Question

Each of water gas and oxygen are ignited $100{\text{cc}}$, and the resultant mixture of gases cooled to room temperature. Calculate the composition of the resultant mixture. (water gas contains $CO$ and ${H_2}$ in equal ratio).

Answer 1

Hint: It is given to us in the question that water gas is a mixture of carbon monoxide and hydrogen and both the gases are present in equal amounts. Thus, we can find the amounts of carbon monoxide and hydrogen easily by finding the total amount of water gas and then dividing its value by 2.

Complete step by step solution:
The reaction taking place can be written as
$CO(g) + {H_2}(g) + {O_2}(g) \to C{O_2}(g) + {H_2}O(l)$
Thus, we can see that one mole each of carbon monoxide, hydrogen and oxygen gases react to form one mole each of carbon dioxide gas and water, or we can say that two moles of water gas react with one mole of oxygen gas to produce one mole each of the products carbon dioxide and water.
We are given the volume of water gas $ = 100{\text{cc}}$ and the volume of oxygen $ = 100{\text{cc}}$ in the question.
Since water gas contains equal amounts of $CO$ and ${H_2}$, thus, we can say that,
Volume of $CO = $ volume of ${H_2} = 50{\text{cc}}$
From the reaction, we can see that the carbon monoxide and hydrogen gas are limiting reagents. After completion of the reaction, $50{\text{cc}}$ of $CO$,${H_2}$ and ${O_2}$ are used up producing $50{\text{cc}}$ of $C{O_2}$.
The initial amount of oxygen was $100{\text{cc}}$.
Thus, the composition of the resultant mixture is $50{\text{cc of }}{{\text{O}}_2} + 50{\text{cc of C}}{{\text{O}}_2}$.

Note: We know from Avogadro’s law that at a fixed temperature and pressure, the number of moles of a gas is directly proportional to the volume of the gas. In other words, we can say that an equal number of moles of gases occupy equal volumes under fixed temperature and pressure conditions.