What is the [Pb+2] in a saturated solution of Pb(OH)2 for each of the following initial pH values?

Ksp Pb(OH)2 = 2.8x10-16

a. pH = 13.00
b. pH = 9.20

To find the concentration of [Pb+2] in a saturated solution of Pb(OH)2, we need to calculate the hydroxide ion concentration, [OH-], and then use it to find the concentration of [Pb+2] based on the balanced equation of the dissolution of Pb(OH)2.

a. pH = 13.00:
In a basic solution, the [OH-] concentration can be calculated using the formula:

[OH-] = 10^-(pOH)

Since pOH is the negative logarithm of the hydroxide ion concentration, we can subtract the given pH value from 14 to get the pOH value:

pOH = 14 - pH
= 14 - 13.00
= 1.00

Using the derived pOH value, we can calculate the [OH-] concentration:

[OH-] = 10^-(pOH)
= 10^-1.00
= 0.1 M

Since the stoichiometry of Pb(OH)2 is 1:2 for Pb+2 and OH-, the [Pb+2] concentration will be twice the [OH-] concentration:

[Pb+2] = 2 * [OH-]
= 2 * 0.1
= 0.2 M

Therefore, the [Pb+2] concentration in a saturated solution of Pb(OH)2 with a pH of 13.00 is 0.2 M.

b. pH = 9.20:
Similarly, we can find the [OH-] concentration using the calculated pOH value:

pOH = 14 - pH
= 14 - 9.20
= 4.80

[OH-] = 10^-(pOH)
= 10^-4.80

Now, we can find the [Pb+2] concentration:

[Pb+2] = 2 * [OH-]

By plugging in the calculated [OH-] concentration, we can find the [Pb+2] concentration in a saturated solution of Pb(OH)2 with a pH of 9.20.

Remember, in this case you need to perform the actual calculations to arrive at the exact value of [Pb+2].