# The pH of 0.02 M solution of an unknown weak acid is 3.7, how would you find the pka of this acid?

##### 1 Answer

Knowing the pH, you know the concentration of protons:

#-log["H"^(+)] = "pH" = 3.7#

#["H"^(+)] = 10^(-3.7)# #"M"#

Now, since the weak (monoprotic) acid dissociates into its conjugate base and a proton, the ** must** be

**equimolar**with the protons given out to the solvent.

#"HA" rightleftharpoons "A"^(-) + "H"^(+)#

Hence,

#K_a = (["H"^(+)]_"eq"^2)/(["HA"]_"eq"]#

Don't forget that the

#= (["H"^(+)]_"eq"^2)/(["HA"]_i - ["H"^(+)]_"eq")#

#= (10^(-3.7) "M")^2/(0.02 "M" - 10^(-3.7) "M")#

#K_a = 2.0105xx10^(-6)# #"M"#

Thus:

#color(blue)("pKa") = -log("K"_a)#

#= -log(2.01059xx10^-6)#

# ~~ color(blue)(5.70)# where the logarithm of any number is unitless.