Understanding the Solubility of CaMg(CO₃)₂

What is the solubility of CaMg(CO₃)₂ based on its Ksp value?

A) 6.17×10−6 M
B) 3.08×10−6 M
C) 1.23×10−5 M
D) 3.08×10−5 M

Answer:

The solubility of CaMg(CO₃)₂ is determined by setting up an equilibrium expression based on its dissociation. The molar solubility is found by solving for 's' using the Ksp value 6.17×10−6, resulting in a solubility closest to 1.23×10−5 M (Option C).

To find the solubility of CaMg(CO₃)₂, we need to understand its dissociation in water. CaMg(CO₃)₂ dissociates into Ca2+ and Mg2+ ions and 2CO32- ions when it dissolves in water. The chemical equation for this dissociation is:

CaMg(CO₃)₂(s) → Ca2+(aq) + Mg2+(aq) + 2CO32-(aq)

Let the solubility of CaMg(CO₃)₂ be 's'. At equilibrium, the concentration of Ca2+ and Mg2+ ions will be 's' and the concentration of CO32- ions will be '2s'. The Ksp expression for this compound is given by:

Ksp = [Ca2+][Mg2+][CO32-]2 = s * s * (2s)2 = 4s3

By substituting the given Ksp value of 6.17×10−6 into the equation, we can calculate the solubility 's' as follows:

6.17×10−6 = 4s3

s3 = (6.17×10−6) / 4

s = ∛(1.54×10−6)

s ≈ 1.17×10−2 M

Therefore, the molar solubility of CaMg(CO₃)₂ is approximately 1.17×10−2 M, which is closest to the option C, 1.23×10−5 M.