Write the expressions for the equilibrium constants \(K_{P}\) of the following thermal decomposition reactions: (a) \(2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons\) $$\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ (b) \(2 \mathrm{CaSO}_{4}(s) \rightleftharpoons\) $$2 \mathrm{CaO}(s)+2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$

Thermal decomposition reactions are processes in which a compound breaks down into two or more substances when heated. This type of reaction is endothermic, meaning it absorbs energy in the form of heat. A typical example involves breaking down carbonates into oxides and carbon dioxide upon heating, as seen in baking soda (sodium bicarbonate) decomposing to form sodium carbonate, water vapor, and carbon dioxide.

Importance in Chemistry

Understanding thermal decomposition is important for several fields including materials science, where it is used in the production of cement and ceramics, and in environmental science, where it can help in assessing pollutant formation.

Relevance to Equilibrium Constants

When analyzing thermal decomposition reactions, the equilibrium constant can be used to predict the extent of decomposition at a given temperature. This is particularly crucial in industrial processes where control of the reaction extent is necessary for product quality.

Partial pressures play a significant role in gas-phase chemical equilibria. The partial pressure is the pressure that a gas would exert if it alone occupied the entire volume of the mixture at the same temperature. In a mixture of gases, the total pressure is the sum of the partial pressures of each individual gas.

Connection to Equilibrium

For a gaseous equilibrium reaction, the equilibrium constant expression in terms of partial pressures (\( K_P \)) incorporates the partial pressures of the gases involved. As demonstrated in the exercise, only gases are included in the equilibrium expression for solids do not have a partial pressure.

It's also critical to note that changes in pressure can shift the position of the equilibrium according to Le Chatelier's principle. Therefore, understanding the concept of partial pressures can help in manipulating and predicting the behavior of a reaction under different pressure conditions.

The equilibrium constant expression is a mathematical way to describe the state of a chemical equilibrium. For reactions involving gases, it is represented by \( K_P \), which relates the partial pressures of the reactants and products at equilibrium.

Interpreting Equilibrium Constants

As seen in the solutions, the magnitude of the equilibrium constant gives insight into the position of equilibrium and the proportions of reactants and products present. A larger \( K_P \) value indicates a reaction that favors the formation of products, while a smaller value suggests a reaction that favors the reactants.

Furthermore, equilibrium expressions are governed by the law of mass action, which maintains that the rate of a chemical reaction is proportional to the product of the concentrations or partial pressures of the reactants. Each substance's coefficient in the balanced chemical equation becomes the exponent in the expression, reflecting the principle that a reaction's driving force is related to the concentration or pressure of its reactants.