From this site we learn that for zinc hydroxide, ##K_(sp)=3xx10^-16##.
How did they know this? How else but by measurement? The ##K_(sp)## value really should have been included with the problem.
So we write out the solubility equilibrium:
##Zn(OH)_2(s) rightleftharpoonsZn^(2+)+2HO^-##
So, here, ##K_(sp)=[Zn^(2+)][HO^-]^2=3xx10^-16##
Given the equilibrium expression, we call the solubility of ##Zn(OH)_2##, ##S##.
Thus ##K_(sp)=[Zn^(2+)][HO^-]^2=Sxx(2S)^2=3xx10^-16##
So we have a cubic to solve:
##4S^3=3xx10^-16##
##S=””^(3)sqrt((3xx10^-16)/(4))=4.22xx10^-6*mol*L^-1##.
To get a gram solubility, we simply multiply this by the molecular mass, ##4.22xx10^-6*mol*L^-1xx99.42*g*mol^-1##
##=0.42*mg*L^-1##, i.e. less than ##”1 ppm”.##
But we are not finished yet. We were asked to find the ##pH## of a saturated solution.
Clearly, ##[HO^-]=8.44xx10^-6*mol*L^-1##; why clearly?
And thus ##pOH=-log_10(8.44xx10^-6)=-(-5.07)=5.07##.
And ##pH=14-pOH=8.93##
Does this value of ##pH## make sense, given that we dissolve an hydroxide? Why?
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