Le Châtelier noted that many industrial processes of his time could be improved by an understanding of chemical equilibria. For example, the reaction of iron oxide with carbon monoxide was used to produce elemental iron and \(\mathrm{CO}_{2}\) according to the reaction $$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)$$ Even in Le Châtelier's time, it was noted that a great deal of CO was wasted, expelled through the chimneys over the furnaces. Le Châtelier wrote, "Because this incomplete reaction was thought to be due to an insufficiently prolonged contact between carbon monoxide and the iron ore [oxide], the dimensions of the furnaces have been increased. In England they have been made as high as thirty meters. But the proportion of carbon monoxide escaping has not diminished, thus demonstrating, by an experiment costing several hundred thousand francs, that the reduction of iron oxide by carbon monoxide is a limited reaction. Acquaintance with the laws of chemical equilibrium would have permitted the same conclusion to be reached more rapidly and far more economically." What does this anecdote tell us about the equilibrium constant for this reaction?

Step by step solution

01

Understand the given reaction

The reaction is given as follows: \[\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)\] Hence, iron oxide (Fe2O3) reacts with carbon monoxide (CO) to form elemental iron (Fe) and carbon dioxide (CO2).

02

Analyze the equilibrium constant in terms of reactants and products

The equilibrium constant, Kc, can be expressed as the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their stoichiometric coefficients: \[K_c = \frac{[\mathrm{CO}_{2}]^3}{[\mathrm{CO}]^3}\] As Fe2O3 and Fe are solids, their concentrations remain constant and do not affect the equilibrium constant.

03

Analyze the anecdote and apply Le Châtelier's principle

The anecdote tells us that even after increasing the dimensions of the furnaces, the proportion of carbon monoxide escaping has not diminished. This indicates that the reaction does not shift towards the products significantly when there is an increase in the contact of carbon monoxide and iron oxide. According to Le Châtelier's principle, if the system is disturbed by changes in concentration, pressure or temperature, the equilibrium will shift to minimize the effect of the disturbance. In this case, the increase in furnace size is like increasing the pressure, which should have forced the reaction to shift towards the side with fewer gas molecules (i.e., the side with iron oxide and carbon monoxide).

04

Conclusions about the equilibrium constant

Since the proportion of escaping carbon monoxide has not diminished even after increasing the furnace dimensions, it implies that the equilibrium constant Kc is relatively small. A small Kc value indicates that the reaction mixture at equilibrium contains a larger concentration of reactants (Fe2O3 and CO) compared to the products (Fe and CO2), which in turn means the reaction is limited and not complete. Therefore, the anecdote tells us that the equilibrium constant for the reaction of iron oxide with carbon monoxide is relatively small, indicating an incomplete or limited reaction where reactants do not completely transform into products.

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