Problems Based on Gay Lussac's Law

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Example: 1

Carbon monoxide burns in oxygen to give carbon dioxide, as per the equation:

Calculate the volume of oxygen required for the complete combustion of 30 litres of carbon monoxide. What is the volume of carbon dioxide produced?

Solution:

2 vol. : 1vol : 2 vol.

30 litres: x litres : y litres

CO : O₂ CO : CO₂

2 : 1 2 : 2

30 : x 30 : y

2x = 30 x 1 2y = 30 x 2

x = 15 y= 30

Volume of oxygen = 15 litres

Volume of carbon dioxide = 30 litres.

Example: 2

In the Haber's process nitrogen and hydrogen combine to form ammonia, according to the following equation:

200 litres of nitrogen is mixed with 1000 litres of hydrogen. Assuming all the nitrogen is used up, calculate the volume of ammonia produced, and the volume of uncombined hydrogen.

Solution:

N₂ : NH₃ N₂ : H₂

1 : 2 1 : 3

200 : x 200: y

x = 2 x 200 y= 200 x 3

x = 400 y = 600

Hence, volume of ammonia Hence, volume of hydrogen produced = 400 litres needed = 600 litres

Volume of excess hydrogen = 1000 - 600 = 400 litres.

Example: 3

About 40 g of sulphur is taken in an enclosed vessel containing 22.4 litres of oxygen. The sulphur is ignited. Calculate the volume of sulphur dioxide formed, and the mass of uncombined sulphur. (1 mole of S= 32 g: molar volume = 22.4 litres)

Solution:

O₂ : SO₂ S : O₂

1 : 1 32 g : 1 vol.

22.4 : x y : 22.4 litres or 1 mole

x = 22.4 litres y = 32 g

Volume of SO₂ produced Mass of uncombined sulphur

= 22.4 litres = 40 - 32 = 8 g

Example: 4

Methane burns in oxygen to form water vapour and carbon dioxide according to the equation:

200 ml of methane is mixed with 500 ml of oxygen and ignited. Calculate the total gaseous volume after the combustion.

Solution:

Methane : Oxygen Methane : Steam Methane : Carbon dioxide

1 : 2 1 : 2 1 : 1

200 : x 200 : y 200 : z

x= 2 x 200 y = 200 x 2 = 400 z = 200

x = 400 y = 400

Volume of oxygen Volume of steam Volume of carbondioxide used up = 400 ml = 400 ml = 200ml

Hence, the volume of uncombined oxygen

= 500 - 400

= 100 ml

Total volume of gases after combustion:

= Volume of steam + Volume of CO₂ + Volume of excess or uncombined O₂

= 400 + 200 + 100

= 700 ml.