Analysis of the gases in a sealed reaction vessel containing \(\mathrm{NH}_{3}, \mathrm{N}_{2},\) and \(\mathrm{H}_{2}\) at equilibrium at \(400^{\circ} \mathrm{C}\) established the concentration of \(\mathrm{N}_{2}\) to be \(1.2 \mathrm{M}\) and the concentration of \(\mathrm{H}_{2}\) to be \(0.24 \mathrm{M}\). \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \quad K_{c}=0.50\) at \(400^{\circ} \mathrm{C}\) Calculate the equilibrium molar concentration of \(\mathrm{NH}_{3}\)

Understanding the equilibrium constant, often represented as Kc, is crucial in the study of chemical reactions that have reached a state of balance. At an established temperature, the equilibrium constant is a value that quantifies the ratio of the concentration of products to the concentration of reactants, each raised to the power of their stoichiometric coefficients in a balanced equation.

In the given exercise, the equilibrium constant for the reaction between N₂ and H₂ forming NH₃ is provided as Kc = 0.50 at 400°C. The key to understanding this is recognizing that a Kc value provides insight into the favorability of the forward or reverse reactions. If the value of Kc is high, the formation of products is favored, and if it is low, the reactants are favored.

To apply this concept to the problem, you would set up the equilibrium constant expression using the molar concentrations of the gases involved (see the given formula in the solution). It is this relationship that allows us to determine the unknown concentration of NH₃, based on the equilibrium constant and the concentrations of N₂ and H₂.

Molar concentration, symbolized as M and also known as molarity, is a measure of the concentration of a solute in a solution. It represents the moles of a substance per liter of solution. This concept is essential in stoichiometry and calculations involving chemical reactions because it allows chemists to quantify the amount of reactants and products.

In the exercise, you're provided with the molar concentrations of nitrogen gas, N₂, (1.2 M) and hydrogen gas, H₂, (0.24 M). These values become the input you need to calculate the equilibrium concentration of ammonia, NH₃. Accuracy in measuring and understanding molar concentrations is key for correctly solving many chemical equilibrium problems.

To find the unknown concentration of NH₃, the molar concentrations of the known substances are substituted into the equilibrium expression, which illustrates the importance of molar concentration in determining the position of equilibrium.

The reaction quotient, denoted Qc, is akin to the equilibrium constant, Kc, but for a reaction that has not necessarily reached equilibrium. It is calculated using the same formula as Kc but with the initial concentrations of the reactants and products. Qc is instrumental in predicting the direction the reaction will shift to reach equilibrium.

If Qc is less than Kc, the reaction will proceed in the forward direction to produce more products. Conversely, if Qc is greater than Kc, the reaction will shift in the reverse direction to produce more reactants.

In the context of our exercise, once the reaction reaches equilibrium, Qc equals Kc, allowing for the system's equilibrium concentrations to be calculated. This condition is crucial to solving for NH₃'s concentration and provides the bridge between the initial reaction conditions and the established equilibrium state.