Nernst equation, solving it vs. pronouncing it

Walther Nernst

The last part of General Chemistry course in the Faculties of Engineering and Agricultural Sciences at my University is electrochemistry (covered by Chapter 8 of the Physical chemistry textbook).

I believe the Nernst equation (below) to be one of the most elegant results of thermodynamics, as well as a really powerful tool for a society which heavily relies on electricity – and, thus, desperately needs it, both for big factories and for personal mobile phones!

Nernst Equation

However, I usually find that students believe this equation to be difficult to understand (my main problem, instead, is to pronounce it, mainly because I’m Italian, and my native language uses far more vowels than the Nobel prize-winner Walther Nernst cares to use in his surname ).

Nernst equation contains every dream of scientists: work, equilibrium constants, logarithms, and predictive ability. Usually chemists prefer to use a log₁₀ instead of a ln (for ease of calculation), but this is a minor issue, since the difference between using them is just a factor of 2.30.

The major issue comes from what it’s inside the logarithm; to correctly use it, one should use activities of the involved species. But activity is a difficult guest to handle (and fugacity doesn’t help simplifying the equation for gases, too!). For this reason, it is usual to use molar concentration for diluted species, and pressure for gases. It has to be noted that this works only if the values themselves are small enough to let us substitute the latter terms to the former ones.

Another problem usually arises when considering the difference between halfcell equation and cell equation. One can obtain electromotive force for a cell in two ways, either solving the cell equation or solving the two halfcell for any electrode and then subtracting the anode potential from the cathode potential.

A difficulty (and usual question) is the following: if I have to use the same number of electrons when balancing the cell reaction, why can I solve each semireaction by its own, and then merely subtract the values? Is not the number of electrons needed anymore?

The truth is: of course, the number of electron involved in each semireaction DOES count, but you already take it into account when calculating the equation… if you double the number of electrons, also exponents in the logarithm double, and so the global effect is null. For this reason, you can use both methods to calculate the emf in your cell (how nice!).

Lastly, the answer to the title question: Nernst equation is simple enough to be used, and so I deem the pronounciation more difficult. Right? Well, unless you have help

Written by: Gaetano Giammarino

Gaetano Giammarino has authored 11 more articles.

He has received a PhD in Computational Chemistry at Università degli Studi della Basilicata, where he teaches General Chemistry in the Faculty of Engineering.

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