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Chapter 24: Problem 73

A manganese complex formed from a solution containing potassium bromide and oxalate ion is purified and analyzed. It contains \(10.0 \% \mathrm{Mn}, 28.6 \%\) potassium, \(8.8 \%\) carbon, and \(29.2 \%\) bromine by mass. The remainder of the compound is oxygen. An aqueous solution of the complex has about the same electrical conductivity as an equimolar solution of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\). Write the formula of the compound, using brackets to denote the manganese and its coordination sphere.

Short Answer

Expert verified
The formula of the manganese complex is \(\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{Br})_{2}\right]\).

Step by step solution

01

Calculate moles of each element in the sample

The first step is to convert the mass percentages of each element into moles. Let's assume we have 100 grams of the sample. Then, for each element, we can calculate its representative moles by dividing the mass by its respective molar mass. Moles of Mn = \(\frac{10.0\% }{54.938\ g/mol} = 0.182\) Moles of K = \(\frac{28.6\%}{39.098\ g/mol} = 0.731\) Moles of C = \(\frac{8.8\%}{12.01\ g/mol} = 0.732\) Moles of Br = \(\frac{29.2\%}{79.904\ g/mol} = 0.365\) 100 - (10.0 + 28.6 + 8.8 + 29.2) = 23.4 Moles of O = \(\frac{23.4\%}{16.00\ g/mol} = 1.463\)
02

Determine the empirical formula of the complex

Next, we need to determine the empirical formula of the complex. In order to do this, we'll divide all of the moles by the smallest number of moles and round to the nearest whole number. Dividing all moles by 0.182 (smallest number of moles): Mn: \(\frac{0.182}{0.182} = 1\) K: \(\frac{0.731}{0.182} \approx 4\) C: \(\frac{0.732}{0.182} \approx 4\) Br: \(\frac{0.365}{0.182} \approx 2\) O: \(\frac{1.463}{0.182} \approx 8\) Based on these calculations, the empirical formula of the complex is \(\mathrm{K}_{4}\mathrm{Mn}\mathrm{C}_{4}\mathrm{Br}_{2}\mathrm{O}_{8}\).
03

Determine the coordination sphere and the charge on the complex

We know that this complex has a coordination sphere like \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\). In the given compound, Fe is surrounded by 6 ligands, and the overall charge is -4. Since the electrical conductivity of the manganese complex's solution is similar to \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), we can assume that it will also have 4 potassium ions as counterions, giving the manganese complex a -4 charge.
04

Write the formula of the complex

From step 3, we now know that the manganese complex has a -4 charge and 4 potassium ions as counterions. Since there are 4 carbon and 8 oxygen atoms in the empirical formula, we can deduce that the oxalate ion, which has a formula of \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\), acts as the ligand. The complex has two oxalate ligands and two bromide ligands. Therefore, the coordination sphere of the complex is \([\mathrm{Mn}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{Br})_{2}]^{4-}\). Finally, the formula of the manganese complex is \(\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{Br})_{2}\right]\).

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Most popular questions from this chapter

(a) What is the difference between a monodentate ligand and a bidentate ligand? (b) How many bidentate ligands are necessary to fill the coordination sphere of a six-coordinate complex? (c) You are told that a certain molecule can serve as a tridentate ligand. Based on this statement, what do you know about the molecule?

(a) A compound with formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?

Metallic elements are essential components of many important enzymes operating within our bodies. Carbonic anhydrase, which contains \(\mathrm{Zn}^{2+}\), is responsible for rapidly interconverting dissolved \(\mathrm{CO}_{2}\) and bicarbonate ion, \(\mathrm{HCO}_{3}^{-} .\) The zinc in carbonic anhydrase is coordinated by three nitrogen-containing groups and a water molecule. The enzyme's action depends on the fact that the coordinated water molecule is more acidic than the bulk solvent molecules. Explain this fact in terms of Lewis acid-base theory (Section 16.11).

The complexes \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{VF}_{6}\right]^{3-}\) are both known. (a) Draw the \(d\) -orbital energy-level diagram for \(\mathrm{V}(\mathrm{III})\) octahedral complexes. (b) What gives rise to the colors of these complexes? (c) Which of the two complexes would you expect to absorb light of higher energy? Explain.

The molecule dimethylphosphinoethane \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{PCH}_{2}-\mathrm{CH}_{2} \mathrm{P}\left(\mathrm{CH}_{3}\right)_{2}\right.\), which is abbreviated \(\left.\mathrm{dmpe}\right]\) is used as a ligand for some complexes that serve as catalysts. A complex that contains this ligand is \(\mathrm{Mo}(\mathrm{CO})_{4}(\) dmpe \()\). (a) Draw the Lewis structure for dmpe, and compare it with ethylenediammine as a coordinating ligand. (b) What is the oxidation state of Mo in \(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right] ?\) (c) Sketch the structure of the \(\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right]^{2-}\) ion, including all the possible isomers.
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