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.
$$\ce{Fe + 2H+ -&gt; Fe^2+ + H2}$$
$$Q=\ce{[Fe^2+]/[H+]^2}$$
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?
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.