Calculate the percent ionization of Nitrous acid in a solution that is 0.253 M in Nitrous aci (HNO2) and 0.111 M in potassium nitrite (KNO2). The acid dissociation constant of nitrous acid is 4.50 * 10^-4. Help?

The nitrous acid is 0.409 % ionized.

We can consider this as both a buffer problem and as an example of the common ion effect.

This is a buffer solution because it contains the weak acid ##"HNO"_2## and its conjugate base ##"NO"_2^-##.

##"HNO"_2 + "H"_2"O" ⇌ "H"_3"O"^+ + "NO"_2^-##

According to the Henderson-Hasselbalch equation,

##"[pH](http://socratic.org/chemistry/acids-and-bases/the-ph-concept)" = "p"K_"a" + log((["NO"_2^(-)])/(["HNO"_2]))##

##"pH" = -log(4.50 × 10^-4) + log((0.111 cancel("mol/L"))/(0.253 cancel("mol/L"))) = "2.985"##

##["H"_3"O"^+] = 10^-2.985 "mol/L" = 1.035 × 10^-3 "mol/L"##

This ##["H"_3"O"^+]## came from ionization of the ##"HNO"_2##.

##"% Ionization" = (["H"_3"O"^+])/(["HNO"_2]_0) × 100 % = (1.035 × 10^-3 cancel("mol/L"))/(0.253 cancel("mol/L")) × 100 % = 0.409 %##

Side note: If we had had just 0.253 mol/L ##"HNO"_2## with no ##"NO"_2^-##, the % ionization would have been 4.22 %. The common ion effect suppressed the ionization by a factor of 10.