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Chapter 14: Problem 104

Write out the stepwise \(K_{\mathrm{a}}\) reactions for citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\), a triprotic acid.

Short Answer

Expert verified
The stepwise dissociation reactions and corresponding Ka expressions for citric acid are: 1. \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}} + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-} (aq)\) $$K_{a1} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}][\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}]}{[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}]}$$ 2. \( \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}^{+}} + \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-} (aq)\) $$K_{a2} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}^+][\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}]}{[\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}]}$$ 3. \( \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}}^{+} + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-} (aq)\) $$K_{a3} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}^+][\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}]}{[\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}]}$$

Step by step solution

01

Identify acidic protons

Citric acid has three acidic protons in its structure. These protons are attached to oxygen atoms in the carboxylic acid (COOH) functional groups, and can dissociate in water to form a hydronium ion (H₃O⁺) and corresponding citrate ion.
02

First dissociation reaction

The first dissociation reaction involves one acidic proton being removed from the citric acid molecule, forming the hydrogen di-citrate ion. The balanced chemical equation for the first dissociation reaction is: $$ \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \left( \mathrm{aq} \right) + \mathrm{H}_{2} \mathrm{O} \left( \mathrm{l} \right) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}} + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-} \left( \mathrm{aq} \right) $$
03

First Ka expression

The acid dissociation constant (Ka) expression for the first dissociation step is: $$ K_{a1} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}][\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}]}{[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}]} $$
04

Second dissociation reaction

The second dissociation reaction involves another acidic proton being removed, this time from the hydrogen di-citrate ion, forming the dihydrogen citrate ion. The balanced chemical equation for the second dissociation reaction is: $$ \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-} \left( \mathrm{aq} \right) + \mathrm{H}_{2} \mathrm{O} \left( \mathrm{l} \right) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}^{+}} + \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-} \left( \mathrm{aq} \right) $$
05

Second Ka expression

The acid dissociation constant (Ka) expression for the second dissociation step is: $$ K_{a2} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}^+][\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}]}{[\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}]} $$
06

Third dissociation reaction

The third and final dissociation reaction involves the last acidic proton being removed, from the dihydrogen citrate ion, forming the tricitrate ion. The balanced chemical equation for the third dissociation reaction is: $$ \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-} \left( \mathrm{aq} \right) + \mathrm{H}_{2} \mathrm{O} \left( \mathrm{l} \right) \longleftrightarrow \mathrm{H}_{3} \mathrm{O}_{\mathrm{a}}^{+} + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-} \left( \mathrm{aq} \right) $$
07

Third Ka expression

The acid dissociation constant (Ka) expression for the third dissociation step is: $$ K_{a3} = \dfrac{[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}^+][\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}]}{[\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}]} $$ These are the final stepwise dissociation reactions and Ka expressions for citric acid.

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Most popular questions from this chapter

Write the reaction and the corresponding \(K_{\mathrm{b}}\) equilibrium expression for each of the following substances acting as bases in water. a. aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) b. dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\)

One mole of a weak acid HA was dissolved in \(2.0 \mathrm{~L}\) of solution. After the system had come to equilibrium, the concentration of HA was found to be \(0.45 M .\) Calculate \(K_{\mathrm{a}}\) for HA.

The \(\mathrm{pH}\) of a \(0.063 \mathrm{M}\) solution of hypobromous acid (HOBr but usually written \(\mathrm{HBrO}\) ) is 4.95. Calculate \(K_{\mathrm{a}}\).

Calculate the \(\mathrm{pH}\) of a \(0.10 \mathrm{M} \mathrm{CoCl}_{3}\) solution. The \(K_{\mathrm{a}}\) value for \(\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) is \(1.0 \times 10^{-5}\).

Trichloroacetic acid \(\left(\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}\right)\) is a corrosive acid that is used to precipitate proteins. The \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of trichloroacetic acid is the same as the \(\mathrm{pH}\) of a \(0.040 \mathrm{M} \mathrm{HClO}_{4}\) solution. Calculate \(K_{\mathrm{a}}\) for trichloroacetic acid.
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