# 19.4: Electrochemical Cell Fundamentals


Hypothes.is Tag = c1403c19 (case sensitive)
Group = UALRChem1403

## Introduction

In the previous section (19.2) electrochemical cells were introduced, related to redox reactions that could be split into half reactions, and shown that a cell could be run in a galvanic (voltaic) or electrolytic mode. In this section we are going to apply some of the fundamentals of electricity that were introduced in section 19.0 to the operations of electrochemical cells.

## Cell EMF and Free Energy

The cell EMF (ElectroMotive Force) or Ecell, which has units of Volts (V), is a measure of the spontaneous "force" that drives electrons through an external circuit from the anode to the cathode, and was introduced in section 19.03. It is a measure of the electric potential energy difference between the two electrodes. An analogy could be drawn between Ecell and the dependence of gravitational potential energy on the height of a waterfall.

Figure $$\PageIndex{1}$$: Just as water spontaneously flows down a waterfall, electrons spontaneously flow from anode to cathode. Here, cell potential is analogous to gravitational potential, and there are two factors relating the work that can be obtained from a waterfall, the height of the water, and the amount of water flowing over the Fall. Likewise, electric work is related to the potential difference and the amount of charge transferred across the potential drop.

Just as the amount of energy (work) that the water can do is dependent on both the quantity of water flowing over the waterfall and its height (mgh, see gravitational potential energy if interested), the electric potential energy is related to the charge transferred and the potential difference, which is related to the maximum possible work.

\begin{align}\text{Electric Work}_{max} & = \text{(Charge)} \times \text{(Potential Difference)} \nonumber \\[5pt] W_e & =qE_{Cell} \end{align}

From section 19.0.2 we know that a Faraday is the charge of a mole of electrons

$F=96,500 \frac{C}{mol \; e^-}$

and the charge "q" of "n" moles electrons is = nF

\begin{align} q & =nF \nonumber \\ q(C) & = -N(\cancel{mol \; e^-})96,500 (\frac{C}{\cancel{mol \; e^-}}) \end{align}

(note: this equation is showing units in parenthesis).

Note, the minus sign comes from the fact that each electron has a negative charge. So

$W_{e} =- nFE_{Cell} \label{19.3.4}$

From Section 18.6.7 we know that the maximum amount of work is related to $$\Delta G$$, which can be related to the electric work

$\Delta G = W_{e} = \Delta G$

$\Delta G = -nFE_{Cell} \label{19.3.6}$

The above makes sense as a spontaneous process has a positive cell potential ($$E > 0$$) and a negative Free Energy difference ($$\Delta G < 0$$).

Note, from the definition of the volt (Equation 19.6 of Section 19.0.3),

$1\,C= 1 \frac{\,J}{V}$

and so Faraday's constant also has units of

$F=96,500 \frac{J}{V \cdot mol \; e^-}$

This can easily be seen by the dimensional analysis of Equation \ref{19.3.4} or \ref{19.3.6}.