Some of the equilibrium constants

In an equilibrium, you will have a series of reactants and products in a reversible reaction. These reactants will also have a mole ratio between them. For example, this reaction: 

N₂ + 3H₂ ⇌ 2NH₃

shows that there is twice as many moles of ammonia, and three times as many moles of hydrogen, as there are of nitrogen, at equilibrium. In general, an equilibrum will look like this:

 aA + bB ⇌ cC + dD

If you wanted to represent the ratio of reactants and products in an equilbrium, you could use an equilibrium constant, which is of this form (note, the square brackets are shorthand for concentration):

The reason why this ratio has any meaningful value is due to the concept of a rate equation. In an equilibrium, you have two different reactions ongoing at a given time - the forward reaction, and the backward reaction. In these reactions, the rate of the reaction is directly proportional to the concentration of given substances; the constant of proportionality here is known as the rate constant. K is merely the ratio of the rate constants of the forward and backward reactions.

And there are several of them. Unfortunately, there doesn't appear to be a definitive list of equlibrium constants online, so this blogpost will likely be inconclusive. But I'll try my hardest either way.

This blogpost goes alphabetically by the subscript of K.

The acid and base equilibrium constants: K_a/K_b - Acids can be ionised in an aqueous solution to a hydrogen ion, and a base. The basic equation for the ionisation of water is:

 HA + H₂O ⇌ H₃O⁺ + A^- 

and the H₃O⁺ ion can be simplified as H⁺, since H₃O⁺ forms when an H⁺ ion binds to a water molecule, so both in effect represent the donation of a proton by the weak acid. [H₂O] doesn't really change, so can be disregarded in the equilibrium expression since we're just dealing with proportionalities here. And the ratio can be described using the acid dissociation constant (K_a), as such:

A very similar relationship applies for bases, and this is where we get the basic ionisation constant (K_b), which is not to be confused with the Boltzmann constant in writing. When a base ionises water, a hydroxide ion is released instead, and the base will accept a proton. Here, the general equation for a base ionising water is:

 B + H₂O ⇌ BH⁺ + OH^-

For the same reasons as before, we get this expression for K_b:

Now, it's worth noting that both of these constants only apply when dealing with weak acids and bases - ie, acids/bases that only partially ionise in water. HCl for instance will dissociate completely into H⁺ and Cl^-, and no equilibrium will be involved. 

Concentration: K_c - I've already described this constant, it's the one I initially discussed at the beginning of the blogpost, and the lead photo is K_c. It's also arguably the classic equilbrium constant, the one everyone is taught at GCSE and which leaves you wondering what the subscript c is for. It is worth noting, however, that K_c only applies when you're dealing with liquids or gases, since chemically-speaking, only fluids have a concentration.

Ligands: K_d/K_f - Complex ions form when a ligand donates an electron pair to a central metal ion. In much the same way as before, we can express this formation through an equilibrium:

aM + bL ⇌ M_aL_b 

Here, M refers to the metal ion, and L refers to the ligands. When you're forming a complex ion, the equilibrium constant is K_f:

And the dissociation of a complex ion into its constituent parts is K_d, where the equilibrium acts in the opposite direction and the constant changes accordingly:

The larger K_f is, the more stable the complex ion is. The larger K_d is, the reverse applies.

Pressure: K_p - This one only applies to gases as only they can be compressed. This time, the notation differs ever so slightly; for the reaction aA + bB ⇌ cC + dD:

Here, the notation p(X) refers to the partial pressure of a substance; the partial pressure is the pressure that a substance in a mixture would exert on a container if acting alone - this value simply refers to the ratio of the moles of the substance in the mixture as well. 

Solubility: K_s(p) - Similar to the dissociation of an acid, solids can also break up into charged components. Take a salt, like NaCl, which is composed of an ionic lattice. When dissolved in water, it can form Na⁺ and Cl^- ions, which will bind to the water molecules. If the solvent is in excess, the lattice will completely break up; however, if the salt is in excess, an equilibrium might form, since the solvent is saturated - the salt has surpassed its solubility limit.

Whilst some salts dissolve completely up to this point, others don't, like in this equation:

Ag₂CrO_4(s) ⇌ 2Ag⁺_(aq) + CrO₄^2-_(aq) 

To estimate the solubility of dear silver chromate, we can use this new equilibrium constant - the solubility product:

Since the activity of silver chromate is almost minimal, we can disregard it in this expression, much like we did with water earlier.

Ionic product of water: K_w - Going back to the initial concept of acid-base equilibria, water can act as both an acid and a base, and dissociate into hydrogen and hydroxide ions:

2H₂O ⇌ H₃O⁺ + OH^- 

For the same reasons as before, we can simplify H₃O⁺ to be H⁺, and disregard [H₂O] completely, to get this:

K_w = [H⁺][OH^-]

From here, it becomes clear as to why water is neutral - the concentrations of hydrogen and hydroxide ions are equal to each other. Hence the pH of a neutral substance can vary, provided it corresponds with the correct temperature - at room temperature, for instance, the pH is 7, but that isn't a given for all conditions.

Which leads me to the final key point about the equilibrium constants - only temperature can influence the value of K to change. Depending on this change, K can shift either to the left or to the right of the equilibrium, which would lead to the rate constant of either the forward or backward reactions changing. Hence, one reaction would be favoured more than the other, and suddenly you've got far less ammonia than you bargained for.  

Now, the title is a bit of a lie. There are far, far, far more equilibrium constants, these just so happened to be the ones that came up the most often online. I've personally studied four of these at school, and the rest are probably going to come up at uni - and I'm sure the unblogged ones will too. Maybe this will become an ongoing series on this blog - if you know of any other equilibrium constants, please tell me.