Question

What mass of ammonium nitrate should be heated to produce 8.96 litres of steam?
[Note: Relative molecular mass of $N{{H}_{4}}N{{O}_{3}}$ is 80]
A) 32g
B) 16g
C) 80g
D) 22.4g

Answer 1

Hint: First write the balanced chemical equation for the decomposition reaction of ammonium nitrate. 1 mole of ammonium nitrate upon heating will give 1 mol of nitrous oxide and 2 mol of steam. Volume occupied by 1mole of the gas is 22.4 litres. Then, $22.4\times 2$ litres of steam will be produced by 80 g of ammonium nitrate.

Complete answer:
Ammonium nitrate upon heating will give nitrous oxide (${{N}_{2}}O$) and steam (${{H}_{2}}O$). The balanced chemical equation for the decomposition reaction of ammonium nitrate ($N{{H}_{4}}N{{O}_{3}}$) upon heating is as shown below:
\[N{{H}_{4}}N{{O}_{3}}\to N{{O}_{2}}+2{{H}_{2}}O\]
1 mole of $N{{H}_{4}}N{{O}_{3}}$ upon heating give 1 mole of $N{{O}_{2}}$ and 2 mole of ${{H}_{2}}O$. Relative molecular mass or molecular mass of $N{{H}_{4}}N{{O}_{3}}$ is 80 g. And we know that molar volume (that is, volume of 1 mole of substance) of any gas at STP is 22.4 litres. Thus, volume of 2 moles of steam i.e., ${{H}_{2}}O$ is $22.4\times 2$ litres. We are asked to find the mass of ammonium nitrate that should be heated to produce 8.96 litres of steam. Thus, by applying unitary method:
$22.4\times 2$ litres of steam is produced by 80 g of ammonium nitrate, $N{{H}_{4}}N{{O}_{3}}$.
$\therefore $ 8.96 litres of steam will be produced by $\dfrac{80}{22.4\times 2}\times 8.96=16g$ of ammonium nitrate.
Hence, 16 g of ammonium nitrate should be heated to produce 8.96 litres of steam.

Thus, option B is the correct answer.

Note:
A balanced chemical equation is the one in which the number of atoms of each involved element on the left-hand side (reactant side) and the right hand side (product side) are equal. 1 mole of any gas occupies 22.4 litres of volume, also known as molar volume. The mass of 1 mole of substance in grams is called its molecular mass or atomic mass.