Calculation of Mass of a Molecule and an Atom

Science > Chemistry > Molecule and Molecular Mass > Calculation of Mass of a Molecule and an Atom

In this article, we shall study the calculation of the mass of molecule and an atom.

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 Mass of Given Moles:

Calculate the mass of the following.

2.5 moles of water:

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

Number of moles of water = 2.5 = n

Mass of water = n × Molar mass

Mass of water = 2.5 × 18 = 45 g

1.2 moles of carbon dioxide

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

Number of moles of carbon dioxide = 1.2

Mass of carbon dioxide = n × Molar mass

Mass of carbon dioxide = 1.2 × 44 = 52.8 g

0.25 moles of sulphuric acid

Molecular mass of sulphuric acid (H₂SO₄) = 1 x 2 + 32 x 1 + 16 x 4 = 2 + 32 + 64 = 98 g

Number of moles of sulphuric acid = 0.25 = n

Mass of sulphuric acid = n × Molar mass

Mass of sulphuric acid = 0.25 × 98 = 24.5 g

0.1 moles of ammonia

Molecular mass of ammonia (NH₃) = 14 x 1 + 1 x 3 = 14 + 3 = 17 g

Number of moles of ammonia = 0.1 = n

Mass of ammonia = n × Molar mass

Mass of ammonia = 0.1 × 17 = 1.7 g

3.5 moles of methane

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

Number of moles of methane = 3.5 = n

Mass of methane = n × Molar mass

Mass of methane = 3.5 × 16 = 56 g

2.4 moles of sulphur dioxide

Molecular mass of sulphur dioxide (SO₂) = 32 x 1 + 16 x 2 = 32 + 32 = 64 g

Number of moles of sulphur dioxide = 2.4 = n

Mass of sulphur dioxide = n × Molar mass

Mass of sulphur dioxide = 2.4 × 64 = 153.6 g

0.6 moles of bromine

Molecular mass of bromine (Br₂) = 40 x 2  = 80 g

Number of moles of bromine = 0.6 = n

Mass of bromine = n × Molar mass

Mass of bromine = 0.6 × 80 = 48 g

To Calculate Mass of a Molecule and Atom:

Calculate the following

mass of one oxygen atom and oxygen molecule in kg.

Molecular mass of oxygen (O₂) = 16 x 2 = 32 g

1 mole of oxygen is 32 g = 32 x 10^-3 kg

1 mole of a substance contains 6.022 x 10²³ molecules

Mass of each molecule of oxygen = (32 x 10^-3)/(6.022 x 10²³)

= 5.314 x 10^-26 kg

Atomicity of oxygen (O₂) molecule is 2

Mass of each atom of oxygen = 5.314 x 10^-26 /2 = 2.657 x 10^-26 kg

mass of one calcium atom in kg.

Molecular mass of calcium (Ca) = 40 g

1 mole of calcium is 40 g = 40 x 10^-3 kg

1 mole of a substance contains 6.022 x 10²³ molecules

Mass of each molecule of calcium = (40 x 10^-3)/(6.022 x 10²³)

= 6.642 x 10^-26 kg

Atomicity of calcium (Ca) molecule is 1

Mass of each atom of calcium = 6.642 x 10^-26 /1 = 6.642 x 10^-26 kg

mass of one nitrogen atom and nitrogen molecule in kg.

Molecular mass of nitrogen (N₂) = 14 x 2 = 28 g

1 mole of nitrogen is 28 g = 28 x 10^-3 kg

1 mole of a substance contains 6.022 x 10²³ molecules

Mass of each molecule of nitrogen = (28 x 10^-3)/(6.022 x 10²³)

= 4.650 x 10^-26 kg

Atomicity of nitrogen (N₂) molecule is 2

Mass of each atom of nitrogen = 4.650 x 10^-26 /2 = 2.325 x 10^-26 kg

mass of one sulphur dioxide molecule in grams.

Molecular mass of sulphur dioxide (SO₂) = 32 x 1 + 16 x 2 = 64 g

1 mole of sulphur dioxide is 64 g

1 mole of a substance contains 6.022 x 10²³ molecules

Mass of each molecule of sulphur dioxide = (64)/(6.022 x 10²³)

= 1.602 x 10^-22 kg

mass of 100 molecules of water.

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

1 mole of water is 18 g = 18 x 10^-3 kg

1 mole of a substance contains 6.022 x 10²³ molecules

Mass of each molecule of water = (18 x 10^-3)/(6.022 x 10²³) = 2.989 x 10^-26 kg

Mass of 100 molecules of water = 2.989 x 10^-26 x 100 = 2.989 x 10^-24 kg

Calculation of Volume at STP

Calculate the volume of following at STP.

8.5 x 10^-4 kg of ammonia

Molecular mass of ammonia (NH₃) = 14 x 1 + 1 x 3 = 14 + 3 = 17 g

= 17 x 10^-3 kg

Number of moles of ammonia = given mass/ molecular mass

= (8.5 x 10^-4)/(17 x 10^-3) =  0.05

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of ammonia = number of moles x 22.4

Volume of  8.5 x 10^-4 kg of ammonia at STP = 0.05 x 22.4 = 1.12 dm³

3.5 x 10^-3 kg of nitrogen

Molecular mass of nitrogen (N₂) = 14 x 2 = 28 g = 28 x 10^-3 kg

Number of moles of nitrogen = given mass/ molecular mass

= (3.5 x 10^-3)/(28 x 10^-3) =  0.125

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of nitrogen= number of moles x 22.4

Volume of  3.5 x 10^-3 kg of nitrogen at STP = 0.125 x 22.4 = 2.8 dm³

14 g of nitrogen

Molecular mass of nitrogen (N₂) = 14 x 2 = 28 g = 28 x 10^-3 kg

Number of moles of nitrogen = given mass/ molecular mass

= (14 x 10^-3)/(28 x 10^-3) =  0.5

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of nitrogen= number of moles x 22.4

Volume of  3.5 x 10^-3 kg of nitrogen at STP = 0.5 x 22.4 = 11.2 dm³

6.023 x 10²² molecules of ammonia

Number of moles of ammonia = Given molecules/ Avogadro’s  number

Number of moles of ammonia = (6.023 x 10²²)/(6.023 x 10²³) = 0.1

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of ammonia = number of moles x 22.4

Volume of 6.023 x 10²² molecules  of ammonia at STP = 0.1 x 22.4 = 2.24 dm³

2.008 x 10²³ molecules of SO₂ at STP.

Number of moles of SO₂ = Given molecules/ Avogadro’s  number

Number of moles of SO₂ = (2.008 x 10²²)/(6.023 x 10²³) = 0.3334

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of SO₂ = number of moles x 22.4

Volume of 2.008 x 10²³ molecules of SO₂ at STP = 0.3334 x 22.4 = 7.469 dm³

0.2 mole of sulphur dioxide.

1 mol of a gas at STP occupies 22.4 dm³ by volume

Volume of sulphur dioxide = number of moles x 22.4

Volume of 0.2 moles of sulphur dioxide at STP = 0.2 x 22.4 = 4.48 dm³

Science > Chemistry > Molecule and Molecular Mass > Calculation of Mass of a Molecule and an Atom