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The solubility of magnesium hydroxide (molar mass, M ) in a 0.1 M NaOH solution is W g per 100 mL at 25^ C . Its solubility product at this temperature is approximately:

Options

  1. A10⁻² ( W M )
  2. BW M
  3. C10⁻¹ ( W M )
  4. D4 10^3 ( W M )^3

Correct answer

C. 10⁻¹ ( W M )

Step-by-step solution

Given the solubility of Mg(OH) ₂ is W g per 100 mL . The molar solubility S in mol/L is: S = W M 1000 100 = 10W M mol/L The dissociation equilibrium of magnesium hydroxide is: Mg(OH) ₂ Mg ²⁺ + 2 OH ^- In a 0.1 M NaOH solution, the concentration of OH ^- ions is dominated by the strong base NaOH . Therefore, [ OH ^-] 0.1 M . The concentration of Mg ²⁺ is equal to the molar solubility S : [ Mg ²⁺] = 10W M The solubility product K_ sp is given by: K_ sp = [ Mg ²⁺][ OH ^-]^2 K_ sp = ( 10W M ) (0.1)^2 K_ sp = ( 10W M )

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