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3 years ago

What is the molar solubility of aucl3 (ksp = 3. 2 x 10-23) in a 0. 013 m solution of magnesium chloride (a soluble salt)?

Chemistry

1 answer:

Inessa [10]3 years ago

4 0

The molar solubility of AuCl₃ in a 0.013 M solution of magnesium chloride is 1.81×10⁻²⁸M.

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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