Question

Write out the stepwise K_a reactions for citric acid (H₃C₆H₅O₇), a triprotic acid.

Short answer

Three K_a values of citric acid (H₃C₆H₅O₇):

${\text{K}}_{\text{a1}}\text{=}\frac{{\text{[H}}^{\text{+}}{\text{][H}}_{\text{2}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{-}}\text{]}}{{\text{[H}}_{\text{3}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_{\text{7}}\text{]}}$

${\text{K}}_{\text{a2}}=\frac{{\text{[H}}^{\text{+}}{\text{][HC}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{2-}}\text{]}}{{\text{[H}}_{\text{2}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{-}}\text{]}}$

${\text{K}}_{{\text{a}}_{\text{3}}}\text{=}\frac{{\text{[H}}^{\text{+}}{\text{][C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{3-}}\text{]}}{{\text{[HC}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{2-}}\text{]}}$

Step-by-step solution

Dissociation of H3C6H5O7

${\text{H}}_3{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_7}_{\left(\mathrm{aq}\right)}\rightleftarrows {{\text{\hspace{0.17em}\hspace{1em}H}}^{\text{+}}}_{\left(\mathrm{aq}\right)}{\text{+\hspace{0.17em}H}}_{\text{2}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_7{{}^{\text{-}}}_{\left(\mathrm{aq}\right)}$

${\text{K}}_{{\text{a}}_{\text{1}}}\text{=}\frac{{\text{[H}}^{\text{+}}{\text{][H}}_{\text{2}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_{\text{7}}}^{\text{-}}\text{]}}{{\text{[H}}_{\text{3}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_{\text{7}}\text{]}}$

Dissociation of H2C6H5O7-

${\text{H}}_{\text{2}}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_7{{}^{\text{-}}}_{\left(\text{aq}\right)}\rightleftarrows {{\text{\hspace{0.17em}\hspace{1em}H}}^{\text{+}}}_{\left(\text{aq}\right)}{\text{+\hspace{0.17em}HC}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_7{{}^{\text{2-}}}_{\text{(aq)}}$

${\text{K}}_{{\mathrm{a}}_2}=\frac{{\text{[H}}^{\text{+}}{\text{][HC}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_7}^{\text{2-}}\text{]}}{{\text{[H}}_2{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_7}^{\text{-}}\text{]}}$

Dissociation of HC6H5O72-

${\text{HC}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_7{{}^{\text{2-}}}_{\text{(aq)}}\rightleftarrows {{\text{\hspace{0.17em}\hspace{1em}H}}^{\text{+}}}_{\left(\text{aq}\right)}{\text{+\hspace{0.17em}C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{O}}_7{{}^{\text{3-}}}_{\left(\text{aq}\right)}$

${\text{K}}_{{}_{\text{a3}}}=\frac{{\text{[H}}^{\text{+}}{\text{][C}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_7}^{\text{3-}}\text{]}}{{\text{[HC}}_{\text{6}}{\text{H}}_{\text{5}}{{\text{O}}_7}^{\text{2-}}\text{]}}$