Question

As you know from Chapter \(7,\) most metal carbonate salts are sparingly soluble in water. Below are listed several metal carbonates along with their solubility products, \(K_{\mathrm{sp}} .\) For each salt, write the equation showing the ionization of the salt in water, and calculate the solubility of the salt in mol/L. $$\begin{aligned}&\text { Salt } \quad K_{\mathrm{sp}}\\\&\mathrm{BaCO}_{3} \quad 5.1 \times 10^{-9}\\\&\mathrm{CdCO}_{3} \quad 5.2 \times 10^{-12}\\\&\mathrm{CaCO}_{3} \quad 2.8 \times 10^{-9}\\\&\mathrm{CoCO}_{3} \quad 1.5 \times 10^{-13}\end{aligned}$$

Short answer

The ionization equations for the given metal carbonates are: 1. BaCO3(s) <=> Ba^2+(aq) + CO3^2-(aq) 2. CdCO3(s) <=> Cd^2+(aq) + CO3^2-(aq) 3. CaCO3(s) <=> Ca^2+(aq) + CO3^2-(aq) 4. CoCO3(s) <=> Co^2+(aq) + CO3^2-(aq) Their solubilities, calculated using their solubility products (Ksp), are: 1. BaCO3: 2.3 × 10^(-5) mol/L 2. CdCO3: 2.3 × 10^(-6) mol/L 3. CaCO3: 1.7 × 10^(-5) mol/L 4. CoCO3: 3.9 × 10^(-7) mol/L

Step-by-step solution

Write Ionization Equations

Write the equations showing the dissolving process of each metal carbonate in water and the formation of its respective ions: 1. BaCO3(s) <=> Ba^2+(aq) + CO3^2-(aq) 2. CdCO3(s) <=> Cd^2+(aq) + CO3^2-(aq) 3. CaCO3(s) <=> Ca^2+(aq) + CO3^2-(aq) 4. CoCO3(s) <=> Co^2+(aq) + CO3^2-(aq)

Calculate Solubility of Each Metal Carbonate

Using the solubility products provided, we will calculate the solubility of each metal carbonate. Assume the solubility of each metal carbonate as 's' mol/L. 1. For BaCO3: Ksp = [Ba^2+][CO3^2-] = s × s = \(5.1 \times10^{-9}\) Solve for 's': s = √(5.1 × 10^(-9)) = 2.3 × 10^(-5) mol/L 2. For CdCO3: Ksp = [Cd^2+][CO3^2-] = s × s = \(5.2\times 10^{-12}\) Solve for 's': s = √(5.2 × 10^(-12)) = 2.3 × 10^(-6) mol/L 3. For CaCO3: Ksp = [Ca^2+][CO3^2-] = s × s = \(2.8 \times 10^{-9}\) Solve for 's': s = √(2.8 × 10^(-9)) = 1.7 × 10^(-5) mol/L 4. For CoCO3: Ksp = [Co^2+][CO3^2-] = s × s = \(1.5 \times 10^{-13}\) Solve for 's': s = √(1.5 × 10^(-13)) = 3.9 × 10^(-7) mol/L The solubilities of metal carbonates are as follows: 1. BaCO3: 2.3 × 10^(-5) mol/L 2. CdCO3: 2.3 × 10^(-6) mol/L 3. CaCO3: 1.7 × 10^(-5) mol/L 4. CoCO3: 3.9 × 10^(-7) mol/L

Key concepts

Ionization Equations

When a metal carbonate dissolves in water, it undergoes a process called ionization, breaking into metal cations and carbonate anions. This process is critical in understanding the solubility behavior of metal carbonates in aqueous solutions. For example, when barium carbonate (BaCO₃) enters water, it separates into barium ions (Ba²⁺) and carbonate ions (CO₃²⁻), which can be represented by the ionization equation: BaCO₃(s) <=> Ba²⁺(aq) + CO₃²⁻(aq). Similarly, for other metal carbonates like cadmium carbonate, calcium carbonate, and cobalt carbonate, their ionization in water can be shown with equations, clearly depicting their respective cations and anions. These equations are the first step in understanding the solubility product concept.

Metal Carbonates Solubility

The solubility of metal carbonates varies and is often quite low, which is why they are described as 'sparingly soluble.' Factors affecting this solubility include the metal's ionic charge and size, as well as the carbonate ion's tendency to form precipitates. Most metal carbonates dissociate poorly in water, leading to low concentrations of ions in solution. These low concentrations are what the solubility product constant (K_sp) represents, acting as an indicator of a salt's solubility. Understanding how to interpret solubility from K_sp values enables us to predict whether a precipitate will form in an aqueous solution under certain conditions.

Ksp Calculations

To calculate the solubility product constant (K_sp), we start with an expression that embodies the equilibrium between the undissociated compound and the ions produced in an aqueous solution. The simplifying assumption for monodentate metal carbonates like BaCO₃ and CdCO₃ is that the solubility, represented by 's', will yield one mole of metal ion and one mole of carbonate ion for every mole of metal carbonate that dissolves. The K_sp expression is thus K_sp = [Metal²⁺][CO₃²⁻] = s × s. By substituting the provided Ksp values and solving for 's', we can find the solubility of these metal carbonates in mol/L, which provides practical insight into the extent to which these compounds will dissolve in water.

Aqueous Solutions Chemistry

The study of aqueous solutions is pivotal in chemistry, especially when it comes to understanding reactions in water. Solubility is an essential concept within this discipline, influencing reactions such as precipitation and complexation. The behavior of ions in water, governed by their charge, size, and the dielectric constant of the water, is crucial in predicting the outcomes of chemical processes. For instance, the differences in the solubility of metal carbonates can be attributed to these ionic characteristics and the dynamics of the aqueous environment. A firm grasp of these principles is necessary to predict the behavior of chemical species in aqueous solutions accurately.