Question

What volume of hydrogen gas, at 273 K and 1 atm pressure will be consumed in obtaining 21.6 g of elemental boron (atomic mass 10.8) from reduction of Boron trichloride by hydrogen?
a) 67.2 L
b) 44.8 L
c) 22.4 L
d) 89.6 L

Answer 1

Hint: Write the reaction for the reduction of Boron trichloride by hydrogen. Then balance the equation and find the right stoichiometric coefficients. Using this, relate the reacting moles to volume using Avogadro’s hypothesis.

Complete step by step answer:
The reaction for reduction of Boron trichloride from hydrogen can be written as –
$2BC{{l}_{3}}+3{{H}_{2}}\to 2B+3HCl$
As we can see, 2 moles of Boron trichloride reacts with 3 moles of dihydrogen to produce 2 moles of elemental boron and 3 moles of hydrochloric acid.
Given, atomic mass of Boron = 10.8 u
Therefore, mass of 2 moles of Boron = 2 x 10.8 g = 21.6 g
So, we can say that –
3 moles of Hydrogen $({{H}_{2}})$ at STP reacts with 2 moles of Borontrichloride$(BC{{l}_{3}})$ to give 21.6 g of Boron$(B)$.
According to Avogadro’s hypothesis, 1 mole of any gas at STP occupies 22.4 L volume.
Since 3 moles of hydrogen gas reacts, therefore we need to calculate volume occupied by 3 moles of hydrogen.
Hence, 3 moles will occupy 3 x 22.4 L = 67.2 L
Therefore, the answer is – option (a) – The volume of hydrogen gas is 67.2 L.

Note: “In 1811, Amadeo Avogadro explained that the volumes of all gases can be easily determined. Avogadro's hypothesis states that equal volumes of all gases at the same temperature and pressure contain equal numbers of particles. Since the total volume that a gas occupies is made up primarily of the empty space between the particles, the actual size of the particles themselves is nearly negligible”.