Write the equilibrium constant expression for (a) \(2 \mathrm{FeCl}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) \(+6 \mathrm{HCl}(g)\) (b) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \rightleftarrows 2 \mathrm{Fe}(l)+3 \mathrm{CO}_{2}(g)\) (c) \(\mathrm{PbSO}_{4}(s) \rightleftarrows \mathrm{Pb}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)\) (d) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}_{2} \mathrm{CO}_{3}(a q)\)

Chemical equilibrium is a dynamic state where the rate of the forward chemical reaction equals the rate of the reverse reaction. This balance means that the concentrations of the reactants and products remain constant over time. It's important to note that being at equilibrium does not imply that the reactants and products are present in equal amounts—it just means their rates of formation are the same.

In writing equilibrium constant expressions, such as those provided in the exercise solutions, we focus on the ratio of the concentrations of products over reactants, raised to the power of their coefficients from the balanced equation. For solids and pure liquids, which do not have concentrations that change in a reaction, these are omitted from the equilibrium expression. This simplicity helps us better predict how the system behaves in response to changes in conditions.

The reaction quotient, Q, serves as a predictor of which direction a reaction will proceed to reach equilibrium. It is calculated in the same way as the equilibrium constant, K, using the current concentrations of the products and reactants in the system:
\[ Q = \frac{[\text{products}]}{[\text{reactants}]} \]

Comparing Q to the equilibrium constant K helps determine the reaction's direction: if \( Q < K \), the reaction tends to form more products, moving forward. If \( Q > K \), the reaction forms more reactants, moving in reverse. If \( Q = K \), the system is at equilibrium. This understanding of Q can guide students in predicting the outcome of concentration changes without complex calculations.

Le Chatelier's Principle states that if a dynamic equilibrium system is subjected to a change in conditions (such as concentration, temperature, or pressure), the system adjusts to counteract the change and re-establish equilibrium. This is crucial for understanding how the system responds to external stresses.

For example, adding more reactant to a system at equilibrium will shift the reaction to form more product, in an attempt to 'use up' the added reactant. Conversely, increasing the product concentration tends to shift the reaction towards the reactants. Temperature changes can also affect the equilibrium position; for endothermic reactions, increasing the temperature shifts the equilibrium to the products' side.

Aqueous and gas phase reactions often have different behaviors when it comes to equilibrium. In the gas phase, pressure and volume changes can significantly influence the position of equilibrium, while in aqueous solutions, the ionic strength and solubility play a larger role.

Moreover, only the species that change concentration in the course of the reaction are included in equilibrium constant expressions. Solids, pure liquids, and solvents in excess, typically water in aqueous solutions, do not appear in these expressions. Recognizing the phase of reactants and products is essential to correctly setting up an equilibrium constant expression and understanding the system's dynamics.