The equilibrium constant \(K_{\mathrm{c}}\) for the reaction \(2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) is 0.83 at \(375^{\circ} \mathrm{C} . \mathrm{A}\) 14.6-g sample of ammonia is placed in a 4.00 -L flask and heated to \(375^{\circ} \mathrm{C}\). Calculate the concentrations of all the gases when equilibrium is reached.

Mastering the ICE table method is a must when dealing with chemical equilibria. The acronym ICE stands for Initial, Change, and Equilibrium, which are the columns used to track the concentration of reactants and products through the process of a reaction reaching equilibrium. The table starts by listing the initial concentrations of reactants and products. After this, we factor in the stoichiometry to determine the changes that occur as substances react. The 'Change' row typically incorporates variables that represent how concentration shifts relative to the stoichiometry of the balanced reaction. Lastly, the 'Equilibrium' row tallies these changes to provide a snapshot of the system when it stabilizes. It's a systematic way to visualize the shift from initial to equilibrium states, which then sets the stage for calculations involving the equilibrium constant.

An ICE table was utilized in the textbook problem to assist in calculating the equilibrium concentrations of ammonia, nitrogen, and hydrogen. By applying stoichiometry, we can denote the interdependence of these concentrations; once the equilibrium constant is introduced, we have a solvable equation to find the unknown variables.

When dealing with equilibrium systems, it's crucial to understand Le Chatelier's Principle. This principle states that if an external condition is applied to a system at equilibrium, the system will adjust itself to partially offset the change. This could involve changes in concentration, temperature, or pressure, and the system will respond to re-establish equilibrium. For instance, if more reactants are added, the system will produce more products, and vice versa.

In the context of our textbook problem, if the system at equilibrium at 375°C for the reaction involving ammonia, nitrogen, and hydrogen were subjected to a change, like a pressure increase, Le Chatelier's Principle predicts the system's shift towards the side with fewer moles of gas to reduce pressure. Understanding this principle helps predict the behavior of the reaction under different conditions, which is invaluable for manipulating reactions to favor the desired outcome.

Why Stoichiometry Is Key in Equilibrium Calculations

Stoichiometry forms the foundation of chemical reactions. It involves the quantitative relationship between reactants and products in a reaction. This relationship follows the balanced chemical equation and dictates how much of one substance reacts with another to form products. For equilibrium calculations, stoichiometry tells us the proportionate amounts of reactants that convert to products, guiding us in setting up conversion factors that help calculate the extent of a reaction.

In our exercise, the reaction of ammonia decomposing into nitrogen and hydrogen follows a clear stoichiometric pattern: for every 2 moles of ammonia that react, 1 mole of nitrogen and 3 moles of hydrogen are produced. This ratio is pivotal as it influences the coefficients used in the ICE table and is applied in calculating equilibrium concentrations.

The equilibrium expression formalizes the relationship between the concentrations of reactants and products. For a given reaction, the equilibrium constant, denoted as K_c (when concentrations are used) or K_p (when partial pressures are used), remains constant at a specific temperature. The general form for a reaction \(aA + bB \rightleftharpoons cC + dD\) is \[K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}\] where the concentrations of products are raised to their respective coefficients in the balanced equation and divided by the concentrations of reactants, each also raised to their respective coefficients.

The equilibrium constant for our ammonia reaction was given as 0.83, and the equilibrium expression for the reaction was used to solve for x, which represented the equilibrium concentration changes. Understanding how to craft and apply the equilibrium expression is crucial for solving equilibrium problems, as it embodies the quantitative aspects of the chemical equilibrium.