Question

Write the equilibrium constant expression for the following equilibria: (a) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)\) (b) \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}{ }^{2-}(a q)\) (c) \(\mathrm{HF}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{F}^{-}(a q)\)

Short answer

The equilibrium constant expressions for the three equilibria are: (a) \(K = \[NH_{3}\] \[HCl]\), (b) \(K = \[Ca^{2+}\] \[CO_{3}^{2-}\]\), and (c) \(K = \[H_{3}O^{+}\] \[F^{-}\] / \[HF]\).

Step-by-step solution

Write the equilibrium constant expression for (a)

For the reaction \(NH_{4}Cl(s) \leftrightarrow NH_{3}(g) + HCl(g)\), the equilibrium constant expression is \(K = \[NH_{3}\] \[HCl]\) since \(NH_{4}Cl\) is a solid and therefore its concentration is excluded.

Write the equilibrium constant expression for (b)

For the reaction \(CaCO_{3}(s) \leftrightarrow Ca^{2+}(aq) + CO_{3}^{2-}(aq)\), the equilibrium constant expression is \(K = \[Ca^{2+}\] \[CO_{3}^{2-}\]\) because \(CaCO_{3}\) is a solid and hence its concentration is not considered.

Write the equilibrium constant expression for (c)

For the reaction \(HF(aq) + H_{2}O(l) \leftrightarrow H_{3}O^{+}(aq) + F^{-}(aq)\), the equilibrium constant expression is \(K = \[H_{3}O^{+}\] \[F^{-}\] / \[HF]\) since \(H_{2}O\) is a pure liquid and thus its concentration is not incorporated.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a central concept in chemistry that helps predict the effects of changing conditions on a chemical equilibrium. When a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract this change and restore a new equilibrium. Here are some important aspects:

• Change in Concentration: If you add more reactants, the system shifts to form more products to reduce the effect of the added reactants. Conversely, if you remove some products, the system will shift to form more products.
• Change in Temperature: An increase in temperature adds heat to the system. For an exothermic reaction (one that releases heat), the equilibrium will shift to the left (toward the reactants). For an endothermic reaction (one that absorbs heat), it will shift to the right (toward products).
• Change in Pressure: This factor mainly affects gas-phase reactions. Increasing the pressure by reducing volume will shift the equilibrium towards the side with fewer gas molecules, while decreasing the pressure will shift it towards the side with more gas molecules.

Le Chatelier's Principle is a handy tool to predict how a system will respond to external stresses, ensuring students grasp the dynamic nature of chemical reactions.

solid state chemistry

Solid state chemistry is a branch of chemistry that focuses on the synthesis, structure, and properties of solid materials. In the context of equilibrium constant expressions, solid substances like ammonium chloride ( NH₄Cl) and calcium carbonate ( CaCO₃) have special properties.

• Pure Solids Do Not Change: Solids have constant concentrations because they maintain a uniform composition and shape, making them not included in the equilibrium constant expression, such as in the reactions you studied.
• Lattice Structure: The arrangement of atoms in a solid affects its stability, reactivity, and equilibrium behavior.
• Applications and Significance: Solid state chemistry is essential for understanding materials used in everyday applications, from construction materials to semiconductors.

By understanding the principles of solid state chemistry, students can better appreciate why specific substances are included or excluded in equilibrium calculations.

aqueous solutions

Aqueous solutions are mixtures where water is the solvent. In chemistry, aqueous solutions play a crucial role, particularly concerning how equilibrium constants are determined for reactions in solution.

• Solvent Properties: Water, being a polar solvent, facilitates the dissolution and ionization of many substances, which is essential for the reactions you explored.
• Concentration Effects: In aqueous reactions like HF + H₂O ↔ H₃O⁺ + F⁻, the concentration of ions in solution helps to define the equilibrium state, highlighted by the exclusion of pure liquid waters' concentration in the constant expression.
• Practical Importance: Aqueous reactions are abundant in biological systems and industrial processes, making the understanding of their equilibria vital for real-world applications.

Recognizing the behavior of aqueous solutions can fundamentally enhance a student's understanding of reactions in liquid environments and how they interact with states of equilibrium.