Salt solubilities can be compared by the concentration of cation formed when the salt dissolves in the general reaction: MaXb(s) ⇌ a Mb+(aq) + b Xa-(aq). Given the following salts and their equilibrium constants for the reaction above at 25°C, which salt is the least soluble?

Question:

A) MgCO₃, Kc = 6.8 × 10⁻⁶

B) BaCO₃, Kc = 2.6 × 10⁻⁹

C) SrCO₃, Kc = 5.6 × 10⁻¹⁰

D) CaCO₃, Kc = 5.0 × 10⁻⁹

The correct option is;

C) SrCO₃, Kc = 5.6 × 10⁻¹⁰

Explanation:

To solve the question, we note that by analyzing each salt as follows

MgCO₃, Kc = 6.8 × 10⁻⁶

MgCO₃  ⇄ Mg + CO₃

Here the kc is given as

and the Ksp can be represented as  

= [Mg][CO₃]

Therefore, for amount of salt we have the solubility product , proportional to kc

Therefore is directly proportional to kc since the salt are 1:1, that is the amount ratio of the dissociated ions, (positive to negative ions concentration ratio) is 1:1

Therefore from the given kc values, we have

MgCO₃, Kc = 6.8 × 10⁻⁶ > CaCO₃, Kc = 5.0 × 10⁻⁹ > BaCO₃, Kc = 2.6 × 10⁻⁹ > SrCO₃, Kc = 5.6 × 10⁻¹⁰

Which gives the salt with the least solubility as, SrCO₃, with Kc = 5.6 × 10⁻¹⁰.