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The solubility of the barium hydroxide after the addition of a 1M solution of barium nitrate is 0.035M
Barium nitrate is a salt that dissolves entirely in solution and is soluble. This indicates that before the salt dissolves, there will be a one molar concentration of barium ions. We may anticipate that the equilibrium will be pushed to the left and the barium hydroxide will be less soluble because we have increased the product side of the reaction. The common ion effect is the name given to this shift in equilibrium.
To ascertain the salt's solubility, we shall use an ICE table.
I. There is a one molar concentration of barium ions (from the barium nitrate) in the solution before the salt starts to dissolve, but there are no hydroxide ions present.
C. The unknown increases in each ion can be referred to as 1+ and 2x, respectively, because every dissolved molecule of barium hydroxide will produce one barium ion and two hydroxide ions. Observe how the previously added one molar concentration in the solution will be combined with the increased barium ion concentration.
E. At this point, we set the solubility equation to the constant representing the solubility product.
[tex]Ba(OH)_{2}[/tex] ⇔ [tex]Ba^{2+} + 2OH^{-}[/tex]
Ksp is defined as:
Ksp = [tex][Ba^{2+}] + [OH^{-}]^{2}[/tex]
5 x [tex]10^{-3}[/tex] = [tex][Ba^{2+}] [OH^{-}]^{2}[/tex]
It added a solution of 1M of [tex]Ba^{2+}[/tex]
5 x [tex]10^{-3}[/tex] = [tex][1M][/tex] [tex][OH^{-}]^{2}[/tex]
The addition of barium hydroxide [tex]Ba(OH)_{2}[/tex] gives:
[tex][Ba^{2+}] = 1M + x[/tex]
[tex][OH^{-}]^{2}[/tex] [tex]= 2x[/tex]
Replacing:
5x[tex]10^{-3}[/tex] = [tex][1+x][/tex] [tex][2x]^{2}[/tex]
[tex]10^{-3} = 4x^{2} + 4x^{3}[/tex]
[tex]x = 0.035 M[/tex]
Your question is incomplete, but most probably your full question was to consider the following balanced equation for the dissociation of barium hydroxide in an aqueous solution.
[tex]Ba(OH)_{2} (s) = Ba^{2+} (aq) + 2OH (aq)\\Ksp = 5* 10^{-3}[/tex]
A 1M solution of barium nitrate is added to the solution. What is the solubility of barium hydroxide after this addition?
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