Problem 94 - Chemistry The Central Science In Si Units

Question

An iron complex formed from a solution containing hydrochloric acid and bipyridine is purified and analyzed. It contains \(9.38 \%\) Fe, \(60.53 \%\) carbon, \(4.06 \%\) hydrogen, and \(14.12 \%\) nitrogen by mass. The remainder of the compound is chlorine. An aqueous solution of the complex has about the same electrical conductivity as an equimolar solution of \(\mathrm{K}_{2}\left[\mathrm{CuCl}_{4}\right] .\) Write the formula of the compound, using brackets to denote the iron and its coordination sphere.

Step-by-Step Solution

Answer

The formula of the compound is \([\text{Fe(bpy)}_3]\text{Cl}_2\).

Step 1: Determine Molar Contribution of Each Element

Calculate the molar mass contributed by each element in the compound. Use the percents and molar masses: Fe (55.85 g/mol), C (12.01 g/mol), H (1.01 g/mol), N (14.01 g/mol), and Cl (35.45 g/mol).

Step 2: Calculate Moles of Each Element

Convert the percentage by mass to grams (assuming a 100 g sample), then calculate moles for each element:- Fe: \( \frac{9.38}{55.85} \approx 0.168 \text{ moles} \)- C: \( \frac{60.53}{12.01} \approx 5.04 \text{ moles} \)- H: \( \frac{4.06}{1.01} \approx 4.02 \text{ moles} \)- N: \( \frac{14.12}{14.01} \approx 1.01 \text{ moles} \)

Step 3: Calculate Chlorine Content

Determine chlorine's mass fraction by subtracting the percent compositions of Fe, C, H, and N from 100%: \( 100 - (9.38 + 60.53 + 4.06 + 14.12) = 11.91\% \). Then convert to moles: \( \frac{11.91}{35.45} \approx 0.336 \text{ moles Cl} \).

Step 4: Determine Empirical Formula

Divide each mole value by Fe's mole value (the smallest):- Fe: \( \frac{0.168}{0.168} \approx 1 \)- C: \( \frac{5.04}{0.168} \approx 30 \)- H: \( \frac{4.02}{0.168} \approx 24 \)- N: \( \frac{1.01}{0.168} \approx 6 \)- Cl: \( \frac{0.336}{0.168} \approx 2 \)Thus, the empirical formula is approximately \( \mathrm{FeC_{30}H_{24}N_6Cl_2} \).

Step 5: Consider Electrical Conductivity Clue

Given that the solution's electrical conductivity is similar to \( \mathrm{K}_{2} ext{[CuCl}_{4}\text{]} \), indicating similar ionic character, this suggests a coordination complex involving Fe with a certain charge outside the brackets to balance. Assuming Fe can be \( \text{Fe}^{2+} \) and \( \text{Fe}^{3+} \), and considering bipyridine as the ligand.

Step 6: Propose Structure with Coordination Sphere

With bipyridine (\( ext{bpy} \)) as a ligand forming a neutral complex and two Cl^- species outside, consider tetracoordinate Fe complex: \( [ ext{Fe(bpy)}_3] ext{Cl}_2 \). This fits the molar ratios and electrical conductivity hints.

Key Concepts

Understanding Empirical Formula

The empirical formula of a compound is the simplest whole-number ratio of its constituent elements. It's determined using the percentage composition of each element and their respective molar masses. Here's a streamlined way of obtaining the empirical formula:

• Assume a sample size (commonly, 100 grams) to match the percentages directly to grams.
• Convert these grams to moles by dividing by the molar mass of each element.
• Find the smallest mole value and divide all mole amounts by this number to get the simplest ratio.

In our exercise, we found that the empirical formula was approximately \( \text{FeC}_{30}\text{H}_{24}\text{N}_{6}\text{Cl}_{2}\) by calculating and comparing these ratios. The empirical formula provides crucial insight into the composition of a compound but does not necessarily show the actual number of atoms per molecule, which would be the molecular formula.
However, it does provide a foundation for understanding more complex structures, like coordination complexes.

Electrical Conductivity and Coordination Complexes

Electrical conductivity measures a solution’s ability to conduct electricity, which is influenced by the presence of ions. In the context of coordination complexes, conductivity can give clues about the ionic nature of the complex in solution. For instance, if a complex has a similar conductivity to an ionic compound, it might suggest that it dissociates into ions in solution. In our case, the complex’s conductivity was akin to that of \( \text{K}_2[\text{CuCl}_4] \). This similarity indicates the presence of free ions and implies that our iron complex dissociates similarly, suggesting ionic species are present. Coordination complexes often have a central metal surrounded by ligands. The nature of these ligands, as well as any counter ions, affects not just the stability of the complex but also how it behaves in a solution. In our specific example, the iron complex was proposed to be \([\text{Fe(bpy)}_3]\text{Cl}_2\), indicating that the structure includes 3 bipyridine ligands around the iron and two chloride ions contributing to ionic character.

Calculating Molar Mass for Coordination Complexes

The molar mass of a compound is the sum of the masses of all the atoms in its empirical formula. This value is essential for various calculations, including those involving mass-to-mole conversions and concentration in solutions. For coordination complexes, determining the molar mass can be slightly more complex due to the inclusion of multiple ligands and potential counter ions. To calculate it:

• Find the molar mass for each element or distinct unit in the compound.
• Multiply this by the number of times this unit appears in the formula.
• Add together all these individual masses for the total molar mass.

Taking our calculation one step further in problem analysis: the \([\text{Fe(bpy)}_3]\text{Cl}_2\) hypothesis required that we account for the full iron complex. Including the mass of iron, bipyridine ligands, and the chlorine ions, the understanding of molar mass is crucial to confirm both the empirical formula accuracy and to assess potential real-world applications of the coordination compound.