## Q. 13.13

Applying Le Châtelier’s Principle to Concentration Changes

The reaction of iron(III) oxide with carbon monoxide occurs in a blast furnace when iron ore is reduced to iron metal:

$\mathrm{Fe}_2 \mathrm{O}_3(s)+3 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{Fe}(l)+3 \mathrm{CO}_2(g)$

Use Le Châtelier’s principle to predict the direction of the net reaction when an equilibrium mixture is disturbed by:

(a) Adding $Fe_2O_3$

(b) Removing $CO_2$

(c) Removing CO; also account for the change using the reaction quotient $Q_c$.

STRATEGY

To predict the direction of net reaction, recall that a concentration stress is relieved by reaction in the direction that consumes an added substance or replenishes a removed substance. This rule does not apply to pure solids or pure liquids because their concentrations have a constant value equal to 1.

## Verified Solution

(a) Because $Fe_2O_3$ is a pure solid, its concentration is equal to 1 and doesn’t change when more $Fe_2O_3$ is added. Therefore, there is no concentration stress and the original equilibrium is undisturbed.

(b) Le Châtelier’s principle predicts that the concentration stress of removed $CO_2$ will be relieved by net reaction from reactants to products to replenish the $CO_2$.

(c) Le Châtelier’s principle predicts that the concentration stress of removed CO will be relieved by net reaction from products to reactants to replenish the CO. The reaction quotient is

$Q_c=\frac{\left[\mathrm{CO}_2\right]_t^3}{[\mathrm{CO}]_t{ }^3}$

When the equilibrium is disturbed by reducing [CO], $Q_c$ increases, so that $Q_c$ > $K_c$. For the system to move to a new state of equilibrium, $Q_c$ must decrease—that is, [ $CO_2$ ] must decrease and [CO] must increase. Therefore, the net reaction goes from products to reactants, as predicted by Le Châtelier’s principle.