CHM-04

Nernst equation

E = E° − (RT/nF) ln Q. Cell potential versus reaction quotient.

Reading speed

ElectrochemistryNernst 1889

Governing equation

E=E^\circ-\dfrac{RT}{nF}\ln Q

$Q \in \left[1\times 10^{-6}, 1000\right]$

where

E^\circ: Standard potential (V)
n: Electrons (—)
Q: Reaction quotient (—)
T: Temperature (K)
E: Cell potential (V)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

E=E^\circ-\dfrac{RT}{nF}\ln Q

$Q \in \left[1\times 10^{-6}, 1000\right]$

$Q = 1\times 10^{-6}$ $E = 1.277$

Along the curve

②

Domain of the variable — blue

Q_{\min} = 1\times 10^{-6},\quad Q_{\max} = 1000

$Q \in \left[1\times 10^{-6}, 1000\right]$

$Q = 1\times 10^{-6}$ $Q = 1\times 10^{-6}$

Along the curve

③

Response curve — green

E=E^\circ-\dfrac{RT}{nF}\ln Q

$Q \in \left[1\times 10^{-6}, 1000\right]$

$Q = 1\times 10^{-6}$ $E = 1.277$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}Q}

$Q \in \left[1\times 10^{-6}, 1000\right]$

$Q = 6.289$ $E^{\prime} = -0.017$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-04 — Nernst equation) is the form associated with Nernst 1889. Working symbols: $E^\circ$ , $n$ , $Q$ , $T$ $\rightarrow$ $E$ . At 25 °C, (59 mV/n) per decade of Q. Equilibrium is E = 0.

Purpose

Purpose: compute

E

from

E^\circ

n

Q

T

in Physical chemistry via

E=E^\circ-\dfrac{RT}{nF}\ln Q

E = E° − (RT/nF) ln Q. Cell potential versus reaction quotient. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E^\circ = 1.100\,\mathrm{V}

n = 2.000\,\mathrm{—}

Q = 0.100\,\mathrm{—}

T = 298.000\,\mathrm{K}

, the governing relation

E=E^\circ-\dfrac{RT}{nF}\ln Q

yields

E = 1.130\,\mathrm{V}

. Reversible cell, activities packed into Q. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Standard potential E^\circ1.1 VElectrons n2 —Reaction quotient Q0.1 —Temperature T298 K

Outputs

Cell potential E1.130 V

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Reversible cell, activities packed into Q.

At 25 °C, (59 mV/n) per decade of Q. Equilibrium is E = 0.

Reading speed

Watch on YouTube