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23 April, 07:15

Calculate how many times more soluble Mg (OH) 2 is in pure water Based on the given value of the Ksp, 5.61*10-11, calculate the ratio of solubility of Mg (OH) 2 dissolved in pure H2O to Mg (OH) 2 dissolved in a 0.130 M NaOH solution.

molar solubility in water = 2.41 x 10^-4

molar solubility of NaOH in 0.130M = 3.32 x 10^-9

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  1. 23 April, 07:41
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    molar solubility in water = 2.412 * 10^-4 mol/L

    molar solubility of NaOH in 0.130M = 3.32 * 10^-9 mol/L

    Mg (OH) 2 is a factor 0.73*10^5 more soluble in pure water than in 0.130 M NaOH

    Explanation:

    The Ksp refers to the partial solubilization of a mostly insoluble salt. This is an equilibrium process.

    The equation for the solubilization reaction of Mg (OH) 2 can be given as:

    Mg (OH) 2 (s) → Mg2 + (aq) + 2OH - (aq)

    Ksp can then be given as followed:

    Ksp = [Mg^2+][OH^-]²

    Step 2: Calculate the solubility in water

    Mg (OH) 2 (s) → Mg2 + (aq) + 2OH - (aq)

    The mole ratio Mg^2 + with OH - is 1:2

    So there will react X of Mg^2 + and 2X of OH-

    The concentration at equilibrium will be XM Mg^2 + and 2X OH-

    Ksp = [Mg^2+][OH^-]²

    5.61*10^-11 = X * (2X) ² = X * 4X² = 4X³

    X = 2.412 * 10^-4 mol/L = solubility in water

    Step 3: Calculate solubility in 0.130 M NaOH

    The initial concentration of Mg^2 + = 0 M

    The initial concentration of OH - = 0.130 M

    The mole ratio Mg^2 + with OH - is 1:2

    So there will react X of Mg^2 + and 2X + 0.130 for OH-

    The concentration at equilibrium will be XM Mg^2 + and 0.130 + 2X OH-

    The value of "[OH-] + 2X" is, because the very small value of X, equal to the value of [OH-].

    Let's consider:

    [Mg+2] = X

    [OH] = 0.130

    Ksp = [Mg^2+][OH^-]²

    5.61*10^-11 = X * (0.130) ²

    5.61*10^-11 = X * (0.130) ^2

    X = 3.32*10^-9 = solubility in 0.130 M NaOH

    Step 4: Calculate how many times Mg (OH) 2 is better soluble in pure water.

    (2.412*10^-4) / (3.32*10^-9) = 0.73 * 10^5

    Mg (OH) 2 is a factor 0.73*10^5 more soluble in pure water than in 0.130 M NaOH
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