Question

One litre ${\mathrm{CO}}_2$ is passed through red hot coke. the volume becomes 1.4 liters at the same temperature and pressure. Write the composition of the product

Answer 1

Step 1: Initial ${\mathrm{CO}}_2$volume

Coke reacts with Carbon dioxide such that coke is reduced to Carbon monoxide.

The chemical reaction of coke that is Carbon with Carbon dioxide(${\mathrm{CO}}_2$) gives two moles of Carbon monoxide($\mathrm{CO}$).

$\underset{\mathrm{Carbon}\mathrm{dioxide}}{{\mathrm{CO}}_2\left(\mathrm{g}\right)}+\underset{\mathrm{Coke}}{\mathrm{C}\left(\mathrm{s}\right)}\to \underset{\mathrm{Carbon}\mathrm{monoxide}}{2\mathrm{CO}\left(\mathrm{g}\right)}$

Therefore, $\mathrm{x}$ litres of Carbon dioxide reacts with the Carbon and give $2\mathrm{x}$ litres of Carbon monoxide

The total volume of the mixture is equal to the sum of the volume of ${\mathrm{CO}}_2$ and $\mathrm{CO}$.

The given volume is $1.4$liters.

Thus the new volume of the Carbon dioxide would be equal to the difference in the initial volume of the Carbon dioxide reacted,

That is ${\mathrm{V}}_{\left(\mathrm{new}\mathrm{volume}\mathrm{of}{\mathrm{CO}}_2\right)}=\mathrm{V}\left(\mathrm{initial}\mathrm{volume}\mathrm{of}{\mathrm{CO}}_2\right)-\mathrm{V}\left(\mathrm{reacted}{\mathrm{CO}}_2\right)=(1-\mathrm{x})\mathrm{L}$

Therefore,

$$\begin{gathered} (1-x)+2x=1.4 \\ 1+x=1.4 \\ x=1.4-1 \\ x=0.4 \end{gathered}$$

That is, the volume of the Carbon dioxide is $\mathrm{x}=0.4\mathrm{L}$

Step 2: Composition of the product

The new volume of the Carbon dioxide is $\left(1-\mathrm{x}\right)=1-0.4=0.6\mathrm{L}$

The volume of the Carbon monoxide is $2\mathrm{x}=2\times 0.4=0.8\mathrm{L}$

Therefore, the composition of the product obtained by the reaction of one litre of Carbon dioxide with coke is $0.6\mathrm{L}$ of Carbon dioxide and $0.8\mathrm{L}$ of Carbon monoxide.