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Chapter 16: Problem 32

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)鈧� is approximately \( 1.25 \times 10^{-11}\: \text{mol/L} \).

Step by step solution

01

1. Write the balanced chemical equation of Co(OH)鈧� dissolving in water

First, we need to know how Co(OH)鈧� behaves in the water when it dissolves. The balanced reaction for the dissolution of cobalt(III) hydroxide is: Co(OH)鈧� (s) 鈬� Co鲁鈦� (aq) + 3OH鈦� (aq)
02

2. Express the solubility in terms of x

Now, let's assume the molar solubility of Co(OH)鈧� is x mol/L. Then at equilibrium: - [Co鲁鈦篯 = x mol/L - [OH鈦籡 = 3x mol/L
03

3. Write the expression for Ksp

Now, let's write the expression for Ksp for this reaction using the molar concentrations at equilibrium: Ksp = [Co鲁鈦篯 [OH鈦籡鲁
04

4. Substitute the given Ksp value and molar concentrations in the Ksp expression

Since the question provides the Ksp value of 2.5 脳 10鈦烩伌鲁, now we can substitute the values in our expression: \( 2.5 \times 10^{-43} \) = (x) (3x)鲁
05

5. Solve for x

To find the molar solubility x, we need to simplify and solve the equation for x: \( 2.5 \times 10^{-43} \) = 27x鈦� Divide both sides by 27: \( x^{4} = \frac{2.5 \times 10^{-43}}{27} \) Now, take the fourth root of both sides: \( x = \left(\frac{2.5 \times 10^{-43}}{27}\right)^{\frac{1}{4}} \)
06

6. Calculate the molar solubility

Finally, we can plug in the given values into our calculator to find the molar solubility: \( x = \left(\frac{2.5 \times 10^{-43}}{27}\right)^{\frac{1}{4}} \approx 1.25 \times 10^{-11}\: \text{mol/L} \) So, the molar solubility of Co(OH)鈧� is approximately \( 1.25 \times 10^{-11}\: \text{mol/L} \).

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Most popular questions from this chapter

The \(K_{\text {sp }}\) of \(\mathrm{Al}(\mathrm{OH})_{3}\) is \(2 \times 10^{-32}\). At what \(\mathrm{pH}\) will a \(0.2 \mathrm{M} \mathrm{Al}^{3+}\) solution begin to show precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}\) ?

You have two salts, \(\mathrm{Ag} \mathrm{X}\) and \(\mathrm{AgY}\), with very similar \(K_{\mathrm{xp}}\) values. You know that \(K_{a}\) for \(\mathrm{HX}\) is much greater than \(K_{n}\) for HY. Which salt is more soluble in acidic solution? Explain.

When \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) is added to a solution containing a metal ion and a precipitate forms, the precipitate generally could be one of two possibilities. What are the two possibilities?

Solutions of sodium thiosulfate are used to dissolve unexposed \(\mathrm{AgBr}\left(K_{\mathrm{sp}}=5.0 \times 10^{-13}\right)\) in the developing process for blackand-white film. What mass of AgBr can dissolve in \(1.00 \mathrm{~L}\) of \(0.500 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} ? \mathrm{Ag}^{+}\) reacts with \(\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}\) to form a complex ion:

A solution contains \(1.0 \times 10^{-5} \mathrm{M} \mathrm{Ag}^{+}\) and \(2.0 \times 10^{-6} \mathrm{M} \mathrm{CN}^{-}\). Will \(\mathrm{AgCN}(s)\) precipitate? \(\left(K_{\mathrm{sp}}\right.\) for \(\mathrm{AgCN}(s)\) is \(2.2 \times 10^{-12}\).)
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