The Ksp for a certain metal hydroxide, M(OH)2 (molar mass = 127) is 3.5 × 10-19. What is the pH for a saturated solution of this hydroxide?
Confused on how to set up this problem...
M(OH)2 ==> M^+2 + 2OH^-
Set up an ICE chart and substitute
Ksp = (M^+2)(OH^-)^2
Ksp = (x)(2x)^2 = 3.5E-19
Solve for x. 2x = (OH^-) then convert to pOH, finally to pH. I get something like 7.6 or so.
Thanks a lot man!
To determine the pH of a saturated solution of a metal hydroxide, we need to consider the dissociation of the hydroxide in water. The expression for the solubility product constant (Ksp) for the metal hydroxide can be written as follows:
M(OH)2 (s) ⇌ M2+(aq) + 2OH-(aq)
The molar solubility of M(OH)2 in water can be represented as "s mol/L". Since every M(OH)2 dissociates to give one M2+ ion and two OH- ions, the equilibrium expression for the dissociation reaction can be written as:
Ksp = [M2+][OH-]^2
Given that the Ksp is 3.5 × 10^-19, we can use this information to determine the equilibrium concentration of the hydroxide ions, [OH-].
Since two OH- ions are produced for every M(OH)2 molecule, the concentration of OH- ions will be 2s. Hence, the equilibrium expression can be modified as follows:
Ksp = [M2+](2s)^2
For the sake of simplicity, let's assume that x represents the equilibrium concentration of M2+ ions. The concentration of OH- ions can then be represented as 2x. Substituting these values into the equation gives:
3.5 × 10^-19 = x(2x)^2
Simplifying the equation:
3.5 × 10^-19 = 4x^3
Rearranging the equation:
x^3 = (3.5 × 10^-19) / 4
Calculating the right-hand side:
x^3 = 8.75 × 10^-20
Taking the cube root of both sides, we find:
x = 2.12 × 10^-6 mol/L
Since the concentration of hydroxide ions is twice the concentration of M2+ ions, the concentration of OH- ions is 2(2.12 × 10^-6) = 4.24 × 10^-6 mol/L.
To find the pH of the saturated solution, we need to determine the pOH first. Since pOH = -log[OH-], we can calculate it as:
pOH = -log(4.24 × 10^-6)
Finally, the pH can be calculated by using the relation pH + pOH = 14:
pH = 14 - pOH
You can now substitute the calculated pOH value into the above equation to find the pH of the saturated solution of M(OH)2.