3) The mineral brucite (Mg(OH) 2 (s)) precipitates when dilute groundwater react

Question

3)     The mineral brucite (Mg(OH)2(s)) precipitates when dilute groundwater reacts with magnesium-rich rocks of the California coast ranges. The reaction consumes hydroxyl ions and there is apparent equilibrium:

Mg+2(aq) + 2 OH-(aq) = Mg(OH)2(s)

If I measure the pH of springs near Jenner to be pH=9.5, what can you tell me about the equilibrium activity (concentration) of magnesium in that solution? (Neglect activity coefficient corrections.) You will need to calculate the dissociation constant of water to answer this question:

H2O(l) = H+(aq) + OH-(aq)

Explanation / Answer

he dissociation constant of water are temperature dependent, so look for Kaat temperature of water
calculate Pka = -log10 Ka  
Use Henderson-Hasselbalch equation for the equation H2O (aq) <-------> H+(aq) + OH-(aq)
PH = Pka + log10 ( [OH-] / [H2O] )
plug in PH = 9.5 and the Pka value and assume [H2O] = 1M and find out [OH-]
The equilibrium concentration of magnesium in the solution will be, [Mg+2] = 2 [OH-]

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