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Chapter 15: Problem 34

Calculate the molar solubility of \(\mathrm{Co}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2.5 \times 10^{-43}\).

Short Answer

Expert verified
The molar solubility of Co(OH)₃, with a Ksp value of \(2.5 × 10^{-43}\), is approximately \(3.01 × 10^{-11}\) mol/L.

Step by step solution

01

Write the balanced dissolution equation

Co(OH)₃(s) → Co³⁺(aq) + 3OH⁻(aq)
02

Set up expression for Ksp

Ksp is the product of the equilibrium concentrations of the ions, raised to the power of their stoichiometric coefficients. For this reaction: Ksp = [Co³⁺] * [OH⁻]³
03

Define molar solubility (s)

Since the dissolution is 1:1 for Co³⁺ and 1:3 for OH⁻, we can represent their concentrations in terms of the molar solubility (s). [Co³⁺] = s [OH⁻] = 3s
04

Substitute concentrations into Ksp expression

Plug the expressions for [Co³⁺] and [OH⁻] into the Ksp expression: Ksp = s * (3s)³
05

Plug in given Ksp value and solve for s

We were given the Ksp value: Ksp = 2.5 × 10⁻⁴³ 2.5 × 10⁻⁴³ = s * (3s)³ Rearranging to solve for s: \(s^4 = \frac{2.5 × 10^{-43}}{27}\) Take the 4th root of both sides: \(s = \sqrt[4]{\frac{2.5 × 10^{-43}}{27}}\)
06

Find the molar solubility

Compute the numerical value of s: s = \( \sqrt[4]{\frac{2.5 × 10^{-43}}{27}} \approx 3.01 × 10^{-11}\) The molar solubility of Co(OH)₃ is approximately 3.01 × 10⁻¹¹ mol/L.

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Most popular questions from this chapter

Calculate the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=8.9 \times 10^{-12}\).

On a hot day, a 200.0 -mL sample of a saturated solution of \(\mathrm{PbI}_{2}\) was allowed to evaporate until dry. If \(240 \mathrm{mg}\) of solid \(\mathrm{PbI}_{2}\) was collected after evaporation was complete, calculate the \(K_{\mathrm{sp}}\) value for \(\mathrm{PbI}_{2}\) on this hot day.

a. Using the \(K_{\mathrm{sp}}\) value for \(\mathrm{Cu}(\mathrm{OH})_{2}\left(1.6 \times 10^{-19}\right)\) and the overall formation constant for \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\left(1.0 \times 10^{13}\right)\) calculate the value for the equilibrium constant for the following reaction: $$\mathrm{Cu}(\mathrm{OH})_{2}(s)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)$$ b. Use the value of the equilibrium constant you calculated in part a to calculate the solubility (in mol/L) of \(\mathrm{Cu}(\mathrm{OH})_{2}\) in \(5.0 M \mathrm{NH}_{3} .\) In \(5.0 \mathrm{M} \mathrm{NH}_{3}\) the concentration of \(\mathrm{OH}^{-}\) is \(0.0095 M\).

Write equations for the stepwise formation of each of the following complex ions. a. \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\) b. \(\mathrm{V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}^{3-}\)

A 50.0 -mL sample of \(0.0413\) \(M\) \(\mathrm{AgNO}_{3}(a q)\) is added to \(50.0 \mathrm{mL}\) of 0.100 \(M \mathrm{NaIO}_{3}(a q) .\) Calculate the \(\left[\mathrm{Ag}^{+}\right]\) at equilibrium in the resulting solution. \(\left[K_{\mathrm{sp}} \text { for } \mathrm{AgIO}_{3}(s)=3.17 \times 10^{-8} .\right]\)
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