 # Thermodynamics

Chemistry
Summary

## Energy, Concentration, and Potential

Summary Energy, Concentration, and Potential

### Electrical Work and Cell Potential

So far we have cited the possibility of doing useful electrical work as the major reason for constructing galvanic cells. Now, we will define exactly what "useful electrical work" means and derive a relationship between work, free energy (G), and cell potential.

>From physics, we know that: Potential (E) = - Work (w) / Charge (q) therefore, w = -qE

Let us now define a quantity called a faraday (F) and let F equal the charge in coulombs per mole of electrons (96,485 C). Then q = nF and w= -nFE.

From thermodynamics we know that ΔG = ΔU -TΔS + Δ(PV) and U = heat + w. Therefore, at constant T and P: ΔG = w. Therefore: ΔG = -nFE and at standard state: ΔGo = -nFEo

Because the sign of ΔG predicts the direction of spontaneous reaction and G and E are directly related by the above equation, we can also use E to predict the direction of spontaneous reaction. As you know, if ΔG is greater than zero, the reaction is non-spontaneous but spontaneous in the reverse direction but if ΔG is less than zero, the reaction is spontaneous as written. ΔG and E have opposite signs from the above equation, therefore, spontaneous reactions will have positive cell potentials.