19.4: Electrochemical Cell Fundamentals
- Page ID
- 60805
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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, or EcellE_{\text{cell}}Ecell, has units of volts (V) and measures the electrical potential difference between the two electrodes. It represents the maximum energy available per unit charge to drive electrons through the external circuit from the anode to the cathode in a spontaneous electrochemical cell (section 19.03). Although the term electromotive force is still widely used, EMF is not a literal force; it is a voltage. An analogy can be made to a waterfall: the greater the height difference, the greater the gravitational potential drop available to do work. Likewise, the greater the cell potential, the greater the electrical potential drop available to do work on moving charge.
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}.
Contributors and Attributions
Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to: