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Chapter 16: Problem 40

For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. \(\mathrm{FeC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.1 \times 10^{-7},\) or $\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-7}$ b. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}, K_{\mathrm{sp}}=8.1 \times 10^{-12},\) or \(\mathrm{Mn}(\mathrm{OH})_{2},\) \(K_{\mathrm{sp}}=2 \times 10^{-13}\)

Short Answer

Expert verified
a. Molar solubility of Cu(IO4)2 < molar solubility of FeC2O4. b. Molar solubility of Ag2CO3 < molar solubility of Mn(OH)2.

Step by step solution

01

a. FeC2O4 and Cu(IO4)2

First, let's write down the dissolution equations and expressions for molar solubility for each solid: FeC2O4 ⟶ Fe^2+ + 2C2O4^2- , molar solubility (FeC2O4) = x Equilibrium constant \(K_{sp} = [Fe^{2+}][C2O4^{2-}]^2 = x * (2x)^2 = (4x^3)\) Cu(IO4)2 ⟶ Cu^2+ + 2IO4^-, molar solubility (Cu(IO4)2) = y Equilibrium constant \(K_{sp} = [Cu^{2+}][IO4^-]^2 = y * (2y)^2 = (4y^3)\) Now we will compare: (4x^3) = \(2.1 \times 10^{-7}\) x = \(\surd[2.1 \times 10^{-7}/4]^{1/3}\) (4y^3) = \(1.4 \times 10^{-7}\) y = \(\surd[1.4 \times 10^{-7}/4]^{1/3}\) As x > y, then molar solubility of Cu(IO4)2 (y) is smaller.
02

b. Ag2CO3 and Mn(OH)2

Again, let's write down the dissolution equations and expressions for molar solubility for each solid: Ag2CO3 ⟶ 2Ag^+ + CO3^2-, molar solubility (Ag2CO3) = x Equilibrium constant \(K_{sp} = [Ag^+]^2[CO3^{2-}] = (2x)^2 * x = (4x^3)\) Mn(OH)2 ⟶ Mn^2+ + 2OH^-, molar solubility (Mn(OH)2) = y Equilibrium constant \(K_{sp} = [Mn^{2+}][OH^-]^2 = y * (2y)^2 = (4y^3)\) Now we will compare: (4x^3) = \(8.1 \times 10^{-12}\) x = \(\surd[8.1 \times 10^{-12}/4]^{1/3}\) (4y^3) = \(2 \times 10^{-13}\) y = \(\surd[2 \times 10^{-13}/4]^{1/3}\) As x < y, then molar solubility of Ag2CO3 (x) is smaller.

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Most popular questions from this chapter

What mass of \(\mathrm{ZnS}\left(K_{\mathrm{sp}}=2.5 \times 10^{-22}\right)\) will dissolve in 300.0 \(\mathrm{mL}\) of \(0.050M\) \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} ?\) Ignore the basic properties of \(\mathrm{S}^{2-}.\)

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