Question

Write equilibrium constant expressions for these heterogeneous equilibria. $$ \begin{array}{l}{\text { a. } 2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})} \\ {\text { b. } \mathrm{C}_{6} \mathrm{H}_{6}(1) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g})}\end{array} $$

Short answer

The short answer for the given heterogeneous equilibria is: a. \( K_c = [\mathrm{H}_{2}\mathrm{O}(\mathrm{g})] \cdot [\mathrm{CO}_{2}(\mathrm{g})] \) b. \( K_c = [\mathrm{C}_{6}\mathrm{H}_{6}(\mathrm{g})] \)

Step-by-step solution

a. 2 NaHCO3(s) ⇌ Na2CO3(s) + H2O(g) + CO2(g)

To write the equilibrium constant expression, we only include the concentrations of gaseous species. The equilibrium constant (Kc) for the reaction is given by: \( K_c = [\mathrm{H}_{2}\mathrm{O}(\mathrm{g})] \cdot [\mathrm{CO}_{2}(\mathrm{g})] \)

b. C6H6(l) ⇌ C6H6(g)

In this reaction, we have one liquid and one gaseous species. Again, we only include the concentration of the gaseous species in the equilibrium constant expression. The equilibrium constant (Kc) is given by: \( K_c = [\mathrm{C}_{6}\mathrm{H}_{6}(\mathrm{g})] \)

Key concepts

Heterogeneous Equilibria

When dealing with chemical reactions where the reactants and products exist in different phases, such as solids, liquids, and gases, we're exploring heterogeneous equilibria. Consider a scenario where you have a solid substance in equilibrium with its gaseous form, or perhaps a reaction involving solids that produce gases. Understanding heterogeneous equilibria is crucial because it shows how different phases can coexist and interact under equilibrium conditions.

In heterogeneous equilibrium reactions, the concentrations of solid and liquid species are generally not included in the equilibrium constant expression. The reason for this exclusion is that the concentrations of pure solids and liquids are constant. Therefore, they do not affect the position of equilibrium, which is only influenced by the concentration or partial pressure of gaseous components and the concentrations of solutes in solution.

For instance, in the reaction where sodium bicarbonate decomposes to form sodium carbonate, water vapor, and carbon dioxide gas, only the gaseous components are considered in the equilibrium constant expression. By focusing on the changes of the gases, chemists gain insight into how the reaction is shifting over time.

Chemical Equilibrium

At the core of these reactions lies the concept of chemical equilibrium. This is a state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no overall change in the concentrations of reactants and products over time. It is essential to recognize that equilibrium does not mean the reactants and products are present in equal amounts, but rather that their ratios remain constant.

Chemical equilibrium can be dynamic. Even though we observe no macroscopic changes, the reactions continue to occur at a molecular level. This dynamic balance is central to understanding how different reactions can be manipulated or predicted in both laboratory and real-world scenarios.

To visualize this better, imagine a crowded room where an equal number of people enter and leave simultaneously. The total number of people in the room remains constant, similar to how the concentrations of reactants and products in a chemical equilibrium remain unchanged.

Kc (Equilibrium Constant)

Exploring the quantitative side of chemical equilibrium, we arrive at the equilibrium constant, represented as \( K_c \). This value expresses the ratio of product concentrations to reactant concentrations at equilibrium, with each raised to the power of their stoichiometric coefficients from the balanced chemical equation. It is a crucial tool for predicting the extent of a reaction and determining the concentrations of different species at equilibrium.

For gaseous reactions, or reactions in which gases are produced or consumed, the concentration terms in the equilibrium constant expression refer to the partial pressures of the gases involved. However, in scenarios involving both solids and gases, like the decomposition of sodium bicarbonate, the equilibrium constant expression simplifies to include only the gaseous components. This is because the concentrations of solid reactants and products are constant and thus omitted from the equation.

Understanding \( K_c \) is not only about calculating a number; it's about understanding the intricacies of the reaction's behavior under different conditions. A high \( K_c \), for instance, suggests products are more favored at equilibrium, while a low \( K_c \) indicates reactants are more favored.