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QUESTION

# 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.

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