Consider the reaction: $$\begin{array}{r} \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g) \\ K_{\mathrm{p}}=81.9 \text { at } 25{ }^{\circ} \mathrm{C} \end{array}$$ Calculate \(\Delta G_{\mathrm{rxn}}\) for the reaction at \(25^{\circ} \mathrm{C}\) under each of the following conditions: a. standard conditions b. at equilibrium c. \(P_{\mathrm{ICl}}=2.55 \mathrm{~atm} ; P_{\mathrm{I}_{2}}=0.325 \mathrm{~atm} ; P_{\mathrm{Cl}_{2}}=0.221 \mathrm{~atm}\)

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of the reactants and products remain constant over time, but not necessarily equal. Even though the reaction continues to occur in both directions, no net change in the amount of each substance is observed.

For the gas-phase reaction involving iodine and chlorine to form ICl, represented as \(\mathrm{I}_{2}(g) + \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g)\), equilibrium is reached when the decomposition of ICl into iodine and chlorine gases occurs at the same rate as their combination to form ICl. This concept is crucial in understanding how reactions proceed and how they can be manipulated in various scientific and industrial processes.

The equilibrium constant (\(K_p\)) is a number that expresses the relationship between the concentrations (or partial pressures in the case of gases) of the products and reactants at chemical equilibrium for a given reaction at a specific temperature. It is derived from the law of mass action, which states that for a reversible reaction at equilibrium and a constant temperature, a certain ratio of concentration terms raised to the power of their stoichiometric coefficients is constant.

In the case of our gas-phase reaction \(K_p = 81.9\), this value indicates the ratio of the partial pressures of the products to those of the reactants raised to their respective stoichiometric coefficients under standard conditions. Understanding \(K_p\) helps predict the direction and extent of a reaction, which is a powerful tool in chemistry.

The reaction quotient (\(Q\)) is a measure that indicates the current state of a reaction - how far it has proceeded towards equilibrium. It is calculated in the same way as the equilibrium constant, using the current concentrations or partial pressures of reactants and products. However, \(Q\) is not necessarily equal to the equilibrium constant \(K_p\) unless the reaction is at equilibrium.

For the reaction in question, \(Q = \frac{(P_{\text{ICl}})^2}{(P_{\text{I}_2})(P_{\text{Cl}_2})}\). If \(QK_p\), the reaction will shift to form more reactants. When \(Q = K_p\), the system is at equilibrium, and there will be no net change in the concentrations of reactants and products.

Partial pressure is the pressure that would be exerted by one of the gases in a mixture if it occupied the entire volume alone. In the context of the reaction \(\mathrm{I}_{2}(g) + \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g)\), the partial pressure of each gas (\(P_{\mathrm{ICl}}\), \(P_{\mathrm{I}_{2}}\), \(P_{\mathrm{Cl}_{2}}\)) plays a crucial role in determining the reaction quotient \(Q\) and thus the direction in which the reaction is proceeding.

Furthermore, the individual partial pressures contribute to the total pressure of the system, and understanding this can be essential for predicting the behavior of gas-phase reactions. When given the partial pressures of the reactants and products, one can calculate their respective concentrations and then determine the reaction's progress towards equilibrium.