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Chapter 11: Problem 36

The polarographic half-wave potentials (versus the SCE) for \(\mathrm{Pb}^{2+}\) and for \(\mathrm{Tl}^{+}\) in \(1 \mathrm{M} \mathrm{HCl}\) are, respectively, \(-0.44 \mathrm{~V}\) and \(-0.45 \mathrm{~V}\). In an electrolyte of \(1 \mathrm{M} \mathrm{NaOH}\), however, the half-wave potentials are \(-0.76 \mathrm{~V}\) for \(\mathrm{Pb}^{2+}\) and \(-0.48 \mathrm{~V}\) for \(\mathrm{Tl}^{+}\). Why does the change in electrolyte have such a significant effect on the half-wave potential for \(\mathrm{Pb}^{2+}\), but not on the half- wave potential for \(\left.\mathrm{T}\right|^{+}\)

Short Answer

Expert verified
The significant effect on Pb虏鈦�'s potential in NaOH arises from complex formation, unlike Tl鈦�, which remains largely unaffected.

Step by step solution

01

Understanding Half-wave Potential

The half-wave potential is an important parameter in polarography. It represents the potential at which half of a substance is reduced at an electrode surface and provides information about the ease of reduction of ions.
02

Comparing Electrolyte Environments

In the given exercise, \(\mathrm{Pb}^{2+}\) and \(\mathrm{Tl}^{+}\) are considered in two different solutions: \(1 \mathrm{M} \mathrm{HCl}\) and \(1\mathrm{M} \mathrm{NaOH}\). The potential for \(\mathrm{Pb}^{2+}\) shifts from \(-0.44 \mathrm{V}\) in HCl to \(-0.76 \mathrm{V}\) in NaOH, which is a significant change. Contrarily, the potential for \(\mathrm{Tl}^{+}\) shifts slightly from \(-0.45 \mathrm{V}\) in HCl to \(-0.48 \mathrm{V}\) in NaOH.
03

Analyzing Pb虏鈦� Behavior

The large shift in \(\mathrm{Pb}^{2+}\)'s half-wave potential from \(-0.44 \mathrm{V}\) to \(-0.76 \mathrm{V}\) in NaOH can be attributed to the formation of \(\mathrm{Pb}(OH)_2\) complex or the modification of the lead ions' chemical environment, thus making the reduction of \(\mathrm{Pb}^{2+}\) to Pb more difficult in the basic medium.
04

Analyzing Tl鈦� Behavior

The small change in \(\mathrm{Tl}^{+}\)'s potential suggests that the thallium ions are not involved in significant complex formation or that their reduction is not significantly influenced by the pH change from acidic (HCl) to basic (NaOH) conditions. Thallium may not react to form additional stable hydroxide complexes that would shift its potential considerably.
05

Conclusion on Electrolyte Effect

The impact of the electrolyte on the half-wave potential is related to the chemical interactions between the metal ions and the components of the electrolyte. In NaOH, \(\mathrm{Pb}^{2+}\) is more affected due to complex formation or solubility shifts, whereas \(\mathrm{Tl}^{+}\) demonstrates minimal impact due to its less reactive nature in forming hydroxide complexes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Half-Wave Potential
Half-wave potential is a term used in polarography, which is a method to analyze the concentration of ions in a solution. It refers to the voltage at which half of the analyte ions are reduced at the electrode surface during a polarographic measurement.

Understanding half-wave potential is crucial because it provides insights into the ease with which a specific ion can be reduced.
  • If the half-wave potential is less negative, it indicates that the ion is reduced more easily.
  • Conversely, a more negative half-wave potential means that more energy is required for the ion to be reduced.
By comparing the half-wave potentials of different ions under the same conditions, one can infer information about their comparative reduction kinetics.
Electrolyte Effect
The choice of electrolyte can significantly affect the half-wave potential of ions in polarographic experiments. Electrolytes are the medium through which ions travel, and they can alter the chemical environment of reacting ions.

Changes in the electrolyte can lead to either an increase or decrease in the observed half-wave potential due to a variety of factors:
  • The electrolyte can impact the solvation layer around the ions.
  • It might engage in complexation with the analyte ions, forming stable or unstable complexes.
  • The pH of the electrolyte can change the chemical form of the ions.
In the presented exercise, we see such effects where \( ext{Pb}^{2+}\) in NaOH shows a significantly different half-wave potential compared to HCl, influenced by changes in solvation or complex formation.
Reduction Potential
Reduction potential is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. It is crucial in electrochemistry as it indicates the position of the equilibrium of a redox reaction.

In the context of polarography, the reduction potential helps us understand how different ions compete for electrons. \(-0.44 \mathrm{\,V}\) for \( ext{Pb}^{2+}\) and \(-0.45 \mathrm{\,V}\) for \( ext{Tl}^{+}\) in \( ext{HCl}\) suggest both ions are easily reduced.
  • Reduction potential changes typically reflect a change in the chemical environment or complexation, like those seen with \( ext{Pb}^{2+}\) in NaOH.
  • Such shifts highlight the dynamic response of ions to different ionic backgrounds in electrolytic solutions.
Understanding reduction potential is key to predicting how ions will behave in various electrolytic environments.
Metal Ion Complexation
Metal ion complexation refers to the interaction of metal ions with other molecules to form a complex. This process can significantly affect the electrochemical behavior of the ions, including their half-wave potential.

