Determine volume of HCl added to propionic acid to get pH=1

[BThomas1219]

Homework Statement

Given 250ml of 0.1M HC3H5O2 (Ka=1.35E-5) What volume of
a)1.0M HCl is needed to lower the pH to 1.00.
b) 1.00M NaC3H5O2 raise pH to 4.00

Homework Equations

pH=pKa-log (HA/A)
ICE chart

The Attempt at a Solution

I used the ice chart for the dissociation of propionic acid. I determined the concentration of H+ and A- to be 1.16E-3. the pH was 2.93. I do not know how to factor in the HCl to determine the volume needed to lower the pH.

 

[Borek]

K_a = \frac {[A^-][H^+]}{[HA]}

rearranged:

\frac {[A^-]}{[HA]} = 10^{pH - pK_a}

At pH 1.0 only about 10^1-4.75=10^-3.75=2x10^-4 of the acetic acid is dissociated. That means in the first case you can - more or less safely - assume presence of acetic acid doesn't matter much, as the first approximation pH will depend mostly on the HCl dilution.

Second case is just a buffer solution, use Henderson-Hasselbalch equation.