Calculate the pKa of hypochlorous acid. The pH of a 0.015 M solution of hypochlorous acid has a pH of 4.64 ?

1 Answer
Truong-Son N.
Apr 12, 2018

#"pK"_a = -log(K_a) = ???#

Well, you can work backwards. The #"pH"# gives the #["H"_3"O"^(+)]#:

#"pH" = -log["H"_3"O"^(+)]#

#10^(-"pH") = ["H"_3"O"^(+)] = 10^(-4.64) = 2.29 xx 10^(-5) "M"#

But hypochlorous acid is a monoprotic acid, and hence,

#"HClO"(aq) + "H"_2"O"(l) rightleftharpoons "ClO"^(-)(aq) + "H"_3"O"^(+)(aq)#

we find that #["H"_3"O"^(+)] = ["ClO"^(-)] = x# at equilibrium. The amount #x# that is generated at equilibrium was dissociated from #"HClO"#, i.e. the concentration dropped from #"0.015 M"# to #"0.015 M" - x#.

Writing the #K_a# expression,

#K_a = (["ClO"^(-)]["H"_3"O"^(+)])/(["HClO"])#

#= x^2/("0.015 M" - x)#

But we know #x#. Therefore,

#color(blue)(K_a) = (2.29 xx 10^(-5) "M")^2/("0.015 M" - 2.29 xx 10^(-5) "M")#

#= color(blue)(3.52 xx 10^(-8))#

How then do you get the #"pK"_a# from here, if #hatp(" ") = -log(" ")#?

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