Calculate the concentration of H2SO3 present in 0.198 M Na2SO3(aq).
Ka1 = 0.015
Ka2 = 1.2 × 10−7
Kw = 1 × 10−14
I calculated this using Kb1 and Kb2 in ICE tables, and I ended up finding the concentration to be the equivalent of Kb2. However, that is not the correct answer and I don't know what I'm doing wrong. Can someone please explain how to do this problem? Thank you!
My answer, 8.333E-8, was incorrect.
To solve this problem you need to calculate the Kb's from the Ka's, using the relationship Kb = 10^(-14)/Ka, and keeping in mind that Ka1 gives Kb2, and vice versa.
The first hydrolysis is:
`CO_3^2- + H_2O -> HCO_3^- + OH^-`
Kb = 1.00 x10^(-14)/1.2 x10^(-7) = 8.3 x10^(-8)
Using an ICE table, you will see that at equilibrium:
if [HCO3-] = x, then [OH-] = x and [CO3 2-] = 0.198-x
8.3x10^(-8) = (x^2)/(.198-x)
neglecting x in the denominator, because it's small, we get
x= 1.28 x10^(-4)
This is less than 5% of 0.192 s it is okay to neglect x.
For the second hydrolysis:
`HCO_3^- + H_2O -> H_2CO_3 + OH^-`
Kb = 1.00 x 10^(-14)/.015 = 6.7 x 10^(-13)
[H2CO3] = x, [OH-] = x, [HCO3] = 1.28 x 10^(-4)-x
6.7 x 10^(-13) = (x^2)/1.28 x 10^(-4) -x
Again, we neglect x in the denominator so that x = 9.2 x 10^(-9) as the final answer. This again less than 5% of the initial concentration of the base so the assumption that it is negligible in the calculation is valid.