91Ó°ÊÓ

In chemical reactions, the equilibrium constant (\( K_p \)) is a crucial figure. It links the concentrations or pressures of reactants and products at equilibrium. For gas-phase reactions like this, the expression utilizes partial pressures. Each pressure is raised to the power of its coefficient in the balanced equation. Consider the equation: \[\mathrm{C}(s) + \mathrm{CO}_2(g) \leftrightharpoons 2 \mathrm{CO}(g)\]While solids like carbon (\( \mathrm{C} \)) do not appear in the\( K_p \) calculation, the gas pressures are included. This is a product over reactant format:\[K_p = \frac{{\left( P_{\mathrm{CO}} \right)^2}}{{P_{\mathrm{CO}_2}}}\]So, knowing\( K_p \) helps predict how much product and reactant will form at equilibrium.

• If\( K_p \) is large, products dominate.
• If\( K_p \) is small, reactants prevail.

This allows chemists to understand and influence reactions.

Partial pressure refers to the individual pressure exerted by a single gas component in a mixture. In equilibrium calculations, especially in gaseous systems like with \(\mathrm{CO}_2(g)\) and \(\mathrm{CO}(g)\), partial pressure is vital. It directly affects the equilibrium state of the reaction.
Consequently, if the total pressure of the system changes, the equilibrium condition shifts. The partial pressure of each gas depends on:

• The total pressure of the system.
• The mole fraction of the gas in the mixture.

In this exercise, \( P_{\mathrm{CO}} \) is given as\(1.50 \text{ bar} \), and by rearranging the equilibrium constant equation:\[P_{\mathrm{CO}_2} = \frac{{\left(1.50\right)^2}}{1.90} \approx 1.18 \text{ bar}\]This shows how the partial pressures govern the equilibrium and balance of the chemical composition.

Le Chatelier's Principle is a guiding tool for predicting the effect of changes on a chemical equilibrium. It asserts that if a dynamic equilibrium is disturbed by changing the conditions, the system adjusts to counteract the imposed change.
In practical terms, this principle can be applied by observing pressure shifts in gas reactions. For instance:

• Increasing the total pressure in a reaction involving gases generally leads to a shift towards the side with fewer gas molecules.
• Decreasing the pressure tends to shift the equilibrium towards the side with more gas molecules.

Using Le Chatelier's insight, if the external conditions of the reaction \(\mathrm{C}(s) + \mathrm{CO}_2(g) \leftrightharpoons 2 \mathrm{CO}(g) \) change, such as by adding or removing \(\mathrm{CO}_2(g)\), the system will adjust to maintain equilibrium.
Understanding this principle allows chemists to control reactions more effectively, optimizing yields and minimizing unwanted by-products in industrial processes.