Carbon monoxide combines with oxygen to form carbon dioxide according to the following equation:
$2 CO + O_{2} \to 2 {CO}_{2}$
$200 {cm}^{3}$ of carbon monoxide is mixed with $200 {cm}^{3}$ of oxygen and the mixture explodes. If the resulting gas is brought to the original temperature and pressure, what will be the volume and composition of the gas obtained after explosion?

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Solution

Step 1: Given information
$200 {cm}^{3}$ of oxygen $(O_{2})$
$200 {cm}^{3}$ of carbon monoxide $(CO)$
The given reaction is as follows:
$2 CO + O_{2} \to 2 {CO}_{2}$
Step 2: Gay-Lussac's Law of combining volumes
According to this law, when gases react to form new gases, the ratio of the volume of gaseous reactants to the gaseous products is expressed as a simple whole-number ratio. The conditions required are constant pressure and temperature.
This law is only applicable to gases. As a result, the volumes of solids and liquids are assumed to be zero.
The balanced chemical reaction is as follows:
$2 CO (g) + O_{2} (g) \to 2 {CO}_{2} (g) 2 vols 1 vol 2 vols$
Step 3: Calculation of the volume of unreacted oxygen
From the balanced equation, it is clear that $2$ volumes of carbon monoxide require $1$ volume of oxygen.
Therefore, $200 {cm}^{3}$ of carbon monoxide will require $\frac{1}{2} \times 200 {cm}^{3} {=100cm}^{3}$ volume of oxygen.
The volume of unreacted oxygen is $= (200 - 100) {cm}^{3} {=100cm}^{3}$
Step 4: Calculation of volume of carbon dioxide formed
From the balanced equation, it is clear that $2$ volumes of carbon monoxide produces $2$ volume of carbon dioxide.
Therefore, $200 {cm}^{3}$ of carbon monoxide will produce $\frac{2}{2} \times 200 {cm}^{3} {=200cm}^{3}$ volume of carbon dioxide.
Hence, the volume of carbon dioxide so formed is $200 {cm}^{3}$ , and $100 {cm}^{3}$ of unreacted oxygen is present.

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