonia at STP occupies 22.4 dm3 by volume.

Number of moles of NH3 = Given volume of NH3 / 22.4 dm3

Number of moles of NH3 = 5.6  dm3 / 22.4 dm3 = 0.25

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 0.25  × 6.022 × 1023

Number of molecules of NH3 = 1.5055  × 1023

Atomicity of NH3 is 4

Hence Number of atoms of NH3 = Number of molecules of NH3 × Atomicity of NH3

Hence Number of atoms of NH3 = 1.5055  × 1023 × 4 = 6.022 × 1023

Number of moles  = 0.25, Number of molecules = 1.5055  × 1023 and Number of atoms =6.022 × 1023

• 7.6 dm3 of hydrogen at STP.

Given volume of hydrogen = 7.6 dm3

1 mole of hydrogen at STP occupies 22.4 dm3 by volume.

Number of moles of H2 = Given volume of H2 / 22.4 dm3

Number of moles of H2 = 7.6 dm3 / 22.4 dm3 =0.34

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 0.34  × 6.022 × 1023

Number of molecules of H2  = 2.047  × 1023

Atomicity of H2 is 2

Hence Number of atoms of H2 = Number of molecules of H2  × Atomicity of H2

Hence Number of atoms of H2 = 2.047  × 1023 × 2 = 4.094  × 1023

Number of moles  = 0.34 , Number of molecules = 2.047  × 1023 and Number of atoms = 4.094  × 1023

• 250.9 dm3 of hydrogen at STP.

Given volume of hydrogen = 250.9 dm3

1 mole of hydrogen at STP occupies 22.4 dm3 by volume.

Number of moles of H2 = Given volume of H2 / 22.4 dm3

Number of moles of H2 = 250.9 dm3 / 22.4 dm3 = 11.2

Now, Number of molecules = No. of moles × Avogadro’s number

Number of molecules = 11.2  × 6.022 × 1023

Number of molecules of H2  = 6.745  × 1024

Atomicity of H2 is 2

Hence Number of atoms of H2 = Number of molecules of H2  × Atomicity of H2

Hence Number of atoms of H2 = 6.745  × 1024 × 2 = 1.349  × 1025

Number of moles  = 11.2 , Number of molecules = 6.745  × 1024 and Number of atoms = 1.349  × 1025

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