14.5 Polyprotic Acids

The polyprotic acids are acids that have more than one proton (H ⁺). Examples of these acids are:

H₂CO₃ Carbonic acid (di protic = 2 protons)

H₂SO₄ Sulfuric acid (di protic = 2 protons)

H₃PO₄ Phosphoric acid (tri protic = 3 protons)

On the other hand, the monoprotic acids have only one proton (H ⁺). Examples of these acids are:

HCl Hydrochloric acid (mono = 1 proton)

CH₃COOH Acetic acid (mono = 1 proton)

HNO₃ Nitric acid (mono = 1 proton)

Monoprotic acids are ionized in one step only but the polyprotic acids are ionized in multiple steps:

Monoprotic acid ionization:

HCl (aq)     +    H₂O (l)       H₃O ⁺ (aq)    +  Cl  ^– (aq)  [one step only]

Polyprotic acid ionization:

H₃PO₄   +     H₂O (l)        H₃O ⁺ (aq)  + H₂PO₄   ^– (aq)

H₂PO₄   ^– (aq)     +     H₂O (l)        H₃O ⁺ (aq)  + HPO₄  ^{2 –} (aq)

HPO₄  ^{2 –} (aq)   +     H₂O (l)        H₃O ⁺ (aq)  + PO₄  ^{3 –} (aq)

Ionization of polyprotic acid:

Example:

H2SO4 (aq)  +  H2O (l)    H3O + (aq)  +  HSO4  –  (aq)

Ka1  = 1.0 x 10   3

 HSO₄  ^–  (aq)  +  H₂O (l)    H₃O ⁺ (aq)  +  SO₄  ^{2 –}  (aq)     K_a2  = 1.2 x 10  ^{– 2}

Calculate: [H₃O ⁺], [HSO₄  ^–] and [SO₄  ^{2 –}] if the concentration of H₂SO₄ is 0.0550 M.

Using ICE table:

H2SO4 (aq)  +  H2O (l)           H3O + (aq)          +       HSO4  –  (aq)

Initial:                  0.0550 M            –                           0                                0

Change:                – X                                                 +X                              +X

Equilibrium:           0.0550 – X                                    +X                              +X

Ka1   = 1.0 x 10   ³ =  { [H₃O ⁺ (aq)] x [HSO₄  ^–  (aq)] }  /  { [HSO₄  ^–  (aq)] }

Using the assumption method: 0.0550 >>> X

1.0 x 10   ³ =  { [X] x [X] }  /  { 0.0550]

X ² = { 0.0550] * [1.0 x 10   ³]

X = √ { 0.0550] * [1.0 x 10   ³] = 7.42 M = [H₃O ⁺] = [HSO₄  ^–]

Now these obtained values will be used for the second step:

HSO₄  ^–  (aq)  +  H₂O (l)    H₃O ⁺ (aq)  +  SO₄  ^{2 –}  (aq)     K_a2  = 1.2 x 10  ^{– 2}

K_a2  = 1.2 x 10  ^{– 2}  = { [H₃O ⁺ (aq)]  * [SO₄  ^{2 –}  (aq)] }  / { [HSO₄  ^–  (aq)] }

1.2 x 10  ^{– 2}  =  {[ 7.42] * [X] }  /  { [7.42] }

X = 1.2 x 10 ^– 2