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I came up with the following question in my NCERT textbook:

Write the Nernst equation and the emf of the following cell at $\pu{298 K}$.

$$\ce{Fe}|\ce{Fe^2+}(\pu{0.001 M})||\ce{H+}(\pu{1 M})|\ce{H2 (g)}(\pu{1 bar})|\ce{Pt (s)}$$

Given: $E^\circ(\ce{Fe^2+}/\ce{Fe}) = \pu{-0.44 V}$.

As per my understanding, the data of activity coefficients must given because the reaction coefficient in terms of concentration is not dimensionless and its logarithm would be meaningless.

$$\ce{Fe + 2H+ -> Fe^2+ + H2}$$

$$Q=\ce{[Fe^2+]/[H+]^2}$$

Secondly, using a unit of concentration other than mol/litre would definitely yield a different value. So I decided to check its solution from a reference book. In the solution, they have used the above expression of molar concentrations.

So, my question is, is this expression correct?

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  • $\begingroup$ In functions, such as log, sine, exp etc. it is implied that all concentration terms are divided by unit concentration, e.g. $1 \pu{mol dm^{-3}}$ or whatever concentration units you use, so that the terms are always dimensionless. Many texts do not mention this. $\endgroup$
    – porphyrin
    Mar 22, 2017 at 11:48

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This is why for equilibrium expressions we use activity and fugacity. Both of these values are dimensionless and are generally quite closely related to the concentration and partial pressure, respectively, for reasonable concentrations.

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  • $\begingroup$ But does that mean the expression is incorrect? $\endgroup$
    – user42819
    Mar 22, 2017 at 0:51
  • $\begingroup$ The expression is fine because you just take the unitless concentration. $\endgroup$
    – Zhe
    Mar 22, 2017 at 13:58

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