a) A polyfunctional acid is an acid that has more than one functional group.
b) The equations of dissociation of phosphoric acid are:
- H₃PO₄ + H₂O ⇄ H₂PO₄⁻ + H₃O⁺
- H₂PO₄⁻ + H₂O ⇄ HPO₄²⁻ + H₃O⁺
- HPO₄²⁻ + H₂O ⇄ PO₄³⁻ + H₃O⁺
c) The equation for calculating the concentration of H₃O⁺ is [tex] [H_{3}O^{+}] = (\frac{K_{1}K_{2}K_{3}[H_{3}PO_{4}]}{[PO_{4}^{-3}]})^{1/3} [/tex]
a) A polyfunctional acid can be defined as an acid that has more than one functional group. Phosphoric acid (H₃PO₄) is an example of polyfunctional acid since it is composed of three hydroxyl groups joined to a phosphorus atom, which is also joined to an oxygen atom by a double bound. In that structure, the three hydrogen atoms of the hydroxyl groups give the acidic behavior to this compound.
b) Phosphoric acid has three equations of dissociation:
- H₃PO₄ + H₂O ⇄ H₂PO₄⁻ + H₃O⁺ (1)
- H₂PO₄⁻ + H₂O ⇄ HPO₄²⁻ + H₃O⁺ (2)
- HPO₄²⁻ + H₂O ⇄ PO₄³⁻ + H₃O⁺ (3)
The dissociation constants for the three above equations are:
[tex] K_{1} = \frac{[H_{2}PO_{4}^{-}][H_{3}O^{+}]}{[H_{3}PO_{4}]} [/tex] (4)
[tex] K_{2} = \frac{[HPO_{4}^{2-}][H_{3}O^{+}]}{[H_{2}PO_{4}^{-}]} [/tex] (5)
[tex] K_{3} = \frac{[PO_{4}^{3-}][H_{3}O^{+}]}{[HPO_{4}^{2-}]} [/tex] (6)
c) We can calculate the concentration of H₃O⁺ for each equilibrium with the equations (4), (5), and (6).
The general reaction of dissociation of phosphoric acid is given by the sum of equations (1), (2), and (3):
H₃PO₄ + 3H₂O ⇄ PO₄³⁻ + 3H₃O⁺ (7)
The concentration of H₃O⁺ for the total dissociation reaction (eq 7) can be found as follows:
[tex] K_{t} = \frac{[PO_{4}^{-3}][H_{3}O^{+}]^{3}}{[H_{3}PO_{4}]} [/tex] (8)
Where:
[tex] K_{t} = K_{1}*K_{2}*K_{3} [/tex]
Hence, by knowing the dissociation constants K₁, K₂ and K₃, and the concentrations of PO₄³⁻ and H₃PO₄, the [H₃O⁺] is:
[tex][H_{3}O^{+}] = (\frac{K_{1}K_{2}K_{3}[H_{3}PO_{4}]}{[PO_{4}^{-3}]})^{1/3}[/tex]
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