[Big-Daddy]

For a reaction in the gaseous phase, we could write several different equilibrium constants. We could have K_c, K_p, K_x. There is also the true thermodynamic K, though I do not know how to calculate it, nor whether, for a gaseous phase reaction, it is the same as one of those I have just mentioned.

When we write ΔG=ΔG°+R·T·log_e(Q), then, is the Q based on concentration, partial pressure, mole fraction, or what? And - most importantly - why?

[Corribus]

Equilibrium constants are really based on activities, which are expressed differently for different states of matter.

[Big-Daddy]

Equilibrium constants are really based on activities, which are expressed differently for different states of matter.

OK K_c is expressed in activities. K_x is surely a straightforward mole fraction ratio - you wouldn't change anything for activity or fugacity here. K_p is partial pressure for ideal gases and fugacity for non-ideal gases.

But there are still 3 different constants here! To be clear, fugacity is not calculated in the same way as activity, so I assume it is different. So K_p(fugacities)≠K_c(activities). And we use activity for all species except solid and gas, for gaseous ones we use fugacity, and for solid phase reactions I don't know.

[Corribus]

Fugacity IS a thermodynamic activity, or near enough to it. (The value of fugacity and activity is exactly the same - only the units change.)  The activities of solids (and pure liquids) in their standard states are generally equal to 1, although they can deviate slightly from this.  In cases where the activity of a solid (such as a solid not in its standard state) needs to be known, it can be determined experimentally or predicted theoretically.

You might want to read up about the concept here:

http://en.wikipedia.org/wiki/Activity_(chemistry)

[Big-Daddy]

Fugacity IS a thermodynamic activity, or near enough to it. (The value of fugacity and activity is exactly the same - only the units change.)  The activities of solids (and pure liquids) in their standard states are generally equal to 1, although they can deviate slightly from this.  In cases where the activity of a solid (such as a solid not in its standard state) needs to be known, it can be determined experimentally or predicted theoretically.

You might want to read up about the concept here:

http://en.wikipedia.org/wiki/Activity_(chemistry)

Are you sure activity and fugacity take the same value for gases? Wikipedia describes fugacity as "the equivalent of activity for partial pressure", but then just as partial pressure does not take the same value as concentration, fugacity wouldn't take the same value as activity - rather, activity of the gas would be derived from the gaseous concentration, just like it is derived from the concentration for any other species in any other state, fugacity would be derived by a slightly different method from the gaseous partial pressure, and partial pressure is finally related to concentration with P=cRT.

If fugacity is really the same as activity (ok, units are different, but the physical relevance is the same, the value has the same real-world effect) for gases, then for all states, solid, liquid, gas and anything in solution, we really want to find the activity (fugacity being the same thing - not that the calculations on Wikipedia's page for fugacity make this obvious to me - i.e. fugacity is "activity for gases") and use this in our equilibrium calculations. And then there is only one equilibrium constant we can write: the one expressed in activities.

[Corribus]

And then there is only one equilibrium constant we can write: the one expressed in activities.

This is the way equilibrium constants SHOULD be expressed, but calculating true activities can be cumbersome and usually molar concentrations (or partial pressures, or fugacities, or whatever) are near-perfect representations of the true activity.