A reaction is represented by this equation: \(\mathrm{A}(a q)+2 \mathrm{B}(a q) \rightleftharpoons 2 \mathrm{C}(a q) \quad K_{c}=1 \times 10^{3}\) (a) Write the mathematical expression for the equilibrium constant. (b) Using concentrations \(\leq 1\) M, identify two sets of concentrations that describe a mixture of \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\) at equilibrium.

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no net change in the concentrations of the reactants and products over time. It is important to note that while the concentrations remain constant, the reactions are still occurring, but at the same rate in both directions.

For the reaction \(\mathrm{A}(aq) + 2\mathrm{B}(aq) \rightleftharpoons 2\mathrm{C}(aq)\), we reach equilibrium when the rate at which \(\mathrm{A}\) and \(\mathrm{B}\) combine to form \(\mathrm{C}\) is exactly balanced by the rate at which \(\mathrm{C}\) breaks down into \(\mathrm{A}\) and \(\mathrm{B}\). The equilibrium constant expression, derived from the law of mass action, quantitatively describes this balance.

The reaction quotient, \(Q\), is a measure that tells us whether a system is at equilibrium, and if not, in which direction it needs to shift to reach equilibrium. It has the same form as the equilibrium constant expression, but it uses the current concentrations of the reactants and products, which may or may not be at equilibrium.

For our reaction \(\mathrm{A} + 2\mathrm{B} \rightleftharpoons 2\mathrm{C}\), the reaction quotient is \(Q = \frac{[C]^2}{[A][B]^2}\). If \(Q < K_c\), the reaction will proceed in the forward direction to produce more products, and if \(Q > K_c\), the reaction will proceed in the reverse direction to produce more reactants until \(Q\) equals \(K_c\) when equilibrium is achieved.

Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change. This principle is vital for predicting how changes in concentration, temperature, and pressure can affect the composition of the equilibrium mixture.

Applying Le Chatelier's principle to our reaction, if more \(\mathrm{A}\) or \(\mathrm{B}\) is added to the system, the equilibrium will shift to the right, increasing the production of \(\mathrm{C}\) until a new equilibrium is established. Conversely, if some \(\mathrm{C}\) is removed, the reaction will shift to produce more \(\mathrm{C}\) in response. The changes occur in a way that partially offsets the disturbance, aligning with Le Chatelier's principle.