Quest (1) determine the ksp for magnesium hydroxide #Mg(OH)_2# where the molar solubility of #Mg(OH)_2# is #1.4xx10^(-4) M#?

We will use ICE table to solve this question.

The dissolution of #Mg(OH)_2# can be written as follows:

#" " " " " " " " " " "# #Mg(OH)_2(s) -> Mg^(2+)(aq) + 2OH^(-)(aq)#

#" " " " " " # Initial: # " " " " " " " " " " " " 0 M " " " " " " 0M#

#" " " " " # Change: # - sM " " " " " " " " " +sM " " " " " +2s M#

#" " " # Equilibrium: # " " " " " " " " " " " " s M " " " " " " " " " 2s M#

The expression of #K_(sp)# can be written as follows:

#K_(sp) = [Mg^(2+)(aq)] *[OH^(-)(aq)]^2#

# => K_(sp) = s*(2s)^2 = 4s^3= 4xx(1.4xx10^-4)^3#

#=> K_(sp)= 1.1 xx10^(-11)#

Quest (2) The #K_(sp)# for #Zn(OH)_2# is #5.0xx10^(-17)# . Determine the molar solubility of #Zn(OH)_2# in a buffer solution with a #pH " of " 11.5#?

We will use ICE table to solve this question.

#pH = 11.5 => [H^+] = 10^(-11.5)#

#=> [OH^-] =10^(-2.5) = 3.2xx10^(-3) M#

The dissolution of #Zn(OH)_2# can be written as follows:

#" " " " " " " " " " "# #Zn(OH)_2(s) -> Zn^(2+)(aq) + 2OH^(-)(aq)#

#" " " " " " # Initial: # " " " " " " " " " " " " 0 M " " " " " 3.2xx10^(-3) M#

#" " " " " # Change: # - sM " " " " " " "" +sM " " " " " +2s M#

#" " " # Equilibrium: # " " " " " " " " " " " " s M " " " " " (3.2xx10^(-3) + 2s) M#

The expression of #K_(sp)# can be written as follows:

#K_(sp) = [Zn^(2+)(aq)] *[OH^(-)(aq)]^2#

#5.0xx10^(-17) =s *(3.2xx10^(-3) + 2s)^2#

Solve for #s=4.9xx10^(-12)M#

Here is a video that explains the solving of Q2 (start at minute 5:14):