Skip to main content
Chemistry LibreTexts

16.3: Equilibrium Constants for Acids and Bases

  • Page ID
    60742
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Introduction

    In general chemistry 1 we calculated the pH of strong acids and bases by considering them to completely dissociate, that is, undergo 100% ionization. We will now look at weak acids and bases, which do not completely dissociate, and use equilibrium constants to calculate equilibrium concentrations. We could solve all these problems using the techniques from the last chapter on equilbria, but instead we are going to develop short cut techniques, and identify when they are valid. But first, we need to define what are equilibrium constants for acid base reactions.

    Weak Acids

    \[HA(aq)+H_2O(l)⇌H_3O^+(aq)+A^-(aq)\]

    At first glance this gives an equilibrium constant of

    \[K=\frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}\]

    But we can consider the water concentration constant because it is much greater than of acid that has ionized. There are two factors at work here, first that the water is the solvent and so [H2O] is larger than [HA], and second, that [HA] is a weak acid, and so at equilibrium the amount ionized is smaller than [HA]. It should be noted that this is a homogenous equlibria, and although we are ignoring the water and treating it as a liquid, it is for a different reason than was used in the last chapter for heterogeneous equilibria.

    This results in Acid Dissociation Constant (Ka) for aqueous systems:

    \[K_{a}=\frac{[H_{3}O^{+}][A^{-}]}{[HA]}\]

    where, \(K_a=K[H_2O]\)

    Ka is only used for weak acids. Strong acids have a large Ka and completely dissociate and so you just state the reaction goes to completion.

    Weak Bases

    There are two types of weak bases, those as modeled by ammonia and amines, which grab a proton from water, and the conjugate bases of weak acids, which are ions, and grab the proton to form the weak acid.

    Type 1:

    \[B(aq) + H_2O(l) ⇌ HB^+(aq) + OH^-(aq)\]

    Note, in this reaction the base removes a proton from the water and following the same logic for weak acids, we consider the water concentration to stay constant because only a small fraction of it reacts with the weak base, so:

    \[K_b=\frac{[HB^+][OH^-]}{[B]}\]

    An example of the first type would be that of methyl amine, CH3NH2.

    \[CH_3NH_2(aq) + H_2O(l) ⇌CH_3NH_3^+(aq)+OH^- (aq) \\ \\ K=\frac{[CH_3NH_3^+][OH^-]}{[CH_3NH_2]} = 5.0x10^{-4}\]

    Type 2:

    \[A^-(aq) + H_2O(l) ⇌ HA(aq) + OH^-(aq)\]

    \[K'_b=\frac{[HA][OH^-]}{[A^-]} \\ \text{ where} \; K_b \; \text{is the basic equilibrium constant of the conjugate base} \; A^- \; \text{of the weak acid HA}\]

    Acid Base Conjugate Pairs

    We will use K(a or b) to represent the acid or base equilibrium constant and K'(b or a) to represent the equilibrium constant of the conjugate pair.

    For an Acid Base Conjugate Pair

    \[\large K_aK_{b'}=K_w\]

    Consider the generic acid HA which has the reaction and equilibrium constant of

    \[HA(aq)+H_2O(l)⇌H_3O^+(aq)+A^-(aq), \; K_{a}=\frac{[H_{3}O^{+}][A^{-}]}{[HA]}\]

    its conjugate base A- has the reaction and equilibrium constant of:

    \[A^-(aq) + H_2O(l) ⇌ HA(aq) + OH^-(aq), K'_b=\frac{[HA][OH^-]}{[A^-]}\]

    \[K_aK'_{b}=\left ( \frac{[H_{3}O^{+}] \textcolor{red}{\cancel{[A^{-}]}}}{ \textcolor{blue}{\cancel{[HA]}}}\right )\left (\frac{ \textcolor{blue}{\cancel{[HA]}}[OH^-]}{ \textcolor{red}{\cancel{[A^-]}}} \right )=[H_{3}O^{+}][OH^-]=K_w=10^{-14}\]

