One of the reaction that takes place in producing steel from iron ore is the reduction of iron (II) oxide by carbon monoxide to give iron metal and $\mathrm{CO}_2$. $\mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g}) ;$ $K_p=0.265$ atm at $1050 \mathrm{~K}$ What are the equilibrium partial pressures of $\mathrm{CO}$ and $\mathrm{CO}_2$ at $1050 \mathrm{~K}$ if the initial partial pressures are : $\mathrm{p}_{\mathrm{CO}}=1.4$ atm and $\mathrm{p}_{\mathrm{CO}_2}=0.80 \mathrm{~atm} ?$

Question

One of the reaction that takes place in producing steel from iron ore is the reduction of iron (II) oxide by carbon monoxide to give iron metal and $\mathrm{CO}_2$. $\mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g}) ;$ $K_p=0.265$ atm at $1050 \mathrm{~K}$ What are the equilibrium partial pressures of $\mathrm{CO}$ and $\mathrm{CO}_2$ at $1050 \mathrm{~K}$ if the initial partial pressures are : $\mathrm{p}_{\mathrm{CO}}=1.4$ atm and $\mathrm{p}_{\mathrm{CO}_2}=0.80 \mathrm{~atm} ?$,

MARKS App · Accepted Answer

$\mathrm{Q}_p=\frac{\mathrm{P}_{\mathrm{CO}_2}}{\mathrm{P}_{\mathrm{CO}}}=\frac{0.80}{1.4}=0.571$ As $\mathrm{Q}_{\mathrm{p}}>\mathrm{K}_{\mathrm{p}}$, reaction will move in the backward direction, i.e. pressure of $\mathrm{CO}_2$ will decrease and that of $\mathrm{CO}$ will increase to attain equilibrium. Hence, if $\mathrm{P}$ is decrease in pressure of $\mathrm{CO}_2$, increase in pressure of $\mathrm{CO}=\mathrm{P}$ At equilibrium, $\mathrm{P}_{\mathrm{CO}_2}=(0.80-\mathrm{P})$ atm, $\mathrm{P}_{\mathrm{CO}}=(1.4+\mathrm{P}) \mathrm{atm}$ $\mathrm{K}_{\mathrm{p}}=\frac{\mathrm{P}_{\mathrm{co}_2}}{\mathrm{P}_{\mathrm{co}}} \therefore 0.265=\frac{0.80-\mathrm{P}}{1.4+\mathrm{P}}$ or $0.265(1.4+\mathrm{P})=0.80-\mathrm{P}$ or $0.371+0.265 \mathrm{P}=0.80-\mathrm{P}$ or $1.265 \mathrm{P}=0.429$ or $\mathrm{P}=0.339$ at equilibrium $\therefore \quad \mathrm{P}_{\mathrm{CO}}=1.4+0.339=1.739 \mathrm{~atm}$ and $\mathrm{P}_{\mathrm{CO}_2}=0.80-0.339=0.461 \mathrm{~atm}$

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