Determine the molar solubility of cadmium hydroxide in pure water. K_sp of cadmi

Question

Determine the molar solubility of cadmium hydroxide in pure water. K_sp of cadmium hydroxide = 7.2 times 10^-15. (Ignore the fact that Cd^2+ is an acidic ion.) What is the pH of a saturated cadmium hydroxide solution? If the pH of a saturated solution of cadmium hydroxide is increased by adding NaOH, does the solubility of cadmium hydroxide increase or decrease. Explain your answer. (Assume no solution volume changes takes place). Determine the molar solubility of cadmium hydroxide in a solution that is buffered at pH 10.50 (Since it is a buffer, assume the pH of the solution does not change as cadmium hydroxide dissolves.) Determine the molar solubility of cadmium hydroxide in a solution that is buttered at pH 9.00. In which solution is cadmium hydroxide the most soluble, pure water, pH 9.00 or pH 10.50? Explain why cadmium hydroxide is most soluble is this solution.

Explanation / Answer

a) Ksp = [Cd2+][OH-]2

let the solubility be 's'

so ..

Ksp = [s][2s]2

or 4s3 = Ksp

or s = (Ksp/4) 1/3

s= 1.22 X 10-5 M

b) since [OH-] = 2 s

or [OH-] = 2.44 X 10-5

or pOH = -log[OH-]

= 4.91

or pH = 14-pOH

= 9.08

c)

if conc of OH- is increased ..then the solubility of cadmium wil decrease ...

as Ksp = [Cd2+][OH-]2

or [Cd2+] = Ksp /[OH-]2

d)

pH = 10.5 ..that means pOH = 14- pH

or pOH = 3.5

or now conc of OH- = 10-3.5

3.16 X 10-4 M

hence now substituting the value of OH- and Ksp to calculate the solubility of cadmium

[Cd2+] = Ksp /[OH-]2

or [Cd2+] = (7.2 X 10-15 / (3.16 X 10-4) 2

= 7.2 X 10-8 M

e) at pH 9 ....pOH = 5 ...hence [OH-] = 10-5

similarly substituting values of OH- and Ksp we have

[Cd2+] = Ksp /[OH-]2

or [Cd2+] = (7.2 X 10-15 / (10-5) 2

= 7.2 X 10-5 M

d) you can see that [OH-] at pH 10.5 is greater than at pH 9

hence the solubilty of cadmium is inversly proportional to the conc OH-

or even from the valued calculated we can see that cadmiun is more soluble at pH 9

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