E°, ΔG°, and K

Three quantities tell you the same story about a reaction - whether it is spontaneous, at equilibrium, or nonspontaneous. They are connected by equations you must know cold for the MCAT.

The Three Master Equations

The Triangle of Relationships

These three equations form a triangle. If you know any one of E°, ΔG°, or K, you can calculate the other two.

The Sign Relationships

All three quantities agree on the direction of spontaneity, but with opposite sign conventions for E° versus ΔG°:

Why the Negative Sign in ΔG° = -nFE°?

The negative sign ensures consistency: E° and ΔG° carry opposite signs for the same reaction direction. A spontaneous galvanic cell has a positive E°cell (electron flow is favorable) but a negative ΔG° (free energy decreases). The negative sign in the equation makes this work out mathematically.

Worked Example

For the Daniell cell (Zn-Cu), E°cell = +1.10 V and n = 2 (two electrons transferred).

Calculate ΔG°:

ΔG° = -nFE° = -(2)(96,485)(1.10) = -212,267 J = -212.3 kJ

Negative ΔG° confirms the reaction is spontaneous.

Calculate K:

ΔG° = -RTlnK

-212,267 = -(8.314)(298)lnK

lnK = 212,267 / 2477.6 = 85.7

$K = e^{85.7} \approx$ $1.5 \times 10^{37}$

This enormous K tells you the reaction essentially goes to completion - products are overwhelmingly favored.

Quick Reference: Faraday’s Constant

Faraday’s constant (F) = 96,485 C/mol. This is the total charge carried by one mole of electrons.

For quick MCAT estimation: $F$ is approximately $10^5$ C/mol. So $\Delta G° = -nFE°$ is approximately $-n(10^5)(E°)$ joules.