The Nernst Equation

1. Thermodynamics of the relationship of E and G - electrical work

- relating G and E: G = - n F E - finding the equilibrium constant from measured cell potentials.

2. Dependence of the cell potential on activity - the Nernst Equation

- the calomel electrode

3. The calomel electrode

4. The pH meter- the glass electrode

Relationship of Cell Potential and G

G = H - TS (const T)

= E + pV - TS (const P)

= (qrev + w) + pV - qrev (reversible, const T)

w = - pV + wel,revexpansi

on workelectrical work

wel = - Q E work = charge * (potential difference)

= - n F E

G = wel,rev

= - n F E (const T, P, reversible)

Joules Coulombs

Volts

Concentration Effects and The Nernst Equation

G = G° + RT ln Q - this allows you to calculate G at non-standard concentrations and

partial pressures.

Ecell = E°cell - (RT/nF) lne Q - the Nernst equation. It allows you to calculate G at non-standard conditions

G = - n F Ecell - this is always true; the cell potential is a very fundamental quantity, just like G

G° is the standard G - all solute concentrations must be 1 M and partial pressures must be 1 atm.

Measuring Equilibrium Constants

Ecell = E°cell - (RT/nF) lne Q - The Nernst equation relates Ecell to E°cell

G = - n F Ecell - this is always true; the cell potential is a very fundamental quantity, just like G

G° = - RT lne K - K can be calculated from G°, which for many compounds can be obtained from thermodynamic tables.

E° = (RT/nF) lne K - For reactions in solution, K and can be measured from a standard cell potential.

G°,

= E°cell - 2.303 (RT/nF) log10 Q= E°cell - (0.0152/n) log10 Q (at T=25°C)

The Nernst Equation

Ecell = E°cell - (0.0592/n) log10 Q at T = 25°C

PbO2(s) + SO42-(aq) + 4 H3O+(aq) + 2 e-

PbSO4(s) + 6 H2O(l)

E°=+1.685 V

Pt(s)

SO42-

(aq)

H3O+

(aq)

slurry of PbO2(s) + PbSO4(s)

E = E° - (.0592/2) log10 [H3O+]4

[SO42-]

1

The cell potential changes by 0.118 V for each pH unit or by 0.0296 V for each factor of 10 change in [SO4

2-]:pH = 0 E = +1.685 V

pH = 4 E = +1.211 V

pH measurement

Standard Hydrogen Electrode:

2 H3O+(aq, 1M) + 2 e- H2(g) + 2 H2O(l)

Pt(s)

H3O+

(aq)

salt bridge

H2(g)

Pt(s)

sat’d KCl(aq)

paste of Hg(l) and Hg2Cl2(s)

standard hydrogen electrode calomel reference electrode

Calomel Electrode:

Hg2Cl2(s) + 2 e- 2Hg(l) + 2 Cl-(sat’d)

E = +0.241 V - (.0592/2) log10 [H3O+]2

= +0.241 + .0592 * pH

E° = +0.241 V

E° = +0.000 V

Ecell pH

KCl(s)

The Glass Electrode and the pH Meter

The glass electrode is non-metallic electrode composed of a special glass that is porous to H3O+.

A diffusion potential develops across the membrane in response to a pH gradient. The potential varies by 59.6 mV for each unit change in pH.Ecell = E°cell -

0.0592 V 2

log10[H+]out2[H+]in

2

Ecell = constant + (0.0592 v) * pH

Notice that Ecell is uniformly sensitive to pH over 14 orders of magnitude!!