At 100°C, the equilibrium constant for the reaction COCl₂(𝑔) ⇌ CO(𝑔) + Cl₂(𝑔) has the value 𝐾_𝑐 = 2.19×10⁻¹⁰. Are the following mixtures of COCl₂, CO, and Cl₂ at 100°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium.
(a) [COCl₂] = 2.00×10⁻³ M, [CO] = 3.3×10⁻⁶ M, [Cl₂] = 6.62×10⁻⁶ M
(b) [COCl₂] = 4.50×10⁻² M, [CO] = 1.1×10⁻⁷ M, [Cl₂] = 2.25×10⁻⁶ M
(c) [COCl₂] = 0.0100 M, [CO] = [Cl₂] = 1.48×10⁻⁶ M

Verified step by step guidance

1. Calculate the reaction quotient, Qc, using the formula Qc = \frac{[CO][Cl_2]}{[COCl_2]}.
2. Substitute the given concentrations into the expression: Qc = \frac{(3.3 \times 10^{-6} \text{ M})(6.62 \times 10^{-6} \text{ M})}{2.00 \times 10^{-3} \text{ M}}.
3. Compare the calculated Qc with the given equilibrium constant Kc = 2.19 \times 10^{-10}.
4. If Qc < Kc, the reaction will proceed in the forward direction to reach equilibrium. If Qc > Kc, the reaction will proceed in the reverse direction.
5. If Qc = Kc, the system is already at equilibrium.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction COCl₂(g) ⇌ CO(g) + Cl₂(g), Kc = [CO][Cl₂] / [COCl₂]. A small Kc value, such as 2.19×10⁻¹⁰, indicates that at equilibrium, the concentration of reactants is much greater than that of products, suggesting the reaction favors the reactants.

Reaction Quotient (Q)

The reaction quotient (Q) is calculated using the same formula as Kc but with the current concentrations of the reactants and products, regardless of whether the system is at equilibrium. By comparing Q to Kc, one can determine the direction in which the reaction will proceed to reach equilibrium. If Q < Kc, the reaction shifts to the right (toward products); if Q > Kc, it shifts to the left (toward reactants).

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium in a chemical reaction, guiding the understanding of how the reaction will shift in response to the concentrations of COCl₂, CO, and Cl₂.