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 $K_{a}$ reactions for citric acid, a triprotic acid, are as follows: 1. First dissociation reaction: \[ H_{3}C_{6}H_{5}O_{7}(aq) \rightleftharpoons H_{2}C_{6}H_{5}O_{7}^{-}(aq) + H_{3}O^{+}(aq) \] with $K_{a1} = \frac{[H_{2}C_{6}H_{5}O_{7}^{-}][H_{3}O^{+}]}{[H_{3}C_{6}H_{5}O_{7}]}$ 2. Second dissociation reaction: \[ H_{2}C_{6}H_{5}O_{7}^{-}(aq) \rightleftharpoons HC_{6}H_{5}O_{7}^{2-}(aq) + H_{3}O^{+}(aq) \] with $K_{a2} = \frac{[HC_{6}H_{5}O_{7}^{2-}][H_{3}O^{+}]}{[H_{2}C_{6}H_{5}O_{7}^{-}]}$ 3. Third dissociation reaction: \[ HC_{6}H_{5}O_{7}^{2-}(aq) \rightleftharpoons C_{6}H_{5}O_{7}^{3-}(aq) + H_{3}O^{+}(aq) \] with $K_{a3} = \frac{[C_{6}H_{5}O_{7}^{3-}][H_{3}O^{+}]}{[HC_{6}H_{5}O_{7}^{2-}]}$

Step by step solution

01

Write the first dissociation reaction

The first proton is removed from citric acid, forming the first conjugate base and releasing a hydronium ion: \[ H_{3}C_{6}H_{5}O_{7}(aq) \rightleftharpoons H_{2}C_{6}H_{5}O_{7}^{-}(aq) + H_{3}O^{+}(aq) \]
02

Write the second dissociation reaction

The second proton is removed from the first conjugate base, forming the second conjugate base and releasing another hydronium ion: \[ H_{2}C_{6}H_{5}O_{7}^{-}(aq) \rightleftharpoons HC_{6}H_{5}O_{7}^{2-}(aq) + H_{3}O^{+}(aq) \]
03

Write the third dissociation reaction

The third proton is removed from the second conjugate base, forming the third conjugate base and releasing another hydronium ion: \[ HC_{6}H_{5}O_{7}^{2-}(aq) \rightleftharpoons C_{6}H_{5}O_{7}^{3-}(aq) + H_{3}O^{+}(aq) \]
04

Write the Ka expressions for each step

The Ka expressions for each step are as follows: For the first dissociation step: \[ K_{a1} = \frac{[H_{2}C_{6}H_{5}O_{7}^{-}][H_{3}O^{+}]}{[H_{3}C_{6}H_{5}O_{7}]} \] For the second dissociation step: \[ K_{a2} = \frac{[HC_{6}H_{5}O_{7}^{2-}][H_{3}O^{+}]}{[H_{2}C_{6}H_{5}O_{7}^{-}]} \] For the third dissociation step: \[ K_{a3} = \frac{[C_{6}H_{5}O_{7}^{3-}][H_{3}O^{+}]}{[HC_{6}H_{5}O_{7}^{2-}]} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider a \(0.60-M\) solution of \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\), lactic acid \(\left(K_{\mathrm{a}}=\right.\) \(\left.1.4 \times 10^{-4}\right)\) a. Which of the following are major species in the solution? i. \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\) ii. \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) iii. \(\mathrm{H}^{+}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) v. \(\mathrm{OH}^{-}\) b. Complete the following ICE table in terms of \(x\), the amount \((\mathrm{mol} / \mathrm{L})\) of lactic acid that dissociates to reach equilibrium. c. What is the equilibrium concentration for \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) ? d. Calculate the \(\mathrm{pH}\) of the solution.

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 \(0.050-M\) 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.

Codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\right)\) is a derivative of morphine that is used as an analgesic, narcotic, or antitussive. It was once commonly used in cough syrups but is now available only by prescription because of its addictive properties. If the \(\mathrm{pH}\) of a \(1.7 \times 10^{-3}-M\) solution of codeine is \(9.59\), calculate \(K_{\mathrm{b}}\).

Calculate the \(\mathrm{pH}\) and \(\left[\mathrm{S}^{2-}\right]\) in a \(0.10-M \mathrm{H}_{2} \mathrm{~S}\) solution. Assume \(K_{\mathrm{a}_{1}}=1.0 \times 10^{-7} ; K_{\mathrm{a}_{2}}=1.0 \times 10^{-19}\).

An acid HX is \(25 \%\) dissociated in water. If the equilibrium concentration of \(\mathrm{HX}\) is \(0.30 \mathrm{M}\), calculate the \(K_{\mathrm{a}}\) value for \(\mathrm{HX}\).

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free