The molar solubility of AuCl₃ in a 0.013 M solution of magnesium chloride is 1.81×10⁻²⁸M.
<h3>What is Ksp?</h3>
The solubility product constant, Ksp, is the equilibrium constant for a solid substance dissolving in an aqueous solution. And for the AuCl₃, Ksp will be written as: Ksp = [Au³⁺][Cl⁻]³
Let the solubility of the AuCl₃ in 0.013M solution of magnesium chloride is x, of Au³⁺ is x and of Cl⁻ is 3x. But we know that MgCl₂ is a strong electrolyte and it completely dissociates into its ions and will produce 2 moles of chloride ions. For this solution let we consider the volume is 1 liter then the concentration of chloride ions in MgCl₂ is 2(0.013)=0.026M.
So, in MgCl₂ solution concentration of Cl⁻ becomes = 3x + 0.026.
Value of Ksp for AuCl₃ = 3.2 × 10⁻²³
On putting all values on the Ksp equation, we get
Ksp = (x)(3x + 0.026)³
Value of 3x is negligible as compared to the 0.026, so the equation becomes
3.2 × 10⁻²³ = (x)(0.026)³
x = 3.2×10⁻²³ / (0.026)³
x = 1.81×10⁻²⁸M
Hence the molar solubility of AuCl₃ in 0.010M MgCl₂ is 1.81×10⁻²⁸M.
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