redox
Half-equations, voltaic cells & standard potentials, Nernst, electrolysis & Faraday.
half-equations · voltaic cells · standard potentials · electrolysis
Half-equations
Balancing (acidic). Balance atoms except O/H; balance O with \(\ce{H2O}\); balance H with \(\ce{H+}\); balance charge with electrons; multiply the half-equations so the electrons cancel.
Balancing (basic). After the acidic balance, add \(\ce{OH-}\) to both sides to neutralize \(\ce{H+}\); cancel \(\ce{H2O}\).
Agents. The oxidizing agent is reduced; the reducing agent is oxidized.
Disproportionation. The same element is both oxidized and reduced; comproportionation is the reverse.
Voltaic cells
Layout. Oxidation at the anode, reduction at the cathode; electrons flow anode → cathode through the wire; ions flow through the salt bridge to maintain charge.
Cell notation. anode | anode ion || cathode ion | cathode; e.g. \(\ce{Zn(s)}\mid\ce{Zn^2+(aq)}\parallel\ce{Cu^2+(aq)}\mid\ce{Cu(s)}\).
Standard electrode potential. Measured against the SHE, \(\ce{H+(aq) + e- <=> 1/2H2(g)}\), \(E\std=0\). \(E\std_{\text{cell}}=E\std_{\text{cathode}}-E\std_{\text{anode}}\) (both as reduction potentials); spontaneous if \(E\std_{\text{cell}}\gt0\), i.e. \(\Delta G\std\lt0\).
Trap. Do not multiply \(E\std\) when scaling half-equations to balance electrons — potentials are intensive; only \(\Delta G\) scales with \(n\).
Thermodynamics/Nernst. \(\Delta G\std=-nFE\std\); \(E=E\std-\dfrac{RT}{nF}\ln Q\); at 298 K, \(E=E\std-\dfrac{0.0592}{n}\log Q\).
Standard potentials
Ordering. Stronger oxidizing agents have more positive \(E\std\); stronger reducing agents have more negative reduction potentials.
| Strong reducers | \(E\std\)/V | Strong oxidizers | \(E\std\)/V |
|---|---|---|---|
| \(\ce{Li+ + e- -> Li}\) | −3.04 | \(\ce{F2/F^-}\) | +2.87 |
| \(\ce{Na+ + e- -> Na}\) | −2.71 | \(\ce{MnO4^-/Mn^2+}\) (acid) | +1.51 |
| \(\ce{Mg^2+ + 2e- -> Mg}\) | −2.37 | \(\ce{Cr2O7^2-/Cr^3+}\) (acid) | +1.36 |
| \(\ce{Al^3+ + 3e- -> Al}\) | −1.66 | \(\ce{Cl2/Cl^-}\) | +1.36 |
| \(\ce{Zn^2+ + 2e- -> Zn}\) | −0.76 | \(\ce{O2/H2O}\) (acid) | +1.23 |
| \(\ce{Fe^2+ + 2e- -> Fe}\) | −0.45 | \(\ce{Br2/Br^-}\) | +1.09 |
| \(\ce{H+ + e- -> 1/2H2}\) | 0.00 | \(\ce{Ag+/Ag}\) | +0.80 |
| \(\ce{Cu^2+ + 2e- -> Cu}\) | +0.34 | \(\ce{Fe^3+/Fe^2+}\) | +0.77 |
Electrolysis
Electrolytic cell. A non-spontaneous reaction driven by DC; anode positive, cathode negative; oxidation still at the anode, reduction still at the cathode.
Sign trap. Anode/cathode signs swap between voltaic and electrolytic cells, but oxidation-at-anode and reduction-at-cathode never change.
Molten salts. Cation → metal at the cathode; anion → nonmetal at the anode.
Aqueous competition. Cathode: cation vs water — metals less reactive than H usually plate; otherwise \(\ce{H2}\) forms. Anode: halides oxidized to halogens if concentrated; otherwise water/\(\ce{OH-}\) give \(\ce{O2}\).
Faraday. Charge \(Q=It\); moles of electrons \(=Q/F\); deposited mass \(m=\dfrac{ItM}{zF}\).
Electroplating. Object as cathode; plating metal as anode/electrolyte; thickness controlled by charge and surface area.
Primary vs secondary cells. Secondary cells are rechargeable — the redox is reversed by an external voltage; primary cells are not practically reversible.