calculate the molar solubility of Pbl2 in 0.100 M Pb(NO3)2.
Ksp = 9.8 x 10^-9
..................PbI2 ==> Pb^2+ + 2I^-
I.................solid...........0............0
C................solid-x........x............2x
E.................solid...........x............2x
Ksp = (Pb^2+)(I^-)^2
........................Pb(NO3)2 ==> Pb^2+ + 2NO3^-
I.........................0.100................0.............0
C.......................-0.100...........0.100........0.200
E...........................0................0.100.........0.200
So plug into Ksp expression above the following:
(Pb^2+) = x from PbI2 and 0.100 from Pb(NO3)2 to make (0.100 + x)
(I^-) = 2x
Post your work if you get stuck.
Solve for x = solubility in mols/L
To calculate the molar solubility of PbI2 in 0.100 M Pb(NO3)2, we need to use the concept of common ion effect and the solubility product constant (Ksp) equation.
The balanced chemical equation for the dissolution of PbI2 is:
PbI2(s) ⇌ Pb2+(aq) + 2I-(aq)
According to the Ksp equation:
Ksp = [Pb2+][I-]^2
Since Pb(NO3)2 is a soluble compound, it dissociates completely into Pb2+ and NO3- ions. Therefore, the initial concentration of Pb2+ ions is the concentration of Pb(NO3)2, which is 0.100 M.
To determine the molar solubility of PbI2, we need to consider the common ion effect, which states that the presence of a common ion in a solution decreases the solubility of a slightly soluble salt.
Since Pb(NO3)2 contains Pb2+ ions, which is the same ion as in PbI2, we need to account for the common ion effect. This means that the concentration of Pb2+ ions from the dissociation of Pb(NO3)2 will decrease the solubility of PbI2.
Let's assume x mol/L of PbI2 dissolves. Therefore, the concentration of Pb2+ ions will be (0.100 - x) M (0.100 M initial concentration of Pb(NO3)2 minus x).
Using the Ksp equation, we can substitute the concentrations into the equation:
Ksp = (0.100 - x)(2x)^2 = 9.8 x 10^-9
Simplifying the equation, we get:
4x^3 - 0.4x^2 + 9.8 x 10^-9 = 0
To solve this equation, you can use numerical methods such as a graphing calculator, a mathematical software, or Excel to find the value of x that satisfies the equation.