Question

Write the correct K \(\mathrm{P}\) expression for this reaction. \(\mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftarrows \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\)

Short answer

\( K_p = P_{\mathrm{CO}_2} \)

Step-by-step solution

Identify Reaction Components

The given chemical equation is \( \mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftarrows \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \). Identify the state of each component: \( \mathrm{CaCO}_{3} \) and \( \mathrm{CaO} \) are solids, while \( \mathrm{CO}_{2} \) is a gas.

Understand K-P Expression Criteria

For the equilibrium constant \( K_p \), only gaseous components are included in the expression. The partial pressures of any gases affect the equilibrium position. Solids and liquids are not included in \( K_p \) expressions because their concentrations are constant.

Formulate the K-P Expression

For the given reaction, the only gaseous component is \( \mathrm{CO}_{2} \). Therefore, the \( K_p \) expression will depend solely on the partial pressure of \( \mathrm{CO}_{2} \), which can be written as: \[ K_p = P_{\mathrm{CO}_2} \] where \( P_{\mathrm{CO}_2} \) represents the partial pressure of carbon dioxide.

Key concepts

Equilibrium Constant

The equilibrium constant, often represented as \( K \), is a fundamental aspect of chemical equilibrium that helps us understand how a reaction behaves at a state of balance. In reactions, the concentration of reactants and products adjust themselves until they reach a specific ratio, characterized by this constant. However, it's important to note that in different conditions and phases, the form of the equilibrium constant can vary. For gases, the equilibrium constant is denoted as \( K_p \), where "p" stands for "pressure," indicating that the equilibrium constant is derived based on the partial pressures of the gaseous reactants and products.

Including solid or liquid components, like in our problem with calcium carbonate and calcium oxide, doesn't affect\( K_p \). Solids and liquids have fixed concentrations due to their states and densities, and thus they aren't factored into \( K_p \) calculations. Instead, only the gaseous component, which is carbon dioxide in this case, is included in the equation. This simplifies representing the equilibrium constant for reactions where gases participate, making predictions about the chemical reactions more straightforward.

Partial Pressure

Partial pressure is a concept that applies uniquely to gases within a mixture. Each gas in a system exerts a pressure proportional to its concentration within the entire gas mixture. This is what we refer to as "partial pressure."

For any gas in a mixture, its partial pressure is a measure of how much pressure it would exert if it alone occupied the entire volume of the mixture. Understanding partial pressures is crucial, especially in the context of chemical equilibrium, because the equilibrium constant \( K_p \) is dependent on these pressures.

In the exercise, carbon dioxide is the only gaseous component, and its partial pressure is directly used in determining the \( K_p \). By monitoring and comparing these pressures, chemists can gauge how changing conditions will shift reactions, leading to the concept of Le Chatelier's Principle, which further explains shifts in equilibrium states.

Chemical Equilibrium

Chemical equilibrium is a dynamic state where the rate of the forward reaction matches the rate of the reverse reaction. This means that even though reactions continue to occur on a microscopic level, the concentrations of reactants and products remain constant over time. It's a balance, not a static end point.

Every reversible reaction has its own unique equilibrium constant, which helps us understand the conditions under which the reaction achieves balance. For the reaction involving calcium carbonate decomposing into calcium oxide and carbon dioxide, achieving equilibrium involves understanding how pressures and reaction conditions influence the ratios of gases produced and consumed.

Changes in conditions, like temperature or pressure, can disrupt this state. When this happens, the system strives to restore equilibrium, often by adjusting the pressures of gases involved. Thus, studying chemical equilibrium enables chemists to control and predict the outcomes of reactions, ensuring desired products are efficiently obtained.