Question

the solubility of calcium arsenate (ca3(aso4)2, molar mass = 398.078 g) in water is measured to be 0.032 g/l. what is ksp for this salt?

Answer 1

The solubility product constant (Ksp) for calcium arsenate is 1.3 x 10⁻¹⁶.

Step-by-step explanation:

The solubility product constant (Ksp) is a measure of the equilibrium between a solid substance and its ions in a saturated solution. It represents the product of the concentrations of the ions raised to the power of their stoichiometric coefficients.

In this case, the solubility of calcium arsenate (Ca3(AsO4)2) is given as 0.032 g/L. To calculate the Ksp, we need to convert this solubility to molar concentration (mol/L) by dividing it by its molar mass. Then, using the stoichiometry of the balanced equation, we can determine the expression for Ksp and solve for its value.

Given that the molar mass of Ca3(AsO4)2 is 398.078 g/mol, the molar solubility of calcium arsenate is 0.032 g/L ÷ 398.078 g/mol = 0.0000805 mol/L.

Using the stoichiometry of the balanced equation, Ca3(AsO4)2 ⇌ 3Ca²+ + 2AsO4³-, the expression for Ksp is Ksp = [Ca²+]³[AsO4³-]² = (3x)³(2x)², where x is the molar solubility.

Now, substitute the molar solubility (0.0000805 mol/L) into the Ksp expression and solve for Ksp:

Ksp = (3 * 0.0000805)³(2 * 0.0000805)² = 1.3 x 10⁻¹⁶

Answer 2

The Ksp for calcium arsenate (Ca3(AsO4)2) is found by converting the given solubility from grams per liter to moles per liter (molarity) and then applying the expression for the solubility product constant (Ksp), resulting in a Ksp of 1.66×10-25.

Step-by-step explanation:

The solubility of calcium arsenate (Ca3(AsO4)2) is given as 0.032 g/L. To find the solubility product constant (Ksp) for the salt, we first need to convert the solubility in grams per liter to moles per liter (molarity). This is done by dividing the solubility by the molar mass of calcium arsenate, which is given as 398.078 g/mol.

Solubility in molarity (M) = 0.032 g/L ÷ 398.078 g/mol = 8.036×10-5 M.

When calcium arsenate dissolves, it dissociates into three calcium ions (Ca2+) and two arsenate ions (AsO43-) as shown in the equation:

Ca3(AsO4)2(s) ⇌ 3 Ca2+(aq) + 2 AsO43-(aq)

The Ksp expression for Ca3(AsO4)2 is:

Ksp = [Ca2+]3[AsO43-]2

Letting x represent the molar solubility of Ca3(AsO4)2, we get:

x = 8.036×10-5 M for the arsenate ion, and for calcium ion, it would be 3x since there are three times as many calcium ions produced.

Therefore, Ksp = (3x)3(x)2 = (3×8.036×10-5 M)3(8.036×10-5 M)2

After calculating, Ksp = 1.66×10-25, which is the solubility product constant for calcium arsenate.