Question

Indicate with an arrow the direction of the equilibrium shift and predict what will happen to the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) (increases, decreases, unchanged, need more information) when the following stresses are applied to the following exothermic reaction: \(2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g)\) The reaction is cooled. \(\mathrm{H}_{2}\) gas is added. \(\mathrm{H}_{2} \mathrm{O}\) is removed. Volume is reduced. A catalyst is added. Fe is added while the reaction temperature is increased.

Short answer

1. Cooling the system will cause the equilibrium to shift in the forward direction, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will increase. 2. Adding more \(\mathrm{H}_{2}\) gas will shift the equilibrium in the reverse direction, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will decrease. 3. Removing some \(\mathrm{H}_{2} \mathrm{O}\) will shift the equilibrium in the forward direction, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will increase. 4. Reducing the volume will not change the equilibrium, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) remains unchanged. 5. Adding a catalyst does not affect the position of the equilibrium, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will be unchanged. 6. Adding more Fe while increasing the temperature will shift the equilibrium in the reverse direction, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will decrease.

Step-by-step solution

1. Reaction Cooled

As the reaction is exothermic, cooling the system will cause the equilibrium to shift in the exothermic direction (forward) to produce heat. Direction: \(2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g)\). Thus, the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will increase.

2. \(\mathrm{H}_{2}\) Gas Added

Adding more \(\mathrm{H}_{2}\) gas increases its concentration, shifting the equilibrium in the direction that consumes it (reverse) to maintain equilibrium. Direction: \(2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \leftarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g)\). Thus, the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will decrease.

3. \(\mathrm{H}_{2} \mathrm{O}\) Removed

Removing some \(\mathrm{H}_{2} \mathrm{O}\) decreases its concentration, shifting the equilibrium in the direction that replenishes it (forward) to maintain equilibrium. Direction: \(2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g)\). Thus, the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will increase.

4. Volume Reduced

Reducing the volume will increase the pressure, which means that the reaction will shift in the direction producing fewer gas moles to minimize the pressure increase. In this reaction, there are 3 moles of gas on each side. Therefore, the equilibrium does not shift, and the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) remains unchanged.

5. Catalyst Added

Adding a catalyst does not affect the position of the equilibrium, though it increases the rate of both the forward and reverse reactions. Thus, the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will be unchanged.

6. Fe Added and Reaction Temperature Increased

Adding more Fe increases its concentration, but since it is a solid, it does not affect the equilibrium position. Increasing the temperature of an exothermic reaction will shift the equilibrium in the endothermic direction (reverse) to absorb the added heat. Direction: \(2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \leftarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g)\). Thus, the amount of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) will decrease.

Key concepts

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept that predicts how a system at equilibrium responds to changes in its conditions. According to this principle, if a dynamic equilibrium is disturbed by changing the conditions such as concentration, temperature, or pressure, the position of equilibrium will shift in order to counteract the change.

This principle is beautifully illustrated with the example of the chemical reaction between iron (Fe) and water (H₂O) gas to form iron(III) oxide (Fe₂O₃) and hydrogen (H₂) gas, which is an exothermic process. When the reaction mixture is cooled, according to Le Chatelier's principle, the system will attempt to increase the temperature by shifting the equilibrium towards the exothermic direction—in this case, towards the formation of Fe₂O₃. As a result, there's an increase in the amount of Fe₂O₃.

In contrast, when H₂ gas is added, the equilibrium shifts in the opposite direction to reduce its concentration, leading to a decrease in Fe₂O₃. Similarly, when H₂O is removed, the equilibrium will shift to produce more H₂O gas, and thus more Fe₂O₃ is formed. Le Chatelier's principle provides a critical framework for understanding how reactions adjust to maintain equilibrium.

Exothermic Reactions

Exothermic reactions are chemical processes that release heat into their surroundings. The reaction of iron with water gas to form iron(III) oxide and hydrogen gas, as presented in our earlier example, is a classic exothermic reaction. During an exothermic reaction, the enthalpy of the reactants is higher than that of the products, resulting in a release of energy.

Understanding exothermic reactions is crucial when applying Le Chatelier's principle: if temperature is one of the conditions that gets changed, the equilibrium will shift in a way to absorb that heat if it's increased (favoring endothermic reaction) or release it if it's decreased (favoring exothermic reaction). For instance, upon cooling the system, the equilibrium shifts towards the production of more Fe₂O₃ and H₂, thereby increasing the amount of Fe₂O₃. Inversely, increasing the reaction temperature induces a shift towards the reactants to absorb the excess heat, reducing the amount of Fe₂O₃ produced.

Equilibrium Shift

An equilibrium shift refers to the change in position of a reversible reaction in response to an altered condition, guiding the system back to its state of balance. When considering a reversible chemical reaction like the iron and water gas reaction, several factors such as changes in concentration, pressure, temperature, or the addition of a catalyst can cause a shift in equilibrium.

The addition of more H₂ gas shifts the equilibrium towards the reactants, while removing H₂O gas shifts it towards the products. Similarly, changing the volume or pressure of the system can cause a shift. However, in the mentioned reaction, since there is an equal number of moles of gas on both sides of the equilibrium, a change in volume or pressure does not affect the position of equilibrium because the system doesn't have a side with fewer gas moles to favor. Lastly, a catalyst does not shift equilibrium but simply allows the system to reach equilibrium faster by accelerating both the forward and reverse reactions. These scenarios exemplify how equilibrium can be shifted to maintain the balance in a dynamic system.