    So there is an inverse relationship across the conjugate pair

    • The Stronger an Acid the Weaker it's Conjugate Base
    • The Weaker an Acid the Stronger it's Conjugate Base
    • The Stronger the Base the Weaker it's Conjugate Acid
    • The Weaker the Base the Stronger it's Conjugate Acid

    <div data-mt-source="1"><img  alt="" style="width: 1300px; height: 450px;" data-cke-saved-src="http://chemwiki.ucdavis.edu/@api/deki/files/65684/CNX_Chem_14_03_strengths.jpg" src="http://chemwiki.ucdavis.edu/@api/deki/files/65684/CNX_Chem_14_03_strengths.jpg"></div>

    Figure\(\PageIndex{1}\): Relationship between acid or base strength and that of their conjugate base or acid.

    Ka and Kb Values for PolyProtic Acids

    PolyProtic Acids

    It is always harder to remove a second proton from an acid because you are removing it from a negative charged species, and even harder to remove the third, as you are removing it from a dianion.

    Consider a triprotic acid

    \[H_3A + H_2O ⇌H_2A^- +H_3O^+ \; \; K_{a1}\]
    \[H_2A^- + H_2O ⇌HA^{-2} +H_3O^+ \; \; K_{a2}\]
    \[HA^{2}- + H_2O ⇌A^{-3} +H_3O^+ \; \; K_{a3}\]

    \[K_{a1}>K_{a2}>K_{a3}\]

    pKa and pKb

    Because pKa and pKb values are so small they are often recorded a pX values, where pX= -logX. So

