When 1 dm ^3 of CO_2 gas is passed over hot coke, the volume of...

The reaction of carbon dioxide with hot coke is given by:

$\text{CO}_2(g) + \text{C}(s) \rightarrow 2\text{CO}(g)$

Initial volume of $\text{CO}_2 = 1$ dm$^3$

Let $x$ dm$^3$ of $\text{CO}_2$ react with hot coke.

Volume of $\text{CO}_2$ remaining $= 1 - x$ dm$^3$

Volume of $\text{CO}$ formed $= 2x$ dm$^3$

Total volume of the gaseous mixture $= (1 - x) + 2x = 1 + x$ dm$^3$

Given that the total volume after the reaction is $1.4$ dm$^3$:

$1 + x = 1.4$

$x = 0.4$ dm$^3$

Volume of $\text{CO}_2$ remaining $= 1 - 0.4 = 0.6$ dm$^3$

Volume of $\text{CO}$ formed $= 2 \times 0.4 = 0.8$ dm$^3$

The composition of the gaseous mixture is $0.8$ dm$^3$ of CO and $0.6$ dm$^3$ of $\text{CO}_2$.

Answer: $0.8$ dm$^3$ of CO, $0.6$ dm$^3$ of $\text{CO}_2$