Question

Calcium carbonate is only slightly soluble in water. a. Write the equilibrium equation for calcium carbonate in solution. b. Write the solubility product constant expression, \(K_{\mathrm{sp}},\) for the equilibrium in a saturated solution of \(\mathrm{CaCO}_{3}\)

Short answer

a. \[ \text{CaCO}_3 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]b. \[ K_{\text{sp}} = [\text{Ca}^{2+}][\text{CO}_{3}^{2-}] \]

Step-by-step solution

Write the Equilibrium Equation

Calcium carbonate (CaCO3) slightly dissolves in water to form calcium ions (Ca^2+) and carbonate ions (CO3^2-). The equilibrium equation for this dissolution in water is: \[ \text{CaCO}_3 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]

Write the Solubility Product Constant Expression

The solubility product constant, \(K_{\text{sp}}\), represents the product of the concentrations of the ions in a saturated solution at equilibrium. For calcium carbonate, \(K_{\text{sp}}\) can be written as: \[ K_{\text{sp}} = [\text{Ca}^{2+}][\text{CO}_{3}^{2-}] \]

Key concepts

calcium carbonate solubility

Calcium carbonate, often found as chalk or limestone, is slightly soluble in water. This low solubility means that only a small amount of calcium carbonate will dissolve in water at any given time.

When calcium carbonate dissolves, it breaks down into its constituent ions:

• Calcium ions (Ca²⁺)
• Carbonate ions (CO₃²⁻)

Picture a glass of water with a tiny amount of calcium carbonate. As it dissolves, calcium and carbonate ions spread throughout the water. However, this dissolution is not complete; the water becomes saturated, and eventually, the dissolution stops. At this point, an equilibrium is said to be established between the undissolved calcium carbonate and the dissolved ions.

equilibrium equation

An equilibrium equation represents the balance between the dissolved and undissolved parts of a solute in a solution. For calcium carbonate, this equation illustrates how it dissolves in water and reaches a point where no more dissolution occurs. It's a snapshot of the balance between the solid and its ions.

The equilibrium equation for calcium carbonate in water is:

\[\text{CaCO}_3 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{CO}_3^{2-} (aq)\]This equation tells us that solid calcium carbonate (CaCO₃) separates into calcium ions (Ca²⁺) and carbonate ions (CO₃²⁻) in water. The double arrow (↔) signifies equilibrium, showing that these processes occur simultaneously and continuously.

In essence, this means calcium carbonate is dissolving and re-forming at the same rate, maintaining a stable level of dissolved ions in the water.

solubility product constant

The solubility product constant, known as Kₛₚ, is a special value used to describe the equilibrium between a solid and its ions in a solution.. Think of it as a measure of how much of a substance can completely dissolve in water to form its ions.

The expression for the solubility product constant of calcium carbonate is:

\[K_{\text{sp}} = [\text{Ca}^{2+}][\text{CO}_{3}^{2-}]\]Here, the brackets [ ] indicate concentrations. This means that Kₛₚ is calculated by multiplying the concentration of calcium ions by the concentration of carbonate ions in a saturated solution.

Kₛₚ helps predict whether a mixture will form a precipitate (solid) or not. If the product of the ion concentrations in a solution exceeds the Kₛₚ value, the excess ions will combine to form more of the solid, pushing the system back to equilibrium. Understanding Kₛₚ allows us to manipulate conditions to either encourage more dissolution or cause precipitation, depending on our needs.