    pKa = -logKa and Ka =10-pka
    pKb = -logKb and Kb =10-pkb

    Table of Ka

    Table \(\PageIndex{1}\): Table of Acid Ionization Constants

    Name Formula Conjugate Base K a1 pKa1 K a2 pKa2 K a3 pKa3 K a4 pKa4
    Acetic acid CH3CO2H CH3CO2- 1.75 × 10−5 4.756            
    Arsenic acid H3AsO4 H2AsO4- 5.5 × 10−3 2.26 1.7 × 10−7 6.76 5.1 × 10−12 11.29    
    Benzoic acid C6H5CO2H C6H5CO2- 6.25 × 10−5 4.204            
    Boric acid H3BO3 H2BO3- 5.4 × 10−10* 9.27* >1 × 10−14* >14*        
    Bromoacetic acid CH2BrCO2H CH2BrCO2- 1.3 × 10−3 2.90            
    Carbonic acid H2CO3 HCO3- 4.5 × 10−7 6.35 4.7 × 10−11 10.33        
    Chloroacetic acid CH2ClCO2H CH2ClCO2- 1.3 × 10−3 2.87            
    Chlorous acid HClO2 ClO2- 1.1 × 10−2 1.94            
    Chromic acid H2CrO4 HCrO4- 1.8 × 10−1 0.74 3.2 × 10−7 6.49        
    Citric acid C6H8O7 C6H7O7- 7.4 × 10−4 3.13 1.7 × 10−5 4.76 4.0 × 10−7 6.40    
    Cyanic acid HCNO HCNO- 3.5 × 10−4 3.46            
    Dichloroacetic acid CHCl2CO2H CHCl2CO2- 4.5 × 10−2 1.35            
    Fluoroacetic acid CH2FCO2H CH2FCO2- 2.6 × 10−3 2.59            
    Formic acid CH2O2 CHO2- 1.8 × 10−4 3.75            
    Hydrazoic acid HN3 N3- 2.5 × 10−5 4.6            
    Hydrocyanic acid HCN CN- 6.2 × 10−10 9.21            
    Hydrofluoric acid HF F- 6.3 × 10−4 3.20            
    Hydrogen selenide H2Se HSe- 1.3 × 10−4 3.89 1.0× 10−11 11.0        
    Hydrogen sulfide H2S HS- 8.9 × 10−8 7.05 1 × 10−19 19        
    Hydrogen telluride H2Te HTe- 2.5 × 10−3‡ 2.6 1 × 10−11 11        
    Hypobromous acid HBrO BrO- 2.8 × 10−9 8.55            
    Hypochlorous acid HClO ClO- 4.0 × 10−8 7.40            
    Hypoiodous acid HIO IO- 3.2 × 10−11 10.5            
    Iodic acid HIO3 IO3- 1.7 × 10−1 0.78            
    Iodoacetic acid CH2ICO2H CH2ICO2- 6.6 × 10−4 3.18            
    Nitrous acid HNO2 NO2- 5.6 × 10−4 3.25            
    Oxalic acid C2H2O4 C2HO4- 5.6 × 10−2 1.25 1.5 × 10−4 3.81        
    Periodic acid HIO4 IO4- 2.3 × 10−2 1.64            
    Phenol C6H5OH C6H5O- 1.0 × 10−10 9.99            
    Phosphoric acid H3PO4 H2PO4- 6.9 × 10−3 2.16 6.2 × 10−8 7.21 4.8 × 10−13 12.32    
    Phosphorous acid H3PO3 H2PO3- 5.0 × 10−2* 1.3* 2.0 × 10−7* 6.70*        
    Pyrophosphoric acid H4P2O7 H3P2O7- 1.2 × 10−1 0.91 7.9 × 10−3 2.10 2.0 × 10−7 6.70 4.8 × 10−10 9.32
    Resorcinol C6H4(OH)2 C6H4O2H- 4.8 × 10−10 9.32 7.9 × 10−12 11.1        
    Selenic acid H2SeO4 HSeO4- Strong Strong 2.0 × 10−2 1.7        
    Selenious acid H2SeO3 HSeO3- 2.4 × 10−3 2.62 4.8 × 10−9 8.32        
    Sulfuric acid H2SO4 HSO4- Strong Strong 1.0 × 10−2 1.99        
    Sulfurous acid H2SO3 HSO3- 1.4 × 10−2 1.85 6.3 × 10−8 7.2        
    meso-Tartaric acid C4H6O6 C4H5O6- 6.8 × 10−4 3.17 1.2 × 10−5 4.91        
    Telluric acid H2TeO4 HTeO4- 2.1 × 10−8‡ 7.68 1.0 × 10−11‡ 11.0        
    Tellurous acid H2TeO3 HTeO3- 5.4 × 10−7 6.27 3.7 × 10−9 8.43        
    Trichloroacetic acid CCl3CO2H CCl3CO2- 2.2 × 10−1 0.66            
    Trifluoroacetic acid CF3CO2H CF3CO2- 3.0 × 10−1 0.52            
    * Measured at 20°C, not 25°C.
    ‡ Measured at 18°C, not 25°C.

    Table of Kb

    Table\(\PageIndex{2}\): Base Ionization Constants

    Name Formula   \(K_b\) \(pK_b\)
    Ammonia NH3 NH4+ 1.8 × 10−5 4.75
    Aniline C6H5NH2 C6H5NH3+ 7.4 × 10−10 9.13
    n-Butylamine C4H9NH2 C4H9NH3+ 4.0 × 10−4 3.40
    sec-Butylamine (CH3)2CHCH2NH2 (CH3)2CHCH2H3+ 3.6 × 10−4 3.44
    tert-Butylamine (CH3)3CNH2 (CH3)3CH3+ 4.8 × 10−4 3.32
    Dimethylamine (CH3)2NH (CH3)2H2+ 5.4 × 10−4 3.27
    Ethylamine C2H5NH2 C2H5NH3+ 4.5 × 10−4 3.35
    Hydrazine N2H4 N2H5+ 1.3 × 10−6 5.9
    Hydroxylamine NH2OH NH3OH+ 8.7 × 10−9 8.06
    Methylamine CH3NH2 CH3NH3+ 4.6 × 10−4 3.34
    Propylamine C3H7NH2 C3H7NH3+ 3.5 × 10−4 3.46
    Pyridine C5H5N C5H6N+ 1.7 × 10−9 8.77
    Trimethylamine (CH3)3N (CH3)3NH+ 6.3 × 10−5 4.20

    Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to:

     


    This page titled 16.3: Equilibrium Constants for Acids and Bases is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Robert Belford.

    • Was this article helpful?