What is the pKa of #CH_3COOH# and #H_3PO_4#?

#\mathbf("CH"_3"COOH")#, ACETIC ACID

Acetic acid is a monoprotic acid, so it only has one #"pKa"#, and it is #4.74#.

If you are more familiar with its #K_a#, which is commonly given as #1.8xx10^(-5)#, then its #"pKa"# is #-log(K_a) = 4.74#.

#\mathbf("H"_3"PO"_4)#, PHOSPHORIC ACID

You can see that phosphoric acid is not monoprotic.

It is polyprotic. It has three protons. So it has three #"pKa"#s.

• #"pKa"_1 = 2.16#
• #"pKa"_2 = 7.21#
• #"pKa"_3 = 12.32#

Each of its #K_a#'s corresponds to a sequential dissociation.

#K_(a1) = (["H"_2"PO"_4^(-)]["H"^(+)])/(["H"_3"PO"_4])#:

#"H"_3"PO"_4(aq) rightleftharpoons "H"_2"PO"_4^(-)(aq) + "H"^(+)(aq)#

#K_(a2) = (["HPO"_4^(2-)]["H"^(+)])/(["H"_2"PO"_4^(-)])#:

#"H"_2"PO"_4^(-)(aq) rightleftharpoons "HPO"_4^(2-)(aq) + "H"^(+)(aq)#

#K_(a3) = (["PO"_4^(3-)]["H"^(+)])/(["HPO"_4^(2-)])#:

#"HPO"_4^(2-)(aq) rightleftharpoons "PO"_4^(3-)(aq) + "H"^(+)(aq)#

Combining all three reactions, we get:

#"H"_3"PO"_4(aq) rightleftharpoons cancel("H"_2"PO"_4^(-)(aq)) + "H"^(+)(aq)#
#cancel("H"_2"PO"_4^(-)(aq)) rightleftharpoons cancel("HPO"_4^(2-)(aq)) + "H"^(+)(aq)#
#cancel("HPO"_4^(2-)(aq)) rightleftharpoons "PO"_4^(3-)(aq) + "H"^(+)(aq)#
#"------------------------------------------------------"#
#color(blue)("H"_3"PO"_4(aq) rightleftharpoons "PO"_4^(3-)(aq) + 3"H"^(+)(aq))#

The full hypothetical one-step dissociation here has the #K_a# of:

#color(blue)(K_(a,"one-step") = K_(a1)K_(a2)K_(a3))#

#= (cancel(["H"_2"PO"_4^(-)])["H"^(+)])/(["H"_3"PO"_4])(cancel(["HPO"_4^(2-)])["H"^(+)])/(cancel(["H"_2"PO"_4^(-)]))(["PO"_4^(3-)]["H"^(+)])/(cancel(["HPO"_4^(2-)]))#

#= color(blue)((["PO"_4^(3-)]["H"^(+)]^3)/(["H"_3"PO"_4]))#

#= 10^(-2.16)*10^(-7.21)*10^(-12.32) = 10^(-21.69)#

#= color(blue)(2.04xx10^(-22))#

In other words, the one-step #K_a# is so small that phosphoric acid heavily favors getting deprotonated one proton at a time, rather than all three in one go.

Hence, its #"pKa"# is NOT given as #-log(10^(-21.69)) ~~ 21.69#. Instead, it is given as #"pKa"_1#, #"pKa"_2#, and #"pKa"_3#.