There are just a few things you need to know about pH.
pH is on a logarithim scale from 1 - 14 ( I think you can have a negative pH, but that is beyond the scope of the DAT) So going from a pH of 4-2 would be an increase of 10^2 in acidity since going from 4-2 is by a difference of two units. (always raise ten to the amount of units)
On this scale, 7 is neutral (Think strong base + strong acid)
Less than 7 is acidic (Think HCL = Very Strong acid - has a low pH= lower pH = more acidic, also anything with a lot of Oxygens becomes more acidic)
Greater than 7 is basic
Very basic = KOH = a high pH
pH is measured by the concentration of H+ions (dealing with acids)
pH = -log(concentration H+)
p0H is measured by the concentration of OH ions
POH= -log (concentration 0H-)
pH + pOH = 14
These formulas are only used if you have a strong acid or strong base.
If a base is given in a problem and it asks for pH, you must first solve for pOH then subtract it from 14 to get pH- I saw a lot of problems like this on achiever and top score...
For weak acids, the Handerson Hasselbach equation is used, since it doesn't completly dissociate into H+ ions.
pH = Pka + log(concentration of base/concentration of acid)
ka x kb = 1 x 10 ^-14
pka = -log ka
pkb = - log kb
ka = acid dissociation constant
kb = base dissociation constant
kw = 1 x 10 ^-14
The math may look complicated but if you change everything to scientific notation it becomes easier. Math is my weak point but I just reviewed some basic logs to save time on these types of questions.
log(1) = 0 which is why a buffer at the pka value is best:
Remember a buffer works best at a pH of pka +/- 1.
pH = pka + log (concentration of base/concentration of acid)
If the concentrations of base and acid are the same, you end up with
pH = pka + log (1)
log(1) = 0
pH = pka
which would be a great buffer.
Hope this helps.