Electrochemistry: Basic Concepts

Last updated
Save as PDF

Page ID: 283158

Contributor
Analytical Sciences Digital Library

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

A REDOX Example

One would predict a spontaneous reaction between….
What is the coefficient in front of Fe²⁺ in the balanced reaction?
What is E° for the total reaction?

ΔG, E and K Example

E^o for the following reaction (as written) is 0.736 volts. Calculate ΔG and K for the reaction.

\[\ce{MnO4- + 8H+ + 5Fe^2+ ⇌ Mn^2+ + 4H2O + 5Fe^3+}\nonumber\]

Calculating Potential of a Cell (Nernst equations)

Calculate the potential for the following cell:

\[\mathrm{Pt \mid Sn^{2+}(0.400\: M),\: Sn^{4+}(0.500\: M) \mid\mid NO_3^-(0.100\: M),\: H^+(pH=2.00),\: HNO_2(0.400\: M) \mid Pt}\nonumber\]

Potentiometry – Cells (line notation with REF)

Calculate the cell potential of the following cell:

Bringing in K_sp

Think about the previous problem…

Calculate the cell potential of the following cell:

\[\mathrm{Ag \mid AgCl_{(s)} \mid AgCl_{(aq)}(sat’d),\: Cl^- (1.00\: M) \mid\mid \textrm{reduction half cell} \mid Pt}\nonumber\]

Couldn’t one use the Ag⁺ + e^- ⇌ Ag_(s) half cell at E^o = 0.799?

“Adding” Reactions

When you “add” chemical reactions, you multiply the K values and/or add the E values.

Given the following E^o values:

\[\ce{Ag+ + e- ⇌ Ag_{(s)}} \textrm{ (0.799 V vs SHE) and}\nonumber\]

\[\ce{AgCl_{(s)} + e- ⇌ Ag_{(s)} + Cl-} \textrm{ (0.222 V vs SHE)}\nonumber\]

Calculate the K_sp for AgCl.

“Mixing” Problems

30.00 mL of 0.120 F NaNO₃ is mixed with 20.00 mL of 0.150 F SnCl₂ and the solutions is buffered at pH=2.00. (NOTE: no gas or solid is observed)

Calculate E^o and K for the spontaneous reaction that will occur.
Calculate the solution potential of the resulting solution.

Potentiometry Problems (mixing, then measuring)

Calculate the cell potential, as measured at a Pt/SCE electrode pair, for a solution prepared by mixing 30.00 mL of 0.120 F NaNO₃ and 20.00 mL of 0.150 F SnCl₂. The solution is buffered at pH=2.00. (except for SCE, this is the same problem as the previous exercise)

Potentiometry Problems, II (mixing, then measuring, EP)

Calculate the cell potential, as measured at a Pt/SCE electrode pair, for a solution prepared by mixing 25.00 mL of 0.120 F NaNO₃ and 20.00 mL of 0.150 F SnCl₂. The solution is buffered at pH=2.00.

KEY: Reactant conc’ns are “Not really zero, just really small….AND in a defined ratio” …as indicated by coefficients in balanced eqn!

Formal Potential (E^o’)

Derive an equation for the pH-dependent formal potential for the dichromate/ chromium III half reaction, and calculate the E^o’ at pH 7.00.

\[\ce{Cr2O7^2- + 14H+ + 6e- ⇌ 2Cr^3+ + 7H2O} \hspace{30px} \mathrm{E^o} = \textrm{1.33 V vs SHE}\nonumber\]

\[E^{0'}_{Cr_2O_7^{2-}/Cr^{3+}} = E^0_{Cr_2O_7^{2-}/Cr^{3+}} - \dfrac{0.0591}{6} \log\left(\dfrac{1}{[H^+]^{14}}\right)\nonumber\]

\[E^{0'}_{Cr_2O_7^{2-}/Cr^{3+}} = E^0_{Cr_2O_7^{2-}/Cr^{3+}} - \dfrac{0.0591(14)}{6} pH\nonumber\]

\[\mathrm{E^{o’}}\textrm{ at pH 7.00 = 0.365 V vs SHE}\nonumber\]

Redox Titration

Consider the titration of 50.00 mL of 0.100 M Cr₂O₇^2- with 0.300 M Fe²⁺ as monitored with a Pt/SCE electrode pair...calculate the measured cell potential and construct the expected titration plot. The pH is maintained at 0.00.