Analysis of a reaction mixture showed that it had the composition \(0.417 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~N}_{2}\), \(0.524 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{H}_{2}\), and \(0.122 \mathrm{~mol}-\mathrm{L}^{-1} \mathrm{NH}_{3}\) at \(800 \mathrm{~K}\), at which temperature \(K_{c}=0.278\) for \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})=2 \mathrm{NH}_{3}(\mathrm{~g}) \cdot(\mathrm{a}) \mathrm{Calculare}\) the reaction quotient. (b) Is the reaction mixture at equilibrium? (c) If not, is there a tendency to form more reactants or more products?

When a chemical reaction occurs, the reactants transform into products, but under certain conditions, the products can also revert back to reactants. Chemical equilibrium is reached when the rates of the forward and reverse reactions are equal, leading to constant concentrations of both reactants and products within the system over time.

This state doesn't imply that the reactants and products are in equal concentrations, but rather that their concentrations have stabilized in a fixed proportion. Even though individual molecules are continuously reacting, there is no net change in the concentration of the species involved.

In our exercise, to determine if the reaction mixture is at equilibrium, we need to calculate the reaction quotient (Q) and compare it with the equilibrium constant (Kc). If Q equals Kc, the system is at equilibrium. If not, it indicates which direction the reaction must proceed to reach equilibrium.

The equilibrium constant (Kc) is a numerical value that relates the concentrations of reactants and products of a reaction at equilibrium at a given temperature. The formula for Kc is derived based on the balanced chemical equation. For a generic reaction: \(aA + bB \leftrightarrow cC + dD\), the equilibrium constant expression would be: \[Kc = \frac{[C]^c[D]^d}{[A]^a[B]^b}\].

Several important points should be noted about Kc: it is dimensionless, it applies only to reactions at equilibrium, and it is dependent on temperature. A Kc value greater than one suggests products are favored at equilibrium, whereas a Kc less than one suggests that reactants are favored. In the provided exercise, the Kc is given as 0.278, meaning at 800 K, the reaction moderately favors the formation of reactants.

A balanced chemical equation faithfully represents the law of conservation of mass, indicating that the number of atoms of each element is conserved in the course of a chemical reaction. It provides the stoichiometry of the reaction, which is essential for calculating the reaction quotient (Q) and the equilibrium constant (Kc).

In each balanced chemical equation, coefficient ratios express the smallest whole-number ratios of moles of reactants and products involved in the reaction. Just as the balanced equation \(N_{2}(g) + 3H_{2}(g) = 2NH_{3}(g)\) indicates that one mole of nitrogen gas reacts with three moles of hydrogen gas to produce two moles of ammonia gas, the coefficients (1, 3, and 2) are used as exponents for their respective species in the equilibrium expression.

A correctly balanced chemical equation is critical for predicting the outcome of a reaction, designing chemical processes, and calculating yields.