At \(2500 . \mathrm{K}\), the equilibrium constant is \(K_{c}=20\). for the reaction \(\mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{ClF}(\mathrm{g})\). An analysis of a reaction vessel at 2500 . \(\mathrm{K}\) revealed the presence of \(0.18 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{Cl}_{2}\), \(0.31 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~F}_{2}\), and \(0.92 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{ClF}\). Will ClF tend to form or to decompose as the reaction proceeds toward equilibrium?

The equilibrium constant, denoted as \(K_c\) in the context of concentrations, is a numerical value that represents the ratio of the concentration of products to that of reactants at equilibrium for a given chemical reaction. It is a fundamental principle in chemistry that provides insight into the extent of a reaction. For example, a high value of \(K_c\) implies that, at equilibrium, the concentration of products is greater than that of reactants, indicating that the reaction tends to go nearly to completion.

To express the equilibrium constant for a reaction, such as \(Cl_2(g) + F_2(g) \rightleftharpoons 2 ClF(g)\), you write the products over the reactants, each raised to the power of their coefficients in the balanced equation:
\[ K_c = \frac{[ClF]^2}{[Cl_2][F_2]} \]
This expression is crucial as it determines how the reaction will adjust when subjected to changes in concentration, pressure, or temperature.

The reaction quotient, \(Q_c\), is similar to the equilibrium constant but is calculated using the concentrations of the reactants and products at any point in time during the reaction, not just at equilibrium. It serves as a predictive tool to determine which way a reaction will shift to achieve equilibrium.

To calculate the reaction quotient for our given reaction, we use the same formula as for \(K_c\), but with the initial concentrations rather than the equilibrium ones:
\[ Q_c = \frac{[ClF]^2}{[Cl_2][F_2]} \]
By comparing \(Q_c\) to \(K_c\), we can predict the reaction's direction. If \(Q_c < K_c\), there are more reactants than at equilibrium, so the reaction will proceed forward, forming more products. Conversely, if \(Q_c > K_c\), the reaction will move in reverse to produce more reactants. This comparison helps in analyzing how the system will change over time.

Le Chatelier's principle provides a qualitative understanding of how a system at equilibrium responds to external changes. When a chemical system at equilibrium experiences a change in concentration, pressure, or temperature, the equilibrium position will shift to counteract that change.

For instance, if the concentration of a reactant is increased, the system will respond by consuming reactants to form more products, shifting the equilibrium position to the right. On the other hand, if the pressure is increased by decreasing the volume, the system will favor the side with fewer gas moles. Temperature changes can also have a profound effect; heating typically favors the endothermic direction of a reaction while cooling favors the exothermic direction.

Applying Le Chatelier's principle to the problem at hand, if the reaction vessel were heated, we'd expect the forward, endothermic reaction to be favored, and more \(ClF\) to form. If additional \(Cl_2\) or \(F_2\) were introduced, the system would adjust by forming more \(ClF\), shifting the equilibrium to the right, following the predictive indications of \(Q_c\) and \(K_c\).