Determining the equilibrium constant of a reaction I'm looking at the lecture slide of my thermodynamics class, and have a question about the the equilibrium constant: for the reaction
$$
SO_4^{-2}+2H^+ <=> H_2SO_4.
$$
The equilibrium constant is given as
$$
K(\tau)=\frac{[H^+]^2[SO_4^{2-}]}{[H_2SO_4]}.
$$
I'm wondering why the concentration of product is in the denominator? I've seen a couple of examples about writing the equilibrium constant but I'm still confused which side of the chemical reaction should be on the nominator and denominator.
 A: The concentration form of an equilibrium constant for a general reaction where activity coefficients are unity is defined as
$$K_{EQ,C}^\star = \prod\ C_j^{\nu_j}$$
The terms $C_j$ are molar concentration of species $j$. The terms $\nu_j$ are the reaction coefficients. The reaction coefficients are the stoichiometric coefficients with negative signs for reactants and positive signs for products. By example, for N$_2$ + 3H$_2$ $\leftrightharpoons$ 2NH$_3$, we would write
$$K_{EQ,C}^\star = C_{N_2}^{-1}\ C_{H_2}^{-3}\ C_{NH_3}^{2} $$
This approach results in a form leading to the common expression: products divided by reactants.
This format is never violated as the definition of an equilibrium constant for a reaction.
A: I think the mathematical formalities have been already introduced.
Let me offer you a spark on what the equilibrium constant actually means, so to clear the air.
Keep in mind every chemical system for a fixed temperature and pressure has a single equilibrium point, no matter how one works out the mathematical expressions.
When stating "unique", I imply that situation in which the Gibbs Free Energy of the System is the absolute minimum, excluding metastable states, which are ultimately local minima ensured by kinetic constraints.
For a set of P and T, minimum G dictates equilibrium.
Given the equation you mentioned, reactants, products and pathways are all set to go.
The actual numerical value for the equilibrium constant is often provided in text books by some sort of "magical" enlightenment.
But, if one dives deeper into its derivation, one could tell it comes from minimizing Gibbs Free Energy!
To keep it simple, experimentalists account for the values, by waiting for conversions to happen and measuring species relative amounts. They compute and provide a k (pKw of water is 14).
And by post processing and working out the well-known x (reaction extent), one is actually following a theoretical path towards the lab experiments. It is an indirect procedure
There are also more advance tools that account for relative species amounts. But again, they lower Gibbs Free Energy for a set of sinks by means of all possible pathways.
I hope this clarifies you a bit. If I were you, I will try to digest the procedure every professor has, to pass exams. But also understanding the essence behind "working out x" and any other "magical" recipe.
