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QUESTION

# What is the pH of a saturated zinc hydroxide solution?

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?