Question

Phosphine ($P{H_3}$) decomposes to produce vapours of phosphorus and ${H_2}$ gas. What will be the change in volume when $100mL$ of phosphine is decomposed?
A. $+ 50mL$
B. $500mL$
C. $+ 75mL$
D. $- 500mL$

Answer 1

Phosphine is a colorless, odorless gas with very high toxicity. The thermal decomposition of phosphine generates phosphorus and hydrogen as products. The phosphorus is a solid and the hydrogen is gas. For determining the change in volume the gas phase has to be considered neglecting the solid phase.

Complete step by step answer: In order to find the change in volume, the decomposition of phosphine has to be understood clearly. The reaction of decomposition of phosphine can be written as:
$4P{H_3} \to {P_4} + 6{H_2}$
The balanced chemical reaction indicates that four moles of phosphine generates one mole of phosphorus and six moles of hydrogen.
The phosphorus exists as a triatomic molecule in elemental form. It is a solid and hence its volume change is negligible according to gas laws.
The volume of phosphine given is$100mL$. The amount of hydrogen produced can be calculated as:
Amount of hydrogen = $\dfrac{6}{4} \times$ amount of phosphine
= $\dfrac{6}{4} \times 100mL$
=$150mL$.
Thus $100mL$ of phosphine gas generates $150mL$ of hydrogen gas.
The change in volume = $150 - 100$
=$50mL$.
So, the correct answer is “Option A”.

Note: Decomposition reaction is very common in everyday life. It is the reverse of the synthesis reaction. The digestion of food in humans is the very common decomposition reaction. The products like carbon, hydrogen, nitrogen, oxygen, carbon dioxide, water etc are simple molecules produced from decomposition reactions. The decomposition reactions are further classified in three types as thermal decomposition, electrolytic decomposition and photo decomposition or photolysis.