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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 (H鈧僌鈦�) 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

A \(0.15 M\) solution of a weak acid is \(3.0 \%\) dissociated. Calculate \(K_{\mathrm{a}} .\)

Differentiate between the terms strength and concentration as they apply to acids and bases. When is HCl strong? Weak? Concentrated? Dilute? Answer the same questions for ammonia. Is the conjugate base of a weak acid a strong base?

Calculate \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) for each solution at \(25^{\circ} \mathrm{C}\). Identify each solution as neutral, acidic, or basic. a. \(\mathrm{pH}=7.40\) (the normal \(\mathrm{pH}\) of blood) b. \(\mathrm{pH}=15.3\) c. \(\mathrm{pH}=-1.0\) d. \(\mathrm{pH}=3.20\) e. \(\mathrm{pOH}=5.0\) f. \(\mathrm{pOH}=9.60\)

Calculate the \(\mathrm{pH}\) of the following solutions. a. \(0.10 \mathrm{M} \mathrm{NaOH}\) b. \(1.0 \times 10^{-10} \mathrm{M} \mathrm{NaOH}\) c. \(2.0 \mathrm{M} \mathrm{NaOH}\)

Sodium azide \(\left(\mathrm{NaN}_{3}\right)\) is sometimes added to water to kill bacteria. Calculate the concentration of all species in a \(0.010 \mathrm{M}\) solution of \(\mathrm{NaN}_{3}\). The \(K_{\mathrm{a}}\) value for hydrazoic acid \(\left(\mathrm{HN}_{3}\right)\) is \(1.9 \times 10^{-5}\)
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