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Chapter 23: Problem 70

The \(K_{\mathrm{f}}\) for the complex ion formation between \(\mathrm{Pb}^{2+}\) and EDTA \(^{4-}\) $$ \mathrm{Pb}^{2+}+\mathrm{EDTA}^{4-} \rightleftharpoons \mathrm{Pb}(\mathrm{EDTA})^{2-} $$ is \(1.0 \times 10^{18}\) at \(25^{\circ} \mathrm{C} .\) Calculate \(\left[\mathrm{Pb}^{2+}\right]\) at equilibrium in a solution containing \(1.0 \times 10^{-3} M \mathrm{~Pb}^{2+}\) and \(2.0 \times 10^{-3} M \mathrm{EDTA}^{4-}\)

Short Answer

Expert verified
\([Pb^{2+}] = 1.0 \times 10^{-9} M\ at\ equilibrium\).

Step by step solution

01

Understand the Reaction

Given the reaction: \(\mathrm{Pb}^{2+}+\mathrm{EDTA}^{4-} \leftrightarrow \mathrm{Pb}(\mathrm{EDTA})^{2-}\). In the beginning, there are \(1.0 \times 10^{-3} M \mathrm{~Pb}^{2+}\) and \(2.0 \times 10^{-3} M \mathrm{EDTA}^{4-}\), and no \(\mathrm{Pb}(\mathrm{EDTA})^{2-}\) complex ions.
02

Setup the ICE table

According to the stoichiometry of the reaction, as the reaction proceeds to equilibrium, \(\mathrm{Pb}^{2+}\) and \( \mathrm{EDTA}^{4-}\) are reduced by x M, consequently, \( \mathrm{Pb}(\mathrm{EDTA})^{2-}\) is increased by x M. The equilibrium concentrations are thus \((1.0 \times 10^{-3} - x) M \mathrm{~Pb}^{2+}\), \((2.0 \times 10^{-3} - x) M \mathrm{EDTA}^{4-}\) and \(x M \mathrm{~Pb(EDTA)}^{2-}\).
03

Apply \(K_{\mathrm{f}}\) formula

According to the formula \( K_{\mathrm{f}} = \frac{(Pb(EDTA)^{2-})}{ (Pb^{2+})(EDTA^{4-})}\), the substitution gives us \(1.0 \times 10^{18} = \frac{x}{ (1.0 \times 10^{-3} - x)(2.0 \times 10^{-3} - x)}\).
04

Simplify and Solve

Because \(K_{\mathrm{f}}\) is huge, we can assume \(x \approx 1.0 \times 10^{-3} M\). Thus, the equation simplifies to \(1.0 \times 10^{18} = \frac{1.0 \times 10^{-3}}{(1.0 \times 10^{-3})(2.0 \times 10^{-3} - 1.0 \times 10^{-3})}\), and solving gives \(x = 1.0 \times 10^{-9} M\).

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Most popular questions from this chapter

The \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) complex is more labile than the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) complex. Suggest an experiment that would prove that \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is a labile complex.

Complete the following statements for the complex ion \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{-}:\) (a) The oxidation number of Cr is _____ (b) The coordination number of Cr is _____ . (c)_____ is a bidentate ligand.

Predict the number of unpaired electrons in the following complex ions: (a) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-},(\mathrm{b})\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)

Draw qualitative diagrams for the crystal field splittings in (a) a linear complex ion \(\mathrm{ML}_{2}\), (b) a trigonalplanar complex ion \(\mathrm{ML}_{3}\), (c) a trigonal-bipyramidal complex ion ML_{5. }

Aqueous copper(II) sulfate solution is blue in color. When aqueous potassium fluoride is added, a green precipitate is formed. When aqueous potassium chloride is added instead, a bright-green solution is formed. Explain what is happening in these two cases.
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