Question

Please answer both parts. Thanks!

Part A)

Mg(OH)2 is a sparingly soluble salt with a solubility product, Ksp, of 5.61×10−11. It is used to control the pH and provide nutrients in the biological (microbial) treatment of municipal wastewater streams. What is the ratio of solubility of Mg(OH)2 dissolved in pure H2O to Mg(OH)2 dissolved in a 0.180 M NaOH solution? Express your answer numerically as the ratio of molar solubility in H2O to the molar solubility in NaOH.

Part B)

What is the pH change of a 0.260 M solution of citric acid (pKa=4.77) if citrate is added to a concentration of 0.140 M with no change in volume? Express the difference in pH numerically to two decimal places.

Answer 1

(A)

Assume solubility as 'x' moles/L

Solubility in pure H2O is:

x = (K_sp/4)^1/3 = (5.6*10^-11/4)^1/3 = 2.41*10^-4 moles/L

Solubility in 0.18 M NaOH is:

[Mg²⁺]*[OH^-]² = Ksp = 5.6*10^-11 = [Mg²⁺]*0.180²

So,

[Mg²⁺] = 1.72*10^-9 moles/L

So reqd ratio = (2.41*10^-4)/(1.72*10^-9) = 140116.28

(B)

Initial [H+] = (0.260*10^-4.77)^0.5 = 0.0021

So, initial pH = -log(0.0021) = 2.67

After adding citrate:

pH = pKa + log([citrate]/[acid]) = 4.77 + log(0140/0.260) = 7.5

So, the pH increases by 4.83 units

Hope this helps !