Question #62737
1 Answer
Explanation:
As you know, formic acid,
Simply put, not all molecules of formic acid will actually donate their acidic proton to the water to increase the concentration of hydronium ions,
You can get an idea about how low the pH of the resulting solution will be by taking a look at the magnitude of the acid dissociation constant,
Because
Your tool of choice here will be an ICE table
#" " "HCOOH"_text((aq]) + "H"_2"O"_text((l]) " "rightleftharpoons" " "H"_3"O"_text((aq])^(+) " "+" " "HCOO"_text((aq])^(-)#
By definition, the acid dissociation constant will be equal to
#K_a = ( ["H"_3"O"^(+)] * ["HCOO"^(-)])/(["HCOOH"])#
In your case, you will have
#K_a = (x * x)/(0.0025 - x) = 3.5 * 10^(-8)#
Now, because
#0.0025 - x ~~ 0.0025#
This will get you
#K_a = x^2/0.0025 = 3.5 * 10^(-8)#
Solve this equation for
#x = sqrt( 0.0025 * 3.5 * 10^(-8)) = 9.35 * 10^(-6)#
Since
#["H"_3"O"^(+)] = x = 9.35 * 10^(-8)"M"#
and thus
#"pH" = - log( ["H"_3"O"^(+)])#
#"pH" = - log( 9.35 * 10^(-6)) = color(green)(5.03)#