# Calculation of Mass of molecules, atoms and Volume at STP

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#### Example – 1:

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

#### Example – 02:

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

#### Example – 03:

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

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