Question

The Ksp of Al(OH)3 is 1.0 x 10-33. What is the solubility of Al(OH)3 in a solution that has a pH =13? Give your answer using scientific notation and to 2 significant figures (i.e., one decimal place).

Answer 1

we have below equation to be used

pH = -log [H3O+]

13 = -log [H3O+]

log [H3O+] = -13

[H3O+] = 10^(-13)

[H3O+] = 1*10^-13 M

we have below equation to be used

[OH-] = (1.0*10^-14)/[H3O+]

[OH-] = (1.0*10^-14)/(1*10^-13)

[OH-] = 0.10 M

At equilibrium:

Al(OH)3 <----> Al3+ + 3 OH-

   s 0.10 + 3s

Ksp = [Al3+][OH-]^3

1*10^-33=(s)*(0.10+ 3s)^3

Since Ksp is small, s can be ignored as compared to 0.1

Above expression thus becomes:

1*10^-33=(s)*(0.10)^3

1*10^-33= (s) * 10^-3

s = 1.0*10^-30 M

Answer: 1.0*10^-30 M