Question

Solid Ca₃(PO₄)₂ is placed into 10.0 L of water. When equilibrium is established, the concentration of Ca²⁺ is 2.3 × 10⁻⁴ M. What is Kc for this equilibrium? Note Kc is sometimes called K. Ca₃(PO₄)₂ (s) ⇌ 3 Ca²⁺ (aq) + 2 PO₄³⁻ (aq)

Answer 1

The equilibrium constant (Kc) for the dissolution of Ca3(PO4)2 is calculated using the concentration of Ca2+ ions at equilibrium and the reaction stoichiometry, resulting in a Kc of 1.3 × 10−33.

Step-by-step explanation:

Calculation of the Equilibrium Constant (Kc) for Ca3(PO4)2

To calculate the equilibrium constant (Kc) for the dissolution of Ca3(PO4)2, we can use the given concentration of Ca2+ ions and the stoichiometry of the dissolution reaction. According to the balanced chemical equation:

Ca3(PO4)2 (s) ⇌ 3 Ca2+ (aq) + 2 PO43- (aq)

If the concentration of Ca2+ at equilibrium is 2.3 × 10−4 M, then using the stoichiometry, the concentration of PO43− will be (2/3) × 2.3 × 10−4 M, which equals 1.53 × 10−4 M. The equilibrium constant Kc (also known as Ksp for solids) can be expressed as:

Kc = [Ca2+]3[PO43−]2

Plugging in the concentrations:

Kc = (2.3 × 10−4 M)3(1.53 × 10−4 M)2

After calculating, we find that:

Kc = 1.3 × 10−33

Thus, the equilibrium constant for the dissolution of Ca3(PO4)2 is 1.3 × 10−33.

Answer 2

To calculate Ksp for the dissolution of Ca₃(PO₄)₂, the concentration of PO₄³⁻ is found using the stoichiometry of the reaction, and Ksp is then determined as a product of the equilibrium concentrations of Ca²+ and PO₄³⁻ ions.

Step-by-step explanation:

The student asked about the equilibrium constant (Kc, commonly referred to as Ksp for solubility products) for the dissolution of solid calcium phosphate, Ca₃(PO₄)₂, in water. The student provided the concentration of Ca²+ ions at equilibrium as 2.3 × 10⁻⁴ M and wanted to know the Kc for this equilibrium. Given the balanced chemical equation Ca₃(PO₄)₂ (s) ⇌ 3 Ca²+ (aq) + 2 PO₄³⁻ (aq), we can set up an expression for Ksp, which is Ksp = [Ca²+]³[PO₄³⁻]². Applying the stoichiometry ratios, we can determine the concentration of PO₄³⁻ ions as (2/3) × (2.3 × 10⁻⁴ M), then calculate the Ksp.

To calculate Kc (Ksp), we need to acknowledge that the ratio of forming Ca²+ ions to PO₄³⁻ ions is 3:2, thus the concentration of PO₄³⁻ will be (2/3) × 2.3 × 10⁻⁴ M. For the given equilibrium concentration of Ca²+, the resulting PO₄³⁻ concentration will be 1.53 × 10⁻⁴ M. The Ksp can be calculated as follows:

Ksp = (2.3 × 10⁻⁴ M)³ × (1.53 × 10⁻⁴ M)²

After doing the math, we can find the numerical value of Ksp which represents the product of equilibrium concentrations for Ca₃(PO₄)₂ dissolution.