Zinc hydroxide, Zn(OH)2(Ksp=4.1 ×10^-17), is nearly insoluble in water but is more soluble in st

Zinc hydroxide, Zn(OH)2(Ksp=4.1 ×10^-17), is nearly...

Zinc hydroxide, ${Zn}({OH})_{2}\left(K_{{sp}}=4.1 \times 10^{-17}\right),$ is nearly insoluble in water but is more soluble in strong base because ${Zn}^{2+}$ forms the soluble complex ion ${Zn}({OH})_{4}^{2-}(K_{{f}}=3 \times 10^{15})$ (a) What is the molar solubility of ${Zn}({OH})_{2}$ in pure water? (You may ignore OH from the self-dissociation of water.) (b) What is the pH of the solution in part (a)? (c) What is the molar solubility of ${Zn}({OH})_{2}$ in 0.10 ${M}$ NaOH?

Zinc hydroxide, ${Zn}({OH})_{2}\left(K_{{sp}}=4.1 \times 10^{-17}\right),$ is nearly insoluble in water but is more soluble in strong base because ${Zn}^{2+}$ forms the soluble complex ion ${Zn}({OH})_{4}^{2-}(K_{{f}}=3 \times 10^{15})$
(a) What is the molar solubility of ${Zn}({OH})_{2}$ in pure water? (You may ignore OH from the self-dissociation of water.)
(b) What is the pH of the solution in part (a)?
(c) What is the molar solubility of ${Zn}({OH})_{2}$ in 0.10 ${M}$ NaOH?

Key Concepts

Solubility Product (Ksp) Equilibrium

This concept involves the equilibrium between a sparingly soluble salt and its ions in solution. The solubility product constant (Ksp) quantifies the degree to which a salt dissociates, and it is fundamental in predicting and calculating the solubility of compounds in water under given conditions. Understanding Ksp allows one to set up the equilibrium expression necessary to compute the concentrations of ions in a saturated solution.

Formation Constant (Kf) and Complex Ion Effects

The formation constant (Kf) is a measure of the stability of a complex ion formed when a metal ion binds with one or more ligands. In solubility problems, a large Kf indicates that the formation of a complex ion can drive the dissolution of an otherwise poorly soluble salt by reducing the concentration of the free metal ion, thereby shifting the equilibrium and enhancing solubility.

Acid-Base Equilibria and pH Calculations

This concept pertains to the equilibrium of hydronium and hydroxide ions in solution, which determines the pH. In solubility equilibria involving hydroxide ions, the concentration of OH? is directly related to both the dissolution of the salt and the self-ionization of water, making it necessary to evaluate the pH of the saturated solution. Accurate pH calculations are essential for understanding solution conditions and predicting the behavior of sparingly soluble compounds in different environments.

Transcript

00:01 The first part of this question is to calculate the molar solubility of zinc hydroxide in pure water.

00:07 So we can do this simply knowing the ksp for zinc hydroxide.

00:14 Because zinc hydroxide solid will go to zinc 2 plus and the ksp is simply the concentration.

00:41 And the zinc is s equal to s, the molar solubus.

00:48 Ability to 2 s.

00:54 So the ksp for zinc hydroxide, which is 4 .1 times 10 to the negative 17, will be equal to s and 2s squared for 4 s cubed.

01:14 So our s then becomes 4 .1 to the negative 17 divided by 4 and then we take the cube root.

01:24 Of that is 2 .1 times 10 to the negative 6 molar.

01:36 It then asks us to calculate the ph of the solution and it turns out that the ph can be calculated from the hydroxide concentration or the hydroxide concentration is equal to 2s or with that being s 4 .34 times 10 to the negative 6 molar, and then ph is equal to the negative log of the hydronium concentration, h3o plus, which we can get from the hydroxide by dividing it into kw, and we get, divide those two, make the negative log 8 .64.

02:42 Now, to know the molar solubility of the zinc, hydroxide in a solution that contains 0 .1 molar sodium hydroxide, where the hydroxide concentration then is equal to zero.

03:03 We need to consider the new equilibrium.

03:07 The zn hydroxide is now going to react with some additional hydroxide and create the zn for two minus and it turns out that the kf value for that is really large three well we'll figure out that k value in a minute kf value is z n2 plus that kf value is what's given at three times 10 and 15.

04:12 We also know that zn -oh2 solid has a ksp value that describes this process.

04:30 Asp is equal to what was given up above 4 .1 times 10 by negative 17.

04:39 So how can we combine these two equations in order to get the above the above? equation here? well, it looks like if we simply add the two equations together, the zincs will cancel, two of the hydroxides will cancel, and we'll end up getting that reaction up there.

05:11 So the k value for this process then is just the product of those two k values shown below, 4 .1 negative 17 and the 3 times 10 to the 15...

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