1)What is the pH of a saturated solution of lead(II) hydroxide? The Ksp= 4.0e-15

Pb(OH)2

4.0e-15 = (x)(2x)^2 = 4x^3

I divided by 4 and took the cube root and got 1.12e-5 but I am not sure I took the cube root correctly.

-log(1.12e-5)= 4.95
14-4.95 = 9.05

The answer choices given are 9.0 and 9.1.

Did I do this correctly?

2) Which pair of mixtures is the most effective buffer system for a pH value of 7.45?

a) Carbonic acid and sodium bicarbonate
b) Sodium bicarbonate and sodium carbonate
c) Sodium dihydrogen phosphate and disodium hydrogen phosphate
d) Hydrogen cyanide and sodium cyanide
e) Ammonia and ammonium chloride

I chose answer c, sodium dihydrogen phosphate abd disodium hydrogen phosphate.

Would you agree?

Thank you for checking my answers.

Thanks for showing your work.

Your 4x^3 = 4.0E-15 is ok. Somewhere in the next two steps you made a math error.
Then x^3 = 4.0E-15/4 = 1E-15
cube root (1E-15) = 1E-5 = x = (OH^-)
Then pOH = 5 and pH = 14-5 = 9

I didn't look up the pK2 value for H3PO4 but I think you are right with c.

Let's go through each question one by one:

1) To determine the pH of a saturated solution of lead(II) hydroxide (Pb(OH)2), we can start by writing the balanced chemical equation for the dissociation of Pb(OH)2:

Pb(OH)2 ⇌ Pb2+ + 2OH-

The Ksp expression for this dissociation is: Ksp = [Pb2+][OH-]^2

Since the Ksp value is given as 4.0e-15, we can assume that the concentration of Pb2+ is equal to the concentration of OH- in this saturated solution. Therefore, we can assign the concentration of OH- as 'x'.

The equilibrium expression can be written as: 4.0e-15 = x(2x)^2 = 4x^3

Simplifying the equation gives: 4.0e-15 = 4x^3

To solve for x, divide both sides of the equation by 4 and take the cube root of both sides: (4.0e-15/4)^(1/3) = x

Calculating this gives x ≈ 6.31e-6

To find the pH, we need to determine the concentration of H+ ions. In this case, we can use the fact that [H+] = [OH-], so [H+] ≈ 6.31e-6 M.

Taking the negative logarithm of the concentration, we have -log(6.31e-6) ≈ 5.2

Therefore, the pH of the saturated Pb(OH)2 solution would be approximately 5.2.

Based on your calculation, you obtained -log(1.12e-5) ≈ 4.95, which is close to the correct answer. However, your calculation of 14 - 4.95 = 9.05 is incorrect since the pOH can't be directly subtracted from 14 to calculate the pH. Therefore, the answer choices of 9.0 and 9.1 are not accurate in this case. The correct answer is around pH 5.2.

2) To determine the most effective buffer system for a pH value of 7.45, we need to consider the conjugate acid-base pairs and their pKa values. The pKa value represents the acidity or basicity of a compound.

a) Carbonic acid (H2CO3) and sodium bicarbonate (NaHCO3) - pKa = 6.3
b) Sodium bicarbonate (NaHCO3) and sodium carbonate (Na2CO3) - pKa = 10.3
c) Sodium dihydrogen phosphate (NaH2PO4) and disodium hydrogen phosphate (Na2HPO4) - pKa = 7.2
d) Hydrogen cyanide (HCN) and sodium cyanide (NaCN) - pKa = 9.2
e) Ammonia (NH3) and ammonium chloride (NH4Cl) - pKa = 9.2

To create an effective buffer system for a pH value of 7.45, we want a weak acid and its conjugate base with pKa values close to the desired pH.

Among the options provided, sodium dihydrogen phosphate (NaH2PO4, pKa = 7.2) and disodium hydrogen phosphate (Na2HPO4) would create the most effective buffer system since their pKa value is closest to the desired pH value of 7.45.

Therefore, your choice of answer c, sodium dihydrogen phosphate and disodium hydrogen phosphate, is correct.

I hope this helps clarify your answers! Don't hesitate to ask if you have any further questions.