Question

Two different compounds have about the same molar solubility. Do they also have about the same \(K_{\text {sp}}\) value?

Short answer

Two different compounds having about the same molar solubility do not necessarily imply that they have the same Ksp values. However, if their molar solubility is similar (s1 ≈ s2), then their Ksp values might also be similar (Ksp(AB) ≈ Ksp(CD)) as Ksp(AB) = \(s_1^2\) and Ksp(CD) = \(s_2^2\). This is just a general observation and might not hold true for every pair of compounds with similar molar solubility. It is important to evaluate each specific case for a more accurate comparison.

Step-by-step solution

Define molar solubility and solubility product constant (Ksp)

Molar solubility is the number of moles of a solute that can dissolve in one liter of a solution to form a saturated solution. The solubility product constant (Ksp) is the equilibrium constant for a chemical reaction in which a solid ionic compound dissolves to yield its ions in a solution. It provides a quantitative measure of the solubility of the compound.

Express the solubility equilibrium and Ksp expressions for two generic compounds

Let's represent the two compounds as AB (with the molar solubility s1) and CD (with the molar solubility s2). The solubility equilibrium for these compounds can be represented as: Compound AB: \(AB_{(s)} \rightleftharpoons A_{(aq)}^+ + B_{(aq)}^-\) Compound CD: \(CD_{(s)} \rightleftharpoons C_{(aq)}^{+} + D_{(aq)}^{-}\) Now we can write the Ksp expressions for these compounds: Ksp(AB) = [A+][B−] = \(s_1^2\) Ksp(CD) = [C+][D−] = \(s_2^2\)

Analyze the relationship between molar solubility and Ksp

Assuming that the two compounds have similar molar solubility (s1 ≈ s2), we can examine the relationship between their Ksp values. Since Ksp(AB) = \(s_1^2\) and Ksp(CD) = \(s_2^2\), if s1 ≈ s2, then it implies that Ksp(AB) ≈ Ksp(CD). Therefore, if two different compounds have about the same molar solubility, they are likely to have about the same Ksp values. However, this is just a general observation and might not hold true for every pair of compounds with similar molar solubility. It is important to evaluate each specific case for a more accurate comparison.

Key concepts

Molar Solubility

Molar solubility is a key concept in chemistry that describes how much of a particular compound can be dissolved in a given amount of solvent before reaching saturation. Simply put, it's the number of moles of a solute that dissolve per liter of solution. Understanding this concept is crucial because it tells us the maximum concentration of the ions that can exist in a solution at equilibrium. When you dissolve a salt in water, it breaks into its constituent ions. The point at which no more salt seems to dissolve is when the solution is saturated. To find the molar solubility, one typically sets up an equilibrium expression involving the ions in solution and applies stoichiometry based on the balanced dissolution equation. Molar solubility provides a direct insight into the saturation limit of a compound, which is fundamental in predicting how substances will behave in different chemical environments.

Equilibrium Constant

The equilibrium constant, often denoted as 'K' in chemistry, quantifies the position of equilibrium in a chemical reaction. For the solubility of salts, the special type of equilibrium constant we use is the solubility product constant, or Ksp. This constant provides important information on how well a compound dissociates into its ions in solution. At equilibrium, the rate at which the solid dissolves into its ions is equal to the rate at which the ions precipitate out of the solution to form the compound. For any solid dissolving in water, represented generally as \(AB_{(s)} \rightleftharpoons A_{(aq)}^+ + B_{(aq)}^-\), the equilibrium constant expression is \([A^+][B^-]\). This reflects the concentration of ions at equilibrium. Ksp values are unique to each compound and determine how much of the compound dissolves at a given temperature.

Ionic Solubility

Ionic solubility refers to the extent to which ionic compounds dissolve in a solvent to form free ions. In aqueous solutions, ionic solubility is dictated by the ion interactions with water molecules and how stable the ions are when surrounded by water. When an ionic compound dissolves, it separates into positive and negative ions, a process known as dissociation. For instance, if we consider a generic compound AB that dissociates in water, it creates A\(^+\) and B\(^-\) ions. The ease with which ions enter the solution depends on several factors, including the lattice energy of the ionic solid and the hydration energy provided by water. Compounds with higher ionic solubility will have larger concentrations of their ions present in the solution, which is closely tied to their molar solubility and Ksp values.

Ksp Expressions

Ksp expressions underscore the heart of understanding ionic solids in aqueous solutions. They algebraically represent the concentration of ions at equilibrium in relation to their solid form. For any dissociation of a compound like \(AB_{(s)} \rightleftharpoons A_{(aq)}^+ + B_{(aq)}^-\), the Ksp expression would be \(K_{sp} = [A^+][B^-]\). The Ksp value is calculated from these concentrations at saturation and reveals the maximum solubility of the compound. Higher Ksp values indicate more soluble compounds, while lower values suggest limited solubility. By comparing the Ksp values of two compounds, one can predict their respective solubility behavior. It's important to remember, even if two compounds have similar molar solubility, minor differences in ion charges, types, or interactions can affect their individual Ksp values. Thus, it is always essential to evaluate specific cases beyond just comparing molar solubility figures.