Calculate the solubility of calcium sulfate in grams solute per 100 grams of solvent. Assume that the volume occupied by the solute in the solution is negligibly small. (Ksp for CaSO4 = 2.4 X 10^-5)
CaSO4>> Ca++ + SO4--
Ksp= x^2
2.4E-5=x^2
x= 4.89E-3 moles/liter
in grams per liter, 4.89E-3*(136)/10 = .067grams/100gH2O
To calculate the solubility of calcium sulfate (CaSO4) in grams of solute per 100 grams of solvent, we need to use the solubility product constant (Ksp) for calcium sulfate.
The solubility product constant (Ksp) is an equilibrium constant that represents the concentration of dissociated ions in a saturated solution at a given temperature. In the case of calcium sulfate, the Ksp value is 2.4 x 10^-5.
To find the solubility in grams per 100 grams of solvent, we need to consider the dissociation of calcium sulfate in water.
The chemical equation for the dissociation of calcium sulfate is:
CaSO4(s) ⇌ Ca2+(aq) + SO4^2-(aq)
Let's assume x moles of calcium sulfate dissolves in water, resulting in x moles of Ca2+ ions and x moles of SO4^2- ions.
Since the volume occupied by the solute in the solution is assumed to be negligibly small, we can assume that the moles of solute in 100 grams of solvent are equal to x moles.
Now let's calculate the solubility using the Ksp expression:
Ksp = [Ca2+][SO4^2-]
Since x moles of Ca2+ and x moles of SO4^2- ions are formed for every x moles of calcium sulfate dissolved, we can substitute these values into the Ksp expression:
2.4 x 10^-5 = x * x
Simplifying further:
2.4 x 10^-5 = x^2
Taking the square root of both sides:
sqrt(2.4 x 10^-5) = x
x = 0.0049 moles
Now that we have the number of moles of calcium sulfate dissolved in 100 grams of solvent, we can calculate the solubility in grams per 100 grams of solvent.
The molar mass of calcium sulfate (CaSO4) is 136.14 g/mol.
Mass of calcium sulfate dissolved = Number of moles * Molar mass
Mass of calcium sulfate dissolved = 0.0049 moles * 136.14 g/mol
Mass of calcium sulfate dissolved = 0.666 gram (rounded to three decimal places)
Therefore, the solubility of calcium sulfate in grams of solute per 100 grams of solvent is approximately 0.666 grams/100 grams of solvent.