91Ó°ÊÓ

The equilibrium constant, often denoted as \( K_c \), is a crucial value in the study of chemical equilibria. It helps to determine the position of equilibrium in a chemical reaction. Imagine \( K_c \) as a snapshot of a reaction at equilibrium, showing the ratio of product concentrations to reactant concentrations. For the reaction given: \( \mathrm{CO}(g) + 2 \mathrm{H}_2(g) \rightleftharpoons \mathrm{CH}_3\mathrm{OH}(g) \), \( K_c \) is calculated using the formula: \[ K_c = \frac{[\mathrm{CH}_3\mathrm{OH}]}{[\mathrm{CO}][\mathrm{H}_2]^2} \] This mathematical expression allows chemists to predict whether a reaction will favor the formation of products or reactants at a given temperature—in this case, 500 K. If \( K_c \) is much larger than 1, the equilibrium position largely favors products. If \( K_c \) is much smaller than 1, it favors reactants. In this example, \( K_c = 10.5 \), meaning the products and reactants are somewhat balanced at equilibrium.

The reaction quotient, \( Q \), is similar to the equilibrium constant \( K_c \), but it applies at any given moment, not just when the system is at equilibrium. By comparing \( Q \) to \( K_c \), you can predict the direction in which a reaction will shift to reach equilibrium. To find \( Q \), use the same formula as \( K_c \): \[ Q = \frac{[\mathrm{CH}_3\mathrm{OH}]}{[\mathrm{CO}][\mathrm{H}_2]^2} \] In this specific exercise, we calculate \( Q \) using initial concentrations: 0.020 M for \( \mathrm{CH}_3\mathrm{OH} \), 0.10 M for \( \mathrm{CO} \), and 0.10 M for \( \mathrm{H}_2 \). Calculating these values gives: \[ Q = \frac{0.020}{(0.10)(0.10)^2} = 20 \] Since the calculated \( Q \) is 20 and the \( K_c \) is 10.5, it indicates that more products are present than the equilibrium would imply, causing the reaction to shift towards the reactants to reach equilibrium.

Le Chatelier's Principle is a helpful concept for understanding how a change in conditions can affect the position of equilibrium. This principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to reduce the effect of that change, trying to balance again. Let's apply this to the exercise. We have a reaction where \( Q = 20 \) compared to \( K_c = 10.5 \). According to Le Chatelier's Principle, because \( Q > K_c \), the system will shift to the left, towards the reactants.

• Increase in product concentration or pressure will result in the reaction moving left to form more reactants.
• When the concentration of \( \mathrm{CH}_3\mathrm{OH} \) is high compared to equilibrium, the reaction reduces \( \mathrm{CH}_3\mathrm{OH} \) while increasing \( \mathrm{CO} \) and \( \mathrm{H}_2 \).

Thus, by following Le Chatelier’s Principle, these equilibrium shifts are predictable, reinforcing the principle's importance in chemical reactions.