Question

Calcium carbide is used for the artificial ripening of fruits. Actually, the fruit ripens because of the heat evolved while calcium carbide reacts with moisture. During the reaction calcium hydroxide and acetylene gas are formed. If $200{\mathrm{cm}}^3$ of acetylene is formed from a certain mass of calcium carbide, find the volume of oxygen required and carbon dioxide formed during complete combustion. The combustion reaction can be represented as below:

$2{\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\to 4{\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

Answer 1

Step 1: Given information

• The volume of acetylene gas combusted is $200{\mathrm{cm}}^3$.
• The combustion reaction is as follows

$2{\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\to 4{\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

Step 2: Application of 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.
• For the given reaction, it is applied as follows

$$\begin{gathered} 2{\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\to 4{\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right) \\ 2\mathrm{vols}5\mathrm{vols}4\mathrm{vols}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}2\mathrm{vols} \end{gathered}$$

Step 3: Calculation of volume of oxygen $\left(O_2\right)$ required for combustion

• From the balanced chemical equation, it is clear that $2$ volumes of acetylene $\left({\mathrm{C}}_2{\mathrm{H}}_2\right)$ react with $5$ volumes of oxygen gas
• Therefore, $200{\mathrm{cm}}^3$ acetylene will react with $\frac{5}{2}\times 200{\mathrm{cm}}^3=500{\mathrm{cm}}^3$ of oxygen gas

Thus, $500{\mathrm{cm}}^3$ is the volume of oxygen $\mathrm{\left(}{\mathrm{O}}_{\mathrm{2}}\mathrm{\right)}$ required for combustion.

Step 4: Calculation of volume of carbon dioxide formed $\left({\mathrm{CO}}_2\right)$ during complete combustion

• From the balanced chemical equation, it is clear that $2$ volumes of acetylene $\left({\mathrm{C}}_2{\mathrm{H}}_2\right)$ on reaction form $4$ volumes of carbon dioxide gas.
• Therefore, $200{\mathrm{cm}}^3$ acetylene on reaction will form $\frac{4}{2}\times 200{\mathrm{cm}}^3=400{\mathrm{cm}}^3$ of carbon dioxide gas.

Thus, $400{\mathrm{cm}}^3$ is the volume of carbon dioxide formed $\mathrm{\left(}{\mathrm{CO}}_{\mathrm{2}}\mathrm{\right)}$ during complete combustion.