Calculation of Number of Moles, Atoms, and Molecules

Science > Chemistry > Molecule and Molecular Mass > Calculation of Number of Moles, Atoms, and Molecules

In this article, we shall study the calculation of number of moles, number of atoms, and molecules in a given moles.

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 = m/M

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

To Calculate Number of Moles:

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

Ans: 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

Ans: 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

Ans: 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

Ans: Number of moles of C  = 5.46 × 10^-3

To Calculate Number of Molecules in a Given mole:

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

Ans: 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

Ans: 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

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

500 mg of carbon dioxide

Molecular mass of carbondioxide (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

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

Calculation of Number of Atoms in a Given Mole:

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 CO₂ = 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

Ans: 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

Ans: 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

Ans: 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

Ans: 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 

Ans: 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 

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

Science > Chemistry > Molecule and Molecular Mass > Calculation of Number of Moles, Atoms, and Molecules