What mass of PbCl2 would be found in 0.48 L of a saturated solution of PbCl2 if the Ksp of PbCl2 is 1.6 x 10-5?
To find the mass of PbCl2 in the given volume of the saturated solution, we need to calculate the amount of PbCl2 that has dissolved in the solution using the solubility product constant (Ksp).
The equation for the dissociation of PbCl2 in water is as follows:
PbCl2 ↔ Pb2+ + 2Cl-
According to the stoichiometry of the reaction, 1 mole of PbCl2 dissolves to produce 1 mole of Pb2+ ions and 2 moles of Cl- ions.
Let's assume that x moles of PbCl2 dissolve in the solution. Therefore, the concentration of Pb2+ ions will be x M, and the concentration of Cl- ions will be 2x M.
Now, we can set up the expression for the solubility product constant:
Ksp = [Pb2+][Cl-]^2
Substituting the concentrations:
Ksp = x * (2x)^2 = 4x^3
Given that Ksp = 1.6 x 10^-5, we can solve for x:
1.6 x 10^-5 = 4x^3
x^3 = (1.6 x 10^-5) / 4
x^3 = 4 x 10^-6
Taking the cube root of both sides:
x = (4 x 10^-6)^(1/3)
x ≈ 0.0159 M
Now, we can calculate the moles of PbCl2 dissolved in the saturated solution:
moles of PbCl2 = concentration of PbCl2 * volume of solution
moles of PbCl2 = 0.0159 M * 0.48 L
moles of PbCl2 ≈ 0.00763 mol
Finally, we can calculate the mass of PbCl2 using its molar mass:
mass of PbCl2 = moles of PbCl2 * molar mass of PbCl2
mass of PbCl2 = 0.00763 mol * (207.2 g/mol + 2 * 35.45 g/mol)
mass of PbCl2 ≈ 9.82 g
Therefore, the mass of PbCl2 found in 0.48 L of the saturated solution is approximately 9.82 grams.
To determine the mass of PbCl2 in a saturated solution, we first need to understand the concept of solubility product constant (Ksp) and how it relates to the concentration of the dissolved ions.
The equation for the solubility product constant of PbCl2 is as follows:
PbCl2 ⇌ Pb2+ + 2Cl-
The Ksp expression for this equilibrium is:
Ksp = [Pb2+][Cl-]²
Given that the Ksp of PbCl2 is 1.6 x 10^-5, we can use this information to find the concentration of Pb2+ and Cl- ions in the solution, and from there, determine the mass of PbCl2.
First, we need to calculate the concentration of PbCl2. Since PbCl2 is a strong electrolyte, it fully dissociates into Pb2+ and Cl- ions when dissolved in water.
Let's assume the concentration of PbCl2 in the saturated solution is 'x' M. This means that the concentration of Pb2+ would also be 'x' M, and the concentration of Cl- would be '2x' M (twice the concentration of Pb2+ due to the stoichiometric relationship).
Using the Ksp expression and substituting the concentrations, we have:
Ksp = [Pb2+][Cl-]²
1.6 x 10^-5 = (x)(2x)²
1.6 x 10^-5 = 4x³
Rearranging the equation:
x³ = (1.6 x 10^-5) / 4
x³ = 4 x 10^-6
x = ∛(4 x 10^-6)
Now, we have determined the concentration of PbCl2 in the saturated solution. To find the mass, we need to convert this concentration to moles of PbCl2 and then calculate the mass using the molar mass of PbCl2.
The molar mass of PbCl2 is calculated as follows:
Molar mass (PbCl2) = atomic mass of Pb + 2 × atomic mass of Cl
Molar mass (PbCl2) = 207.2 g/mol + 2 × 35.5 g/mol
Molar mass (PbCl2) = 278.2 g/mol
Using Avogadro's number (6.022 x 10^23), we can now calculate the mass using the concentration:
Mass of PbCl2 = concentration (in mol/L) × volume (in L) × molar mass (in g/mol)
Therefore, the mass of PbCl2 in 0.48 L of the saturated solution can be calculated as:
Mass of PbCl2 = (∛(4 x 10^-6)) × 0.48 L × 278.2 g/mol
Now, you can use a scientific calculator or computational software to determine the final mass.
..........PbCl2(s) ==> Pb^2+ + 2Cl^-
x = solubility..x.......x.......2x
Ksp = (Pb^2+)(Cl^-)^2
Ksp = (x)(2x)^2
Solve for x which will give you the moles/L of PbCl2.
Mols/L x 0.48 L = moles in 480 mL.
Then moles x molar mass PbCl2 = grams PbCl2.