para-Aminobenzoic acid, PABA, is a powerful sunscreening agent whose salts are used widely in sun tanning and screening lotions. The parent acid, which we may symbolize as H-Paba, is a weak acid with a pka of 4.92. What will be the [H+] and pH of a 0.030 M solution of this acid? I need help solving this.

Answers ( if you want to check ):

pH = 3.22
[H+] = 6.0 x 10^-4 mol/l

Start with the definition of Ka and pKa.

.



For a general acid, Ka is defined

where [] indicates the concentration.

(Equation 1)

(Note the units of Ka and the units of the concentrations.)

At first it looks like we have one equation and three unknowns. However, remember that this comes from the following equillibrium



if we start with pure HPABA, whose concentration is C (0.030 M), then

where x is the amount that's dissociated and (Equation 2)

(Equation 3)

So we have three equations and three unknowns. Substituting into equation 1, we have



rearranging



Solving yields (we ignore the negative root)

Therefore

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For very weak acids, many people ignore the x in (C-x), and just calculate from there:

If x is small compared to C,



and we have almost the same answer (pH =3.222) .

Thanks a lot for the help... I just want to know when to use the quadratic formula or just drop the x's because sometimes I wouldn't know if it's a weak acid. Are there any other ways to find out?

If you drop the x in the denominator, you can get an estimate of x. If it's small compared to C, you're finished.