91Ó°ÊÓ

In chemical reactions, the concept of the equilibrium constant \( K_c \) is fundamental. It tells us how the concentrations of reactants and products relate when a reaction reaches equilibrium. For a reaction such as \( \mathrm{CO}_{2}(g) + \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g) + \mathrm{H}_2\mathrm{O}(g) \), the equilibrium constant is expressed using the formula:

• \( K_c = \frac{[\mathrm{CO}][\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{CO}_{2}][\mathrm{H}_{2}]} \)

This equation shows that at equilibrium, the ratio of product concentrations to reactant concentrations equals the equilibrium constant, \( K_c \). It's a numeric value that remains unchanged as long as temperature does not vary, and it helps predict how much of each substance is present after a reaction has equilibrated.

The reaction quotient, \( Q_c \), serves a vital role in predicting the direction a reaction will proceed before reaching equilibrium. By comparing \( Q_c \) to \( K_c \), one can determine if the reaction will move towards forming more products or reactants. When initially calculating \( Q_c \) using the same expression as \( K_c \), remember:

• If \( Q_c < K_c \), the reaction proceeds to the right, favoring product formation.
• If \( Q_c > K_c \), the reaction shifts left, favoring reactants.
• If \( Q_c = K_c \), the reaction is at equilibrium.

Understanding the reaction quotient helps to assess how close a reaction mixture is to equilibrium and predict concentration adjustments.

Calculating concentrations involves determining initial values and how they change as the reaction approaches equilibrium. For example, with initial moles provided in a specific container volume, it is straightforward:

• Determine initial concentration: \([\mathrm{CO}_{2}]_0 = [\mathrm{H}_{2}]_0 = \frac{1.50 \text{ mol}}{3.00 \text{ L}} = 0.50 \text{ M}\)

As the reaction proceeds, reactant concentrations decrease while product concentrations grow. Use an unknown \( x \) to represent the change. Then substitute these changes in the equilibrium expression to solve for \( x \); note how changes reflect upon initial values and result in equilibrium concentrations.

The equilibrium expression is crucial in solving for unknown concentrations in a chemical reaction at equilibrium. Start by substituting the changes in concentrations into the equilibrium constant expression. For instance, for our system:

• \( K_c = \frac{x^2}{(0.50-x)^2} = 0.802 \)

Solving this expression provides the change in concentration, \( x \). Substitute \( x \) back to find each individual concentration of reactants and products, ultimately serving as a tool to understand the extent of the reaction and to confirm that the calculated concentrations respect the given \( K_c \) value.