What must be the minimum concentration of dichloroacetic acid in 1.00L buffer solution of a pH 0.91 dichloroacetic acid/sodium dichloroacetate buffer if the pH changes by 0.2 units when 0.057 moles HCl are added?

Dichloroacetic Cl2CHCOOH ka= 5.50E-02 pka= 1.26

1 answer

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It took awhile but here it is.
For pH = 0.91,you have
0.91 = 1.26 + log (base)/(acid)
B/A = approx 0.447 but you need to go through this and all calculations that follow to get more accurate numbers. What you want to do now is to add 57 millimols H^+ to the base(which I will call ClAc^-) so that the pH will change from 0.91 to 0.71 and you want to know the acid (which I will call HClAc) will be for that to happen.
.........ClAc^- + H^+ --> HClAc
I.........B.......0........A
add...............57...........
C........-57.....-57......+57
E........B-57.....0.......A+57

0.71 = 1.26 + log (B-57)/(A+57)
but B = 0.447A
0.71 = 1.26 + log (0.447A-57)/(A+57)
Solve for A. I get approx 440 millimols which in 1000 mL will be 0.44M and since the base is 0.447 x that it will be approx 197 millimols or 0.197 M. I like to check these things to make sure it works. It may not be exactly 0.71 because I've rounded here and there but if you go through it will more accurate numbers it should come out ok.
.......ClAc^- + H^+ ==> HClAc
I.......197.....0........440
add............57...........
C.......-57...-57.........+57
E.......140....0.........497

pH = 1.26 + log(140/497)
pH = 0.7098 which rounds to 0.71