Question

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

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

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 = \(\frac{23.4\%}{16.00\ g/mol} = 1.463\)

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 \(\mathrm{K}_{4}\mathrm{Mn}\mathrm{C}_{4}\mathrm{Br}_{2}\mathrm{O}_{8}\).

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.

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 \(\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{Br})_{2}\right]\).