91Ó°ÊÓ

The equilibrium constant, denoted as \(K_c\), is a fundamental concept in chemical equilibrium. It provides a quantitative measure of the extent to which a chemical reaction proceeds. In essence, \(K_c\) indicates the ratio of the concentrations of the products to the reactants at equilibrium. For the reaction \(2 \text{SO}_{2}(g) + \text{O}_{2}(g) \rightleftharpoons 2 \text{SO}_{3}(g)\), the expression is formulated as:

• \[ K_c = \frac{[\text{SO}_3]^2}{[\text{SO}_2]^2[\text{O}_2]} \]

Here, each concentration is raised to the power of its stoichiometric coefficient.
In the given example, the \(K_c\) value is extraordinarily large, at \(8.0 \times 10^{35}\). Such a large \(K_c\) implies that, at equilibrium, the concentration of products (\(\text{SO}_3\)) is much greater than that of the reactants (\(\text{SO}_2\) and \(\text{O}_2\)). This means the forward reaction is highly favored, converting a significant amount of reactants into products.

Le Chatelier's Principle is a key concept that helps predict the effect of changing conditions on chemical equilibrium. It states that if a dynamic equilibrium is disturbed by an external change (such as concentration, temperature, or pressure), the system will adjust itself to partially counteract the effect of the disturbance and a new equilibrium is established.
This principle can be applied to understand how changes affect concentrations. In our \(\text{SO}_{2}\) and \(\text{O}_{2}\) reaction, if somehow the concentration of \(\text{SO}_{3}\) decreases, the system will respond by shifting toward the products, increasing \([\text{SO}_{3}]\) and reducing \([\text{SO}_{2}]\) and \([\text{O}_{2}]\).
Conversely, increasing the concentration of \(\text{SO}_{2}\) or \(\text{O}_{2}\) will shift the equilibrium towards more \(\text{SO}_{3}\) production.

• This principle is vital for controlling reactions in an industrial setting.
• It aids in maximizing the yield of desired products in chemical synthesis.

Equilibrium calculations are essential for predicting concentrations of substances at equilibrium. These calculations are particularly applicable when the equilibrium constant \(K_c\) and initial concentrations are known. Let's walk through the steps using our example reaction.

• First, write the equilibrium expression using the known \(K_c\): \[ K_c = \frac{[\text{SO}_3]^2}{[\text{SO}_2]^2[\text{O}_2]} \]
• Given that \([\text{SO}_3] = 1.0 \text{ M}\) and say \([\text{SO}_2] = [\text{O}_2] = x\), substitute these into the expression:
• Solving for the concentration of \(\text{SO}_2\), we set up the equation: \[ 8.0 \times 10^{35} = \frac{1}{x^3} \]
• Rearrange to find \(x\): \[ x^3 = \frac{1}{8.0 \times 10^{35}} \]
• Extract the cube root: \[ x = \left(\frac{1}{8.0 \times 10^{35}}\right)^{1/3} \approx 1.08 \times 10^{-12} \text{ M} \]

This extremely low concentration of \(\text{SO}_2\) confirms that the forward reaction proceeds almost to completion, corroborating the large \(K_c\) value's suggestion that \(\text{SO}_3\) is primarily produced.