- Compare the reaction quotient \(Q = 525\) with the equilibrium constant \(K = 46.3\).
- Recognize that \(Q > K\) implies the system has an excess of products relative to the equilibrium state.
- Determine that the reaction proceeds in the reverse direction to consume products and form reactants to reach equilibrium.
- Conclude that the equilibrium shifts to the left, which corresponds to option \(\boxed{b}\).
Explanation
- Analysis of the Chemical System
We are given a chemical reaction \(H_2(g) + I_2(g) \Leftrightarrow 2HI(g)\) with an equilibrium constant \(K = 46.3\) and a reaction quotient \(Q = 525\). The reaction quotient \(Q\) represents the ratio of the product concentrations (or partial pressures) to the reactant concentrations at a non-equilibrium state, while the equilibrium constant \(K\) represents this same ratio specifically at equilibrium. By comparing \(Q\) and \(K\), we can predict the direction in which the reaction will proceed to establish equilibrium.
- Predicting the Direction of the Shift
The principles governing the direction of a reversible reaction are:
- If \(Q < K\), the system has a lower concentration of products relative to reactants than it does at equilibrium. Therefore, the reaction will proceed in the forward direction (shift right) to increase the product concentration.
- If \(Q > K\), the system has a higher concentration of products relative to reactants than it does at equilibrium. Therefore, the reaction will proceed in the reverse direction (shift left) to decrease the product concentration and increase the reactant concentration.
- If \(Q = K\), the system is already at equilibrium, and there will be no net shift.
Given that \(Q = 525\) and \(K = 46.3\), we observe that \(Q > K\). This indicates that the current system contains an excess of products relative to reactants.
- Conclusion and Final Answer
Since \(Q = 525 > K = 46.3\), the system must shift to reduce the value of \(Q\) until it equals \(K\). This reduction occurs by consuming the products and forming more reactants. Thus, the equilibrium will shift to the left, favoring the reactants. Comparing this result with the provided options, option (b) correctly states that the equilibrium will shift to the left to favor the reactants. Therefore, the correct answer is (b).
Examples
In the chemical industry, understanding the reaction quotient \(Q\) and equilibrium constant \(K\) is vital for process optimization. For example, in an industrial ammonia synthesis plant (the Haber process), engineers continuously monitor concentrations of reactants (nitrogen and hydrogen) and products (ammonia). By calculating \(Q\) and comparing it to the known equilibrium constant \(K\) at the reactor's temperature, they can adjust pressures or flow rates to push the equilibrium toward producing more ammonia, maximizing efficiency and minimizing waste. This mathematical comparison serves as a diagnostic tool for maintaining optimal productivity in real-world chemical manufacturing.