At the start of the reaction \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)\) the concentrations are \(\left[\mathrm{H}_{2}\right]=0.100 \mathrm{M},\left[\mathrm{I}_{2}\right]=0.100 \mathrm{M},[\mathrm{HI}]=0.000 \mathrm{M}\). At \(427^{\circ} \mathrm{C}\), the equilibrium concentrations are \([\mathrm{HI}]=0.158 \mathrm{M},\left[\mathrm{H}_{2}\right]=0.021 \mathrm{M},\left[\mathrm{I}_{2}\right]=0.021 \mathrm{M}\). Calculate \(K_{\mathrm{eq}}\) for this reaction.

Understanding chemical equilibrium is crucial for interpreting how reactions occur and how systems respond to changes. At the macroscopic level, chemical equilibrium occurs in a closed system when the rate of the forward reaction, where reactants turn into products, equals the rate of the reverse reaction, where products revert back to reactants.

While at equilibrium, concentrations of reactants and products remain constant over time, but this doesn't imply that the amounts of reactants and products are equal; rather, it means that they've reached a state of balance. An important aspect of chemical equilibrium is that it's dynamic. This means that even though there's no net change at the macroscopic level, on the molecular level, reactants are still being converted to products and vice versa.

For the reaction given in the exercise, \(\mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)\), the equilibrium was achieved when the rate at which \(H_2\) and \(I_2\) combine to form \(HI\) equaled the rate at which \(HI\) dissociated back into \(H_2\) and \(I_2\). Hence, although the reactants and products continuously interconvert, their concentrations do not change.

Equilibrium concentrations refer to the concentrations of reactants and products in a chemical reaction when the system has reached equilibrium. These concentrations are crucial for determining the equilibrium constant\(K_{eq}\) for that reaction, which quantifies the ratio of product concentrations to reactant concentrations at equilibrium.

In the textbook exercise, the equilibrium concentrations provided enable us to calculate the value of \(K_{eq}\). For example, the equilibrium concentration of \(HI\) was given as 0.158 M, and that of \(H_2\) and \(I_2\) was both 0.021 M. These exact values show how far the reaction has proceeded and what the balance between the reactants and products is at equilibrium. Understanding equilibrium concentrations not only helps in calculating \(K_{eq}\), but also is essential when predicting how a system will respond to stress. This response is described by Le Chatelier's principle.

Keep in mind, equilibrium doesn't mean the reactants and products have the same concentrations, but rather that their ratios are stable over time, which can be expressed by the equilibrium constant.

The reaction quotient, denoted as\(Q\), is a snapshot of a reaction at a moment in time and is used to predict the direction in which a reaction will proceed to achieve equilibrium. It is calculated using the same equation as the equilibrium constant,\(K_{eq}\), but with the concentrations of reactants and products that are not necessarily at equilibrium.

The formula is: \[Q= \frac{[\text{products}]}{[\text{reactants}]}\], characterized by stoichiometric coefficients as exponents, similar to this exercise's equilibrium constant expression. If\(Q < K_{eq}\), the forward reaction is favored to reach equilibrium. If\(Q > K_{eq}\), then the reverse reaction is favored, and if\(Q = K_{eq}\), the system is already at equilibrium.

In our exercise, had we been given non-equilibrium concentrations, we could've used \(Q\) to predict which way the reaction would need to shift to reach equilibrium. This is incredibly useful when one has to understand how changing conditions, like temperature or pressure, will affect a reaction in process.