In polarography, complexation can explain shifts in the observed half-wave potential as it modifies the standard reduction potentials of ions.
  • For instance, complexation with hydroxide ions in NaOH can lead \( ext{Pb}^{2+}\) to form \( ext{Pb(OH)}_2\), altering its chemical state and making reduction more difficult.
  • This is why there is a sizeable shift in \( ext{Pb}^{2+}\)'s half-wave potential, illustrating complexation's profound influence.
  • Meanwhile, \( ext{Tl}^{+}\) in NaOH may not partake in extensive complexation, thus showing a lesser shift in half-wave potential.
Recognizing the role of complexation is critical for predicting how the ions' reactivity will be modified by the electrolytes.

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Most popular questions from this chapter

Explain why each of the following decreases the analysis time in controlled- potential coulometry: a larger surface area for the working electrode; a smaller volume of solution; and a faster stirring rate.

Mifflin and associates described a membrane electrode for the quantitative analysis of penicillin in which the enzyme penicillinase is immobilized in a polyacrylamide gel coated on the glass membrane of a \(\mathrm{pH}\) electrode. \({ }^{22}\) The following data were collected using a set of penicillin standards. \begin{tabular}{cc} [penicillin] (M) & potential (mV) \\ \hline \(1.0 \times 10^{-2}\) & 220 \\ \(2.0 \times 10^{-3}\) & 204 \\ \(1.0 \times 10^{-3}\) & 190 \\ \(2.0 \times 10^{-4}\) & 153 \\ \(1.0 \times 10^{-4}\) & 135 \\ \(1.0 \times 10^{-5}\) & 96 \\ \(1.0 \times 10^{-6}\) & 80 \end{tabular} (a) Over what range of concentrations is there a linear response? (b) What is the calibration curve's equation for this concentration range? (c) What is the concentration of penicillin in a sample that yields a potential of \(142 \mathrm{mV?}\)

The amount of sulfur in aromatic monomers is determined by differential pulse polarography. Standard solutions are prepared for analysis by dissolving \(1.000 \mathrm{~mL}\) of the purified monomer in \(25.00 \mathrm{~mL}\) of an electrolytic solvent, adding a known amount of sulfur, deaerating, and measuring the peak current. The following results were obtained for a set of calibration standards. \begin{tabular}{cc} \mug S added & peak current \((\mu \mathrm{A})\) \\ \hline 0 & 0.14 \\ 28 & 0.70 \\ 56 & 1.23 \\ 112 & 2.41 \\ 168 & 3.42 \end{tabular} Analysis of a \(1.000-\mathrm{mL}\) sample, treated in the same manner as the standards, gives a peak current of \(1.77 \mu \mathrm{A}\). Report the \(\mathrm{mg} \mathrm{S} / \mathrm{mL}\) in the sample.

Zinc is used as an internal standard in an analysis of thallium by differential pulse polarography. A standard solution of \(5.00 \times 10^{-5} \mathrm{M} \mathrm{Zn}^{2+}\) and \(2.50 \times 10^{-5} \mathrm{M} \mathrm{Tl}^{+}\) has peak currents of \(5.71 \mu \mathrm{A}\) and \(3.19 \mu \mathrm{A}\), respectively. An 8.713 -g sample of a zinc-free alloy is dissolved in acid, transferred to a \(500-\mathrm{mL}\) volumetric flask, and diluted to volume. A \(25.0-\) \(\mathrm{mL}\) portion of this solution is mixed with \(25.0 \mathrm{~mL}\) of \(5.00 \times 10^{-4} \mathrm{M}\) \(\mathrm{Zn}^{2+}\). Analysis of this solution gives peak currents of \(12.3 \mu \mathrm{A}\) and of \(20.2 \mu \mathrm{A}\) for \(\mathrm{Zn}^{2+}\) and \(\mathrm{Tl}^{+}\), respectively. Report the \(\% \mathrm{w} / \mathrm{w} \mathrm{Tl}\) in the alloy.

The production of adiponitrile, \(\mathrm{NC}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CN},\) from acrylonitrile, \(\mathrm{CH}_{2}=\mathrm{CHCN},\) is an important industrial process. A \(0.594 \mathrm{-g}\) sample of acrylonitrile is placed in a \(1-\mathrm{L}\) volumetric flask and diluted to volume. An exhaustive controlled-potential electrolysis of a \(1.00-\mathrm{mL}\) portion of the diluted acrylonitrile requires \(1.080 \mathrm{C}\) of charge. What is the value of \(n\) for the reduction of acrylonitrile to adiponitrile?
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