Question

What is molar solubility? How can you obtain the molar solubility of a compound from \(K_{\mathrm{sp}} ?\)

Short answer

Molar solubility is the number of moles of solute per liter of solution that form a saturated solution. To obtain molar solubility from the solubility product constant (\(K_{\text{sp}}\) ), take the square root of \(K_{\text{sp}}\) if the compound dissociates into one ion of each type.

Step-by-step solution

Defining Molar Solubility

Molar solubility is defined as the number of moles of a solute that can be dissolved in a liter of solvent to form a saturated solution at a given temperature. It is typically expressed in moles per liter (mol/L).

Relating Molar Solubility to Solubility Product Constant

The solubility product constant (\( K_{\text{sp}} \) ) is a value that describes the equilibrium between a solid and its ions in a saturated solution. For a general salt with formula AB that dissociates into A+ and B- ions in solution, the equation for the equilibrium is: AB (s) ⇌ A+ (aq) + B- (aq), with the equilibrium expression being: \( K_{\text{sp}} = [A^+] \times [B^-] \). To find the molar solubility (S) of the salt, we set \( [A^+] = [B^-] = S \) and solve the equation \( K_{\text{sp}} = S^2 \).

Calculating Molar Solubility

To calculate the molar solubility, take the square root of the solubility product constant (\( K_{\text{sp}} \)). This is because the concentrations of the ions are both equal to the molar solubility (S), leading to the expression: \( K_{\text{sp}} = S \times S = S^2 \). Therefore, the molar solubility (S) can be obtained by taking the square root of the solubility product: \( S = \sqrt{K_{\text{sp}}} \).

Key concepts

Solubility Product Constant

Understanding the solubility product constant, denoted as K_sp, is essential when studying the solubility of ionic compounds in aqueous solutions. It quantifies the maximum amount of a solute that can dissolve in a solvent to form a saturated solution, and thus represents a special kind of equilibrium constant. Specifically for salts, which are composed of cations and anions, the K_sp value indicates the degree to which the salt can dissociate into its ions in water.

An easy way to conceptualize this is to imagine a tug-of-war between the solid salt wanting to remain intact and the water's ability to pull it apart into ions. The K_sp value is like the score of the match, showing how much of the salt ends up as ions in solution at equilibrium. It's calculated by multiplying the concentrations of the cations and anions at this point. Importantly, temperature affects K_sp significantly, as solubility patterns can change with temperature shifts.

Saturated Solution

A saturated solution represents a state of dynamic equilibrium between the undissolved solute and the dissolved ions in a solution. It's achieved when the maximum solubility of a solute in a solvent has been reached at a given temperature and pressure. No more solute can dissolve; instead, the rate of solute dissolving equals the rate of dissolution happening in reverse, which means that solute particles are continuously being exchanged between the solid and dissolved phases without any net change.

The 'full glass' metaphor helps here: just as a full glass cannot hold any more water without spilling, a saturated solution holds the maximum concentration of solute, with any additional amount remaining undissolved. Students should visualize solute particles in a saturated solution as in constant motion, dissolving and precipitating at an equal rate.

Equilibrium Constant

The equilibrium constant, expressed as K_eq or just K, is a crucial number that describes the ratio of the concentrations of the products to the reactants of a reversible reaction at equilibrium. It tells us about the position of equilibrium—the farther the value is above 1, the more products are favored over reactants.

Since reversible reactions can move forward and backward under the right conditions, imagine a balancing scale where K represents the position it settles into when left untouched. For solubility, this constant specifically becomes K_sp for ionic solids in a solution. Knowing the equilibrium constant helps predict whether a reaction is likely to proceed, stay mostly as is, or favor the formation of reactants.

Dissociation of Salts

Dissociation of salts, a process key to understanding solubility, refers to the breaking apart of ionic compounds into their constituent ions when they dissolve in water. This separation is crucial for the salts to interact with the solvent and hence become a part of the solution.

Imagine table salt (sodium chloride) being scattered into water—the Na⁺ and Cl⁻ ions drift apart, dispersing evenly throughout. This behavior of salts is guided by the characteristics of the ions and the solvent. Polar solvents like water with their partial charges can effectively surround and isolate the ions. Students can view this as each ion finding a new dance partner in water molecules, becoming solvated and, thus, stable in the aqueous environment.