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The equilibrium constant, denoted as \(K_c\), is a vital concept in chemical equilibrium that helps us understand the extent of a reaction at a given temperature. It is determined by the concentrations of the reactants and products at equilibrium. For the reaction \(3\text{O}_2(g) \rightleftharpoons 2\text{O}_3(g)\), the equilibrium constant expression is written as:
\[K_c = \frac{[\text{O}_3]^2}{[\text{O}_2]^3}\]
This formula relates the concentrations of ozone \([\text{O}_3]\) and oxygen \([\text{O}_2]\) when the system is in equilibrium. A reaction with a very low \(K_c\), such as \(2.0 \times 10^{-50}\), suggests that at equilibrium, the concentration of products (ozone) is much smaller compared to that of reactants (oxygen).

• The \(K_c\) value remains constant for a given temperature and specific reaction.
• It provides insight into which side of the reaction is favored at equilibrium.
• A tiny \(K_c\) typically indicates that the reaction doesn't proceed significantly to the products side under the given conditions.

Ozone concentration in an equilibrium system tells us the amount of ozone present when the reaction reaches a stable state. In our reaction, the equilibrium concentration of ozone, denoted as \([\text{O}_3]\), can be calculated once we know the \(K_c\) and the concentration of oxygen \([\text{O}_2]\).
For the problem, the equilibrium concentration of oxygen is given as \(1.6 \times 10^{-2} \text{ M}\). Substituting this and the \(K_c\) value into the equilibrium expression allows us to solve for \([\text{O}_3]\). The small value of \([\text{O}_3]\), calculated to be \(2.86 \times 10^{-28} \text{ M}\), reflects the reaction's strong preference for remaining as oxygen.

• Concentration is often measured in molarity (M), which is moles of solute per liter of solution.
• The incredibly small ozone concentration means that under these conditions, very little ozone forms.
• Adjustments in temperature or pressure could affect these concentrations significantly.

The reaction quotient \(Q\) is similar to the equilibrium constant, but it is used to assess the state of a reaction at any point in time, not just at equilibrium. For the reaction between \(3\text{O}_2(g)\) and \(2\text{O}_3(g)\), the expression for \(Q\) is the same as for \(K_c\):
\[Q = \frac{[\text{O}_3]^2}{[\text{O}_2]^3}\]
The difference is that \(Q\) can be calculated using initial concentrations. Comparing \(Q\) to \(K_c\) indicates the reaction's progress:

• If \(Q = K_c\), the system is at equilibrium.
• If \(Q < K_c\), the reaction will proceed forward to produce more products.
• If \(Q > K_c\), the reaction will shift to form more reactants.

Understanding \(Q\) helps predict the direction in which a reaction must proceed to reach equilibrium and it is a powerful tool in managing chemical reactions.