Question

(a) True or false: "solubility" and "solubility-product con. stant" are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: ${\mathrm{MnCO}}_3,\mathrm{Hg}(\mathrm{OH}{)}_2$, and ${\mathrm{Cu}}_3{\left({\mathrm{PO}}_4\right)}_2$.

Short answer

(a) False. Solubility refers to the maximum concentration of a solute that can be dissolved in a solvent, while the solubility-product constant (Ksp) is an equilibrium constant representing the relationship between dissolved and undissolved species. (b) Solubility-Product Constant Expressions: 1. ${\mathrm{MnCO}}_3$: $K_{sp}=[{\mathrm{Mn}}^{2+}][{\mathrm{CO}}_3^{2-}]$ 2. ${\mathrm{Hg}(\mathrm{OH})}_2$: $K_{sp}=[{\mathrm{Hg}}^{2+}][{\mathrm{OH}}^{-}{]}^2$ 3. ${\mathrm{Cu}}_3({\mathrm{PO}}_4{)}_2$: $K_{sp}=[{\mathrm{Cu}}^{2+}{]}^3[{\mathrm{PO}}_4^{3-}{]}^2$

Step-by-step solution

Answer to Part (a) - Solubility versus Solubility-Product Constant

Solubility refers to the maximum concentration of a solute that can be dissolved in a solvent to form a saturated solution at a given temperature. It is expressed in terms of moles per liter (M) or grams per liter (g/L). On the other hand, the solubility-product constant, often denoted by Ksp, is a numerical value that represents the equilibrium between the dissolved ions and the undissolved solid in a saturated solution. In short, solubility refers to the maximum concentration of a solute that can be dissolved, while the solubility-product constant is an equilibrium constant representing the relationship between dissolved and undissolved species. So, the statement "solubility" and "solubility-product constant" are the same number for a given compound is False.

Answer to Part (b) - Writing Solubility-Product Constant Expressions

For a given ionic compound AbCd, which dissociates into a cations A^+ and d anions B^-, the balanced dissociation equation and solubility-product constant expression would be: AbCd <-> aA^+ + bB^- Ksp = [A^+]^a[B^-]^b 1. For ${\mathrm{MnCO}}_3$: Dissociation Equation: ${\mathrm{MnCO}}_3(s)\rightleftharpoons {\mathrm{Mn}}^{2+}(aq)+{\mathrm{CO}}_3^{2-}(aq)$ Solubility-Product Constant Expression: $K_{sp}=[{\mathrm{Mn}}^{2+}][{\mathrm{CO}}_3^{2-}]$ 2. For ${\mathrm{Hg}(\mathrm{OH})}_2$: Dissociation Equation: ${\mathrm{Hg}(\mathrm{OH})}_2(s)\rightleftharpoons {\mathrm{Hg}}^{2+}(aq)+2{\mathrm{OH}}^{-}(aq)$ Solubility-Product Constant Expression: $K_{sp}=[{\mathrm{Hg}}^{2+}][{\mathrm{OH}}^{-}{]}^2$ 3. For ${\mathrm{Cu}}_3({\mathrm{PO}}_4{)}_2$: Dissociation Equation: ${\mathrm{Cu}}_3({\mathrm{PO}}_4{)}_2(s)\rightleftharpoons 3{\mathrm{Cu}}^{2+}(aq)+2{\mathrm{PO}}_4^{3-}(aq)$ Solubility-Product Constant Expression: $K_{sp}=[{\mathrm{Cu}}^{2+}{]}^3[{\mathrm{PO}}_4^{3-}{]}^2$

Key concepts

Understanding Solubility

When it comes to understanding how substances dissolve in liquids, the term solubility is central. Solubility is the maximum amount of a solute that can dissolve in a given solvent at a specific temperature and pressure, resulting in a saturated solution. It can be influenced by various factors, including temperature, pressure, and the nature of the solvent and solute.

Imagine solubility as the 'limit' to how much sugar you can dissolve in your tea; once you've reached that limit, additional sugar won't dissolve and will settle at the bottom. Solubility is typically measured in units like moles per liter (M) or grams per liter (g/L), showing how much solute the solvent can hold before becoming saturated.

This concept is key in fields such as chemistry, environmental science, and pharmaceuticals because it determines the extent to which substances mix and react with one another in solutions.

Equilibrium Constant (Ksp) Basics

In solubility context, the equilibrium constant, specifically known as the solubility-product constant (Ksp), plays a vital role. It quantifies the relationship between the dissolved ions and solid particles in a saturated solution at equilibrium. Unlike solubility, which is expressed as a concentration, the Ksp value is unitless, serving as a mathematical representation of the product of the ion concentrations, each raised to the power of their respective coefficients in a balanced chemical equation.

The Ksp value gives us insight into the solute's tendency to dissolve in a solvent. A larger Ksp indicates greater solubility, while a lower Ksp suggests lower solubility. This value is particularly useful for predicting whether a precipitate will form when two solutions are mixed. In essence, knowing the Ksp assists chemists in anticipating the behavior of ionic compounds in various conditions.

Ionic Compounds & Solubility

An ionic compound consists of positively charged ions (cations) and negatively charged ions (anions) held together by electrostatic forces known as ionic bonds. Common examples include table salt (NaCl) and Epsom salt (MgSO4). In water, many of these compounds dissociate into their ions, a process influenced by the compound's solubility.

Factors such as lattice energy— the energy required to separate the ions in the solid—and hydration energy—the energy release when ions interact with water—play crucial roles in the solubility of ionic compounds. The balance between these energies helps determine if an ionic compound will be highly soluble or sparingly soluble in water.

Understanding the solubility of ionic compounds is important in areas such as medicine, for drug formulation, and in environmental science, to predict the movement and impact of ions in water systems.

The Dissociation Equation Connection

A dissociation equation represents the process in which a solid ionic compound separates into its component ions in a solvent. The equation is written as a reversible reaction, indicating that the dissociation is an equilibrium process, where the rate of the solid dissolving into ions is equal to the rate of ions coming together to form the solid.

For example, when salt dissolves in water, the dissociation equation is written as:
NaCl(s) ↔ Na+(aq) + Cl-(aq)This equation illustrates that solid sodium chloride (NaCl) dissociates into sodium ions (Na+) and chloride ions (Cl-) in water (aq denotes aqueous or dissolved in water).

The dissociation equation lays the groundwork for calculating the solubility-product constant (Ksp), which requires balancing the equation and using the concentrations of the resulting ions. It is the cornerstone of understanding the solubility behavior of an ionic compound and is widely used in predicting the outcomes of chemical reactions that involve precipitation.