A contradiction regarding the reaction coefficient expression in the Nernst equation

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?

• 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. Mar 22, 2017 at 11:48