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As a theoretical chemist, my entire exposure to reaction quotients and equilibrium constants ($Q$ and $K$) is through thermodynamics ($\Delta G^\ominus = - RT \ln K_{eq}$ and so on).

So as I started teaching first-year chemistry I was very surprised to encounter the concept of expressing gas activities in molarity and a "concentration reaction quotient" $K_c$ for gas reactions, such as

For the reaction $\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$, find $Q$ if $\ce{[N2(g)]}$ = 0.04 M and $\ce{[H2(g)]}$ = 0.09 M. If $K$ = 0.040, in which direction will the reaction shift to attain equilibrium? (adapted from LibreTexts)

Students also learn$^{\text{[citation needed]}}$ to "convert between $K_c$ and $K_p$" and to use $K_c$ in ICE (initial, change, equilibrium) tables to calculate quantities. Upon seeing all this my burning question is:

Do real world lab chemists ever express gas activities with molarity??

I have several theoretical and general objections:

  1. How could anyone ever know what $Q$ or $K$ (unsubscripted) means for a general gas phase reaction, since $K$ is usually unitless (since activities are unitless)?

  2. We can compare $Q$ or $K$ with 1 to see if a reaction is product- or reactant-dominant, either instantaneously or at equilibrium. But (for example) $K_c$ and $K_p$ will often differ by orders of magnitude and be on opposite sides of 1. What does that mean??

  3. Don't heterogeneous-phase reactions get even more confusing, since gases could be quoted in either concentration or partial pressure? Do we need even more Henry's Law unit conventions?

  4. Even if real world lab chemists wrote down gas molarities, it seems confusing enough that we should avoid burdening undergraduate students with these calculations. Evidence that students don't get it can be found on Chemistry SE here, here, here, here, here, here, or here.

But if it really is used often enough in professional lab chemistry to merit being in a first year chemistry textbook then I'll just have to teach it, I guess.

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    $\begingroup$ I assume molarities or mass concentrations may be useful for design of production open system processes in context of mass/molar inventory. $\endgroup$
    – Poutnik
    Commented Sep 26, 2023 at 7:08
  • $\begingroup$ Kp is not considered dimensionless unless the partial pressures are expressed in bars (or the same units as the pressure in the standard state). $\endgroup$
    – Chet Miller
    Commented Sep 26, 2023 at 11:03
  • $\begingroup$ @ChetMiller If I'm reading the IUPAC definitions of Kp and K correctly, it seems (by those definitions) $K_p$ always has units of pressure^(change of gas moles), $K$ never has units, and $K$ and $K_p$ happen to numerically coincide when $K_p$ is calculated in pressure units corresponding to the standard pressure. But I'm a computer nerd, and I'm sure you're right about how actual chemists communicate using those quantities. $\endgroup$
    – Shern Ren Tee
    Commented Sep 26, 2023 at 12:12
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    $\begingroup$ Even though $K$ doesn't have a dimension, it is defined relative to "standard conditions." (In the thermodynamic formulation, the change in Gibbs free energy is relative to a standard G.) If you went to a remote island where they defined a different set of standard conditions than you're used to, they'd have different values of K. $\endgroup$
    – anon
    Commented Sep 26, 2023 at 14:03
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    $\begingroup$ You may want to consult a chem eng textbook as a reference. $\endgroup$
    – Buck Thorn ♦
    Commented Sep 27, 2023 at 10:24

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