At \(100^{\circ} \mathrm{C}\) the equilibrium constant for the reaction \(\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)\) has the value \(K_{c}=\) \(2.19 \times 10^{-10} .\) Are the following mixtures of \(\mathrm{COCl}_{2}, \mathrm{CO}\) and \(\mathrm{Cl}_{2}\) at \(100^{\circ} \mathrm{C}\) at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium. (a) \(\quad\left[\mathrm{COCl}_{2}\right]=2.00 \times 10^{-3} \mathrm{M}, \quad[\mathrm{CO}]=3.3 \times 10^{-6} \mathrm{M},\) \(\left[\mathrm{Cl}_{2}\right]=6.62 \times 10^{-6} \mathrm{M} ;\) (b) \(\left[\mathrm{COCl}_{2}\right]=4.50 \times 10^{-2} \mathrm{M}\) \([\mathrm{CO}]=1.1 \times 10^{-7} \mathrm{M},\left[\mathrm{Cl}_{2}\right]=2.25 \times 10^{-6} \mathrm{M} ;(\mathrm{c})\left[\mathrm{COCl}_{2}\right]=\) \(0.0100 M,[\mathrm{CO}]=\left[\mathrm{Cl}_{2}\right]=1.48 \times 10^{-6} \mathrm{M}\)

The equilibrium constant, represented as K_c, is a fundamental concept in chemical equilibrium that characterizes the composition of the reaction mixture at equilibrium. It is a specific value that depends on the temperature for any balanced chemical equation. In simple terms, it tells us the ratio of the concentration of products to reactants at equilibrium for a reaction that can occur in both forward and reverse directions.

For the reaction COCl₂(g) ⇌ CO(g) + Cl₂(g), the equilibrium constant K_c is expressed as:
K_c = \( \frac{[CO][Cl_2]}{[COCl_2]} \) (here [X] denotes the concentration of X).

The specified K_c of \(2.19 \times 10^{-10}\) at \(100^\circ C\) means that at this temperature, when the system achieves equilibrium, the concentrations of CO, Cl₂, and COCl₂ will have constants that fit into this formula to yield the given K_c. Understanding this concept allows students to predict the direction in which a reaction in a non-equilibrium state will shift to achieve equilibrium.

The reaction quotient, Q_c, is like the equilibrium constant, K_c, except it applies to any point in time during the reaction and not just at equilibrium. It is a snapshot of a moment during the reaction process, indicating whether the system is at equilibrium or which direction it needs to shift to reach equilibrium.

Q_c is calculated exactly the same way we calculate K_c, using the current concentrations of the reactants and products. When you compare Q_c to K_c, you can determine the reaction's progress:

• If Q_c = K_c, the system is at equilibrium.
• If Q_c > K_c, there are more products than expected, and the reaction will shift in reverse to reach equilibrium.
• If Q_c < K_c, there are fewer products than expected, and the reaction will shift forward to produce more products and reach equilibrium.

This analytical tool is vital for predicting the movement of reactions under different conditions and helps students understand chemical kinetics and equilibria beyond mere memorization of static values.

The equilibrium state of a chemical reaction is the condition in which the rate of the forward reaction equals the rate of the reverse reaction. At equilibrium, the concentrations of the reactants and products remain constant over time. It's important not to confuse this with the idea that reactions stop at equilibrium; in reality, both forward and reverse reactions continue to occur but at equal rates so that the overall quantities of reactants and products do not change.

Identifying whether a system is at equilibrium involves comparing the reaction quotient, Q_c, with the equilibrium constant, K_c. As shown in the exercise, if the calculated Q_c matches K_c for a given temperature, the system is in equilibrium. If not, the direction in which the reaction must shift is indicated by the relative sizes of Q_c and K_c. This understanding is crucial because students often think that equilibrium means equal concentrations of reactants and products, which is not always the case. It means no net change in concentrations.