# Why is "activity" of gaseous component equal to its partial pressure but that of aqueous component its concentration?

While solving an electrochemistry problem I had to calculate the reaction quotient of this reaction:

$$\ce{2Fe(s) + 4H+(aq) + O2(g) -> 2Fe^{2+} (aq) + 2H2O (l)}$$

It turns out to be: $$\ce{Q=\dfrac{[\ce{Fe}^{2+}]^{2}}{[\ce{H+}]^4p\ce{O2}}}$$

where square brackets mean concentration and $$p$$ denotes partial pressure. Here's what I do know: activity of solid and liquid components is 1, and that of aqueous components is their concentration.

However, why is the activity of gaseous components their partial pressure? Is this fact experimental or can it be derived?

• @Maurice I picked it straight from an online lecture, but a Google search of the exact phrasing of the question returns multiple solution sites like this one. I don't know about plausibility, but looking at the amount of results I'm sure this is from some famous problem book. Jul 16 at 19:06
• Are you sure of your equation ? Because usually oxygen $\ce{O2}$ reacts with iron in acidic solution to produce ferric ions $\ce{Fe^{3+}}$, according to : $$\ce{4 Fe + 3 O2 + 12 H^+ -> 4 Fe^{3+} + 6 H2O}$$ Jul 16 at 19:07

## 1 Answer

Thermodynamics courses usually start by calculating amounts of heat and amounts of work enterring a container. And the work is $$\pu{p\Delta V}$$. No mention of concentration ! Just the pressure. Afterwards, enthalpy is introduced, then gas chemistry is developed, always using pressures. Equilibrium constants are then introduced, always with gases and pressures. And suddenly appears the necessity of defining equilibrium constants in liquid phase, where pressures have no obvious meaning. Here the authors of the course state that, thanks to Henry's law, it makes sense to replace the pressure by the concentration (or the activity) which is easier to determine than pressure. Concentration or activity are supposed to be proportional to pressure. Fortunately, this change of parameter does work well in practice. The equilibrium constants determined by using concentration allow nice predictions, and are verified for example in electrochemistry (Nernst law). But it should be known that as soon as a gas intervenes in a chemical reaction, it is safer to use its pressure.