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The solubility of barium sulphate, BaSO4, is 2.4 x 10-4 g/100 mL of solution. Calculate the Ksp of this solution.
To calculate the solubility product constant (Ksp) for barium sulphate (BaSO4), you need to use the given solubility information.
Ksp is the equilibrium constant for the dissolution of an insoluble compound in water. It can be calculated by using the concentrations of the ions in the solution.
The balanced chemical equation for the dissociation of barium sulphate is:
BaSO4(s) ⟶ Ba2+(aq) + SO4 2-(aq)
From the equation, you can determine that the concentration of Ba2+ ions in the solution will be equal to the solubility of barium sulphate, which is given as 2.4 x 10-4 g/100 mL.
To convert this concentration from grams to moles, you need to know the molar mass of barium sulphate. The molar mass of BaSO4 is:
Ba: 137.33 g/mol
S: 32.06 g/mol
O: 16.00 g/mol
Total: 137.33 + 32.06 + (16.00 x 4) = 233.38 g/mol
Next, you need to convert the solubility of BaSO4 from grams/100 mL to moles/L. Divide the given solubility by the molar mass and convert mL to L:
2.4 x 10-4 g/100 mL = 2.4 x 10-3 g/L
2.4 x 10-3 g/L ÷ 233.38 g/mol = 1.028 x 10-5 mol/L
Since the stoichiometry of the balanced equation shows that 1 mole of barium sulphate dissociates to produce 1 mole of barium ions (Ba2+) and 1 mole of sulfate ions (SO4 2-), the concentration of SO4 2- ions will also be equal to the solubility of BaSO4.
Therefore, the concentration of SO4 2- ions is also 1.028 x 10-5 mol/L.
Now you can use the concentrations of Ba2+ and SO4 2- ions to calculate the Ksp.
The Ksp expression for barium sulphate can be written as:
Ksp = [Ba2+][SO4 2-]
Plug in the concentrations of Ba2+ and SO4 2-:
Ksp = (1.028 x 10-5)(1.028 x 10-5) = 1.058 x 10-10
Therefore, the Ksp of this solution is 1.058 x 10-10.
To calculate the Ksp (solubility product constant) of the solution, we need to know the molar solubility of BaSO4, which represents the number of moles of BaSO4 dissolved per liter of solution.
Given:
- The solubility of BaSO4 is 2.4 x 10-4 g/100 mL of solution.
To convert g/100 mL to moles/L, we need to consider the molar mass of BaSO4.
The molar mass of BaSO4 is:
1 mol of Ba = 137.33 g/mol
1 mol of S = 32.07 g/mol
4 mol of O = 4 x 16.00 g/mol = 64.00 g/mol
Total molar mass of BaSO4 = 137.33 + 32.07 + 64.00 = 233.40 g/mol
Now, we can calculate the molar solubility:
Molar solubility = (solubility in g/100 mL) / (molar mass in g/mol)
Molar solubility = (2.4 x 10-4 g/100 mL) / (233.40 g/mol)
= (2.4 x 10-6 g/mL) / (2.334 x 10-1 mol/L)
= 1.03 x 10-5 mol/L
Now we can determine the Ksp using the molar solubility:
Ksp = [Ba2+][SO42-]
In BaSO4, there is a 1:1 ratio of Ba2+ to SO42-. Therefore, the molar solubility represents the concentration of both ions.
Ksp = (molar solubility)2
= (1.03 x 10-5 mol/L)2
= 1.06 x 10-10
Therefore, the Ksp of the solution is 1.06 x 10-10.