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J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry 4th edition

Problem 16.66

Calculate the solubility of Mg(OH)2 in a buffer solution that is 0.75 M NH3 and 0.50 M NH4Cl.






Answer:

The solubility of magnesium hydroxide will depend upon the concentration of hydroxide present (hydroxide is a common ion between the buffer and the salt). Thus, the first step in the problem is to find the concentration of hydroxide in the buffer. Then, a typical solubility equilibrium problem can be solved. Assume 25 °C.

Buffer solution:

 

NH4Cl(aq)

NH4+(aq)

+

Cl(aq)

 

NH3(aq)

+

H2O(l)

NH4+(aq)

+

OH(aq)

 

Initial

0.75

     

0.50

 

0

Change

– x

     

+ x

 

+ x

Equilibrium

0.75 – x

     

0.50 + x

 

x

Approximation is allowed, so

x = [OH] = 2.7×10–5 M



Solubility of Mg(OH)2

The hydroxide ion concentration will not change because of the buffer, so

 

Mg(OH)2(s)

Mg2+(aq)

+

2 OH(aq)

 

Ksp = [Mg2+]e[OH]e2 = 1.8×10–11

Initial

   

0

 

2.7×10–5

Change

   

+ x

 

+ 0

Equilibrium

   

x

 

2.7×10–5

1.8×10–11 = [x][2.7×10–5]2

x = molar solubility of Mg(OH)2 (in the buffer) = 0.025 M