The pH at which Mg(OH)₂[ Kₛₚ=1 × 10⁻¹¹] begins to precipitate from a solution containing 0.10 M Mg²⁺ ions is __________.

Solution

Chemistry ma’am · 3 steps

Precipitation starts the moment the ionic product just reaches Kₛₚ, so find the hydroxide that does it.

1. Condition to precipitate. Mg(OH)₂ starts to come out of solution when the ionic product [Mg²⁺][OH⁻]² just equals Kₛₚ. Put in [Mg²⁺] = 0.10 M and solve for [OH⁻].

   [OH⁻]² = Kₛₚ/[Mg²⁺] = (1 × 10⁻¹¹)/0.10 = 1 × 10⁻¹⁰

2. Take the root. [OH⁻] = √(1 × 10⁻¹⁰) = 1 × 10⁻⁵ M, so pOH = 5.
3. So. pH = 14 - pOH = 14 - 5 = 9.

The common slip: 5. Stopping at the pOH gives 5. The question asks for pH, so subtract it from 14.

The idea to keep. For a hydroxide precipitating, set the ionic product equal to Kₛₚ, solve for [OH⁻], then convert pOH to pH with pH + pOH = 14.

Answer from the NTA final answer key. Solution by PrepWiser.