Problem 10 - Analytical Chemistry

Question

Iron(III) is polarographically reduced to iron(II) at potentials more negative than about \(+0.4 \mathrm{~V}\) versus SCE and is further reduced to iron(0) at \(-1.5 \mathrm{~V}\) versus SCE. Iron(II) is also reduced to the metal at \(-1.5 \mathrm{~V}\). A polarogram is run (using a DME) on a solution containing \(\mathrm{Fe}^{3+}\) and/or \(\mathrm{Fe}^{2+}\). A current is recorded at zero applied volts, and its magnitude is \(12.5 \mu \mathrm{A}\). A wave is also recorded with \(E_{1 / 2}\) equal to \(-1.5 \mathrm{~V}\) versus \(\mathrm{SCE},\) and its height is \(30.0 \mu \mathrm{A} .\) Identify the iron species in solution \((3+\) and/or \(2+)\) and calculate the relative concentration of each.

Step-by-Step Solution

Answer

Fe(III) and Fe(II) are both present; relative concentrations are 5:7.

Step 1: Review Potential Ranges for Reduction Reactions

Iron(III), or \(\mathrm{Fe}^{3+}\), is reduced to iron(II), \(\mathrm{Fe}^{2+}\), at potentials more negative than about \(+0.4 \mathrm{~V}\). Both \(\mathrm{Fe}^{3+}\) and \(\mathrm{Fe}^{2+}\) are reduced to iron(0) at \(-1.5 \mathrm{~V}\). The presence of a wave at \(-1.5 \mathrm{~V}\) suggests the reduction of \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) to metallic iron.

Step 2: Analyze Polarographic Data

A wave recorded at \(E_{1/2} = -1.5 \mathrm{~V}\) with a height of \(30.0 \mu \mathrm{A}\) suggests an overall current due to the reduction of iron species to metallic iron. The current recorded at zero applied volts reflects a pre-wave potentially due to \(\mathrm{Fe}^{3+}\) reducing to \(\mathrm{Fe}^{2+}\).

Step 3: Calculate Contribution of Each Species

The current at zero applied volts, \(12.5 \mu \mathrm{A}\), is attributed to the reduction of \(\mathrm{Fe}^{3+}\) to \(\mathrm{Fe}^{2+}\). The wave at \(-1.5\mathrm{~V}\) accounts for \(30.0 \mu \mathrm{A}\) total, which includes contributions from both \(\mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{0}\) and \(\mathrm{Fe}^{3+} \rightarrow \mathrm{Fe}^{0}\). Since some current in the total wave (\(\mathrm{Fe}^{0}\) formation) also comes from \(\mathrm{Fe}^{3+}\), we can deduce that \(\mathrm{Fe}^{2+}\) contributes \(30.0 - 12.5 = 17.5 \mu \mathrm{A}\).

Step 4: Determine Relative Concentrations

From the above caluclation, \(\mathrm{Fe}^{3+}\) contributes \(12.5 \mu \mathrm{A}\) and \(\mathrm{Fe}^{2+}\) contributes \(17.5 \mu \mathrm{A}\). The total reduction current of \(\mathrm{Fe}^{3+} + \mathrm{Fe}^{2+} = 30.0 \mu \mathrm{A}\). Thus, relative concentrations of \(\mathrm{Fe}^{3+} : \mathrm{Fe}^{2+}\) are in the ratio \(12.5:17.5\).

Key Concepts

Reduction Potential

Reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced. It is measured in volts (V) relative to a standard reference. In electrochemistry, this reference is often the Standard Calomel Electrode (SCE).
For iron species,

• iron(III) or \( \mathrm{Fe}^{3+} \) is reduced to iron(II) \( \mathrm{Fe}^{2+} \) at potentials more negative than \(+0.4 \mathrm{~V}\) versus SCE. This indicates that at potentials more negative than this value, \( \mathrm{Fe}^{3+} \) will gain electrons to become \( \mathrm{Fe}^{2+} \).
• Both \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \) are reduced to metallic iron \( \mathrm{Fe}^{0} \) at \(-1.5 \mathrm{~V}\) versus SCE, showing their potentials to transform into a metallic state.

Understanding these potentials is crucial in predicting the flow of electron transfer in reactions and characterizing the electrochemical behavior of the species involved.

Polarogram Analysis

A polarogram is a graphical representation of current versus voltage obtained during polarographic analysis. It is used to determine the concentration and type of a specific analyte within a solution.
The characteristics of a polarogram involve a half-wave potential \(E_{1/2}\), which is a specific potential where the current is half of its maximum value, specific to the reduction or oxidation of a particular species.
In the given exercise, two observations were noted:

• A pre-wave current of \(12.5 \mu \mathrm{A}\) at zero applied volts, indicative of \( \mathrm{Fe}^{3+} \) reducing to \( \mathrm{Fe}^{2+} \).
• A wave with \(E_{1/2}\) at \(-1.5 \mathrm{~V}\) with a height of \(30.0 \mu \mathrm{A}\), which includes the reduction of iron species to metallic iron \( \mathrm{Fe}^{0} \).

This analysis helps in identifying the kinds of iron present in the solution and their respective behaviors during the electrochemical reduction process.

Iron Species Concentration

Determining the concentration of different iron species involves analyzing the contributions of their individual reduction currents. In a mixed solution of \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \) ions:

• \( \mathrm{Fe}^{3+} \) to \( \mathrm{Fe}^{2+} \) conversion at zero volts accounts for \(12.5 \mu \mathrm{A}\). This current is solely due to the initial reduction to \( \mathrm{Fe}^{2+} \).
• The total current at \(-1.5 \mathrm{~V}\), \(30.0 \mu \mathrm{A}\), includes currents due to the further reduction processes resulting in metallic iron.
• Subtracting the pre-wave current (\(12.5 \mu \mathrm{A}\)) from the total current at \(-1.5 \mathrm{~V}\) gives \(17.5 \mu \mathrm{A}\), which is attributed to the reduction from \( \mathrm{Fe}^{2+} \) to \( \mathrm{Fe}^{0} \).

Thus, the relative concentrations of \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \) can be interpreted from their respective contributions to the total current, shown to be in a ratio of \( 12.5:17.5 \). This informs us about the predominance of \( \mathrm{Fe}^{2+} \) over \( \mathrm{Fe}^{3+} \) in the solution.