Not sure what type of problems you’re trying to tackle, Garf, but the general types of problems involved in Acid/Base equilibria involve:
-
Determining the [H+] (or pH); Determining the [OH-] (or pOH), where denotes “the concentration of”, when given equilibrium constants
-
Determining the equilibrium constant when given concentration values.
Problems of type 2 are fairly straightforward:
K=(product of the concentrations of ions in solution at equilibrium) / (concentration of acid at equilibrium).
Problems of type 1 are a bit trickier, but the general methodology is:
Given: HA <–> H+ + A-
K(for HA)
Starting concentration of HA (let’s call this value C)
Find: [HA], [H+], [A-] at equilibrium
Solved as follows:
Let [H+] = [A-] = x (where we are trying to solve for x)
K(HA) = [H+][A-]/[HA] = (x)(x)/(C - x)
This yields the quadratic equation K(HA)*(C-x) = x^2, which can then be solved for x.
Sometimes, to speed up the calculation, the approximation (C-x) ~= C is used, since x is usually small in magnitude when compared to C. Then, the approximate solution becomes:
x = sqrt(K(HA)*C) Using this approximation, you then have to go back and check to ensure that the assumption (C-x) ~= C is valid (i.e., that x really is small when compared to C). Note also that you can only use this approximation if you are not asked to find [HA], since, with the approximation, you are essentially ignoring changes in [HA].
There are variants on this type of problem. One variant is the buffer solution problem where starting values for both HA and A- concentrations are given. For these, you merely factor in the additional A- concentration (let’s call this B) in your calculations as in:
K(HA) = (x)(x+B)/(C-x)
Another type of problem involves multiprotic acids, that is, acids which deprotonate over multiple steps. For instance:
H[sub]3[/sub]A <–> H[sub]2[/sub]A- + H+
H[sub]2[/sub]A- <–> HA-- + H+
etc…
These are solved by using systems of simultaneous equations. The math starts to get really messy if you can’t use the (C-x) ~= C approximation.
Of course, for base equilibria, make appropriate substitutions to the terms, but the math is the same.
Hopefully, some of this is helpful… post back, and let us know what types of problems you’re trying to solve.