In a given experiment, \(5.2\) moles of pure NOCl was placed in an otherwise empty \(2.0-\mathrm{L}\) container. Equilibrium was established by the following reaction: $$ 2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \quad K=1.6 \times 10^{-5} $$ a. Using numerical values for the concentrations in the Initial row and expressions containing the variable \(x\) in both the Change and Equilibrium rows, complete the following table summarizing what happens as this reaction reaches equilibrium. Let \(x=\) the concentration of \(\mathrm{Cl}_{2}\) that is present at equilibrium. b. Calculate the equilibrium concentrations for all species.

The equilibrium constant, denoted as K, is a vital figure in chemistry as it quantifies the extent of a chemical reaction at equilibrium. For the reaction illustrated as
\(2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g) + \mathrm{Cl}_{2}(g)\),
the equilibrium constant expression is constructed by raising the concentrations of the products to their stoichiometric coefficients and dividing by the concentration of the reactants similarly raised. Symbolically, this is represented as:
\[K = \frac{[\mathrm{NO}]^2 \times [\mathrm{Cl}_{2}]}{[\mathrm{NOCl}]^2}\].
Here, the square brackets denote the concentration of the gaseous species at equilibrium, and the raised powers correspond to their respective coefficients in the balanced equation. In our problem, K is given as \(1.6 \times 10^{-5}\), signifying the reaction favors the reactants at equilibrium due to its small value.

Initial concentration refers to the amount of reactant or product present in a reaction mixture before any reaction has taken place. In our example, the initial concentration of NOCl is calculated by dividing the initial number of moles by the volume of the container. The calculation is simple:
\[\text{Initial Concentration} = \frac{\text{moles of NOCl}}{\text{Volume of the container}}\].
With \(5.2\) moles of NOCl in a \(2.0-\mathrm{L}\) container, the concentration starts at \(2.6\) M. Initially, NO and Cl₂ are not present hence their concentrations are \(0\) M.

An ICE table is an organized way to apply stoichiometry to track changes in concentration over the course of a reaction until it reaches equilibrium. ICE stands for Initial, Change, and Equilibrium. It starts with the Initial concentrations, then considers the Changes that occur as the system reaches equilibrium, and finally, the Equilibrium concentrations. In our case, the ICE table is set up with the initial concentrations of NOCl, changes (-2x for NOCl and +2x for NO, +x for Cl₂ due to the stoichiometry of the reaction), and expressions using x for the equilibrium concentrations. This provides the necessary framework to solve for x, where x represents the increase in concentration of Cl₂ at equilibrium. Once x is determined through the equilibrium constant expression, it can be plugged back into the equilibrium expressions to find the exact concentrations of all substances at equilibrium.

Equilibrium concentration is the concentration of each reactant and product in a chemical reaction mixture at the state of equilibrium. By using the ICE table and the value of x determined from the equilibrium constant, one can calculate these concentrations. The equilibrium concentration of NOCl is obtained by subtracting 2x from its initial concentration, while that of NO and Cl₂ is obtained by multiplying their change by x. As shown in the solution steps, the final equilibrium concentrations are \(2.59704\) M for NOCl, \(2.96 \times 10^{-3}\) M for NO, and \(1.48 \times 10^{-3}\) M for Cl₂. Accurate calculation of these concentrations is critical for predicting how a system responds to changes in conditions and for applications in chemical engineering and research.