Skip to main content
Chemistry LibreTexts

16.12: Formation Constants

  • Page ID
    135872
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)

    The following table provides \(K_i\) and \(\beta_i\) values for selected metal–ligand complexes, arranged by the ligand. All values are from Martell, A. E.; Smith, R. M. Critical Stability Constants, Vols. 1–4. Plenum Press: New York, 1976. Unless otherwise stated, values are for 25 oC and zero ionic strength. Those values in brackets are considered less reliable.

    Acetate

    \(\ce{CH3COO-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Mg2+ 1.27
    Ca2+ 1.18
    Ba2+ 1.07
    Mn2+ 1.40
    Fe2+ 1.40
    Co2+ 1.46
    Ni2+ 1.43
    Cu2+ 2.22 1.41
    Ag+ 0.73 –0.09
    Zn2+ 1.57
    Cd2+ 1.93 1.22 –0.89
    Pb2+ 2.68 1.40

    Ammonia

    \(\ce{NH3}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Ag+ 3.31 3.91
    Co2+ (T = 20 °C) 1.99 1.51 0.93 0.64 0.06 –0.73
    Ni2+ 2.72 2.17 1.66 1.12 0.67 –0.03
    Cu2+ 4.04 3.43 2.80 1.48
    Zn2+ 2.21 2.29 2.36 2.03
    Cd2+ 2.55 2.01 1.34 0.84

    Chloride

    \(\ce{Cl-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Cu2+ 0.40
    Fe3+ 1.48 0.65

    Ag+ (\(\mu = 5.0 \text{ M}\))

    3.70 1.92 0.78 –0.3
    Zn2+ 0.43 0.18 –0.11 –0.3
    Cd2+ 1.98 1.62 –0.2 –0.7
    Pb2+ 1.59 0.21 –0.1 –0.3

    Cyanide

    \(\ce{CN-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Fe2+ 35.4 (\(\beta_6\))
    Fe3+ 43.6 (\(\beta_6\))
    Ag+ 20.48 (\(\beta_2\)) 0.92
    Zn2+ 11.07 (\(\beta_2\)) 4.98 3.57
    Cd2+ 6.01 5.11 4.53 2.27
    Hg2+ 17.00 15.75 3.56 2.66
    Ni2+ 30.22 (\(\beta_4\))

    Ethylenediamine

    \(\ce{H2NCH2CH2NH2}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Ni2+ 7.38 6.18 4.11
    Cu2+ 10.48 9.07
    Ag+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 4.700 3.00
    Zn2+ 5.66 4.98 3.25
    Cd2+ 5.41 4.50 2.78

    EDTA

    The chemical structure of EDTA is shown.

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Mg2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 8.79
    Ca2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 10.69
    Ba2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 7.86
    Bi3+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 27.8
    Co2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 16.31
    Ni2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 18.62
    Cu2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 18.80
    Cr3+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) [23.4]
    Fe3+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 25.1
    Ag+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 7.32
    Zn2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 16.50
    Cd2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 16.46
    Hg2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 21.7
    Pb2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 18.04
    Al3+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 16.3

    Fluoride

    \(\ce{F-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Al3+ 6.11 5.01 3.88 3.0 1.4 0.4

    Hydroxide

    \(\ce{OH-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Al3+ 9.01 [9.69] [8.3] 6.0
    Co2+ 4.3 4.1 1.3 0.5
    Fe2+ 4.5 ]2.9] 2,6 –0.4
    Fe3+ 11.81 10.5 12.1
    Ni2+ 4.1 3.9 3.
    Pb2+ 6.3 4.6 3.0
    Zn2+ 5.0 [6.1] 2.5 [1.2]

    Iodide

    \(\ce{I-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Ag+ 6.58 [5.12] [1.4]
    Cd2+ (T = 18 °C) 2.28 1.64 1.08 1.0
    Pb2+ 1.92 1.28 0.7 0.6

    Nitriloacetate

    The chemical structure of nitriloacetate is shown.

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Mg2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 5.41
    Ca2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 6.41
    Ba2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 4.82
    Mn2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 7.44
    Fe2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 8.33
    Co2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 10.38
    Ni2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 11.53
    Cu2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 12.96
    Fe3+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 15.9
    Zn2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 10.67
    Cd2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 9.83
    Pb2+ (T = 20 °C, \(\mu = 0.1 \text{ M}\)) 11.39

    Oxalate

    \(\ce{C2O4^{2-}}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Ca2+ (\(\mu = 1 \text{ M}\)) 1.66 1.03
    Fe2+ (\(\mu = 1 \text{ M}\)) 3.05 2.10
    Co2+ 4.72 2.28
    Ni2+ 5.16
    Cu2+ 6.23 4.04
    Fe3+ (\(\mu = 0.5 \text{ M}\)) 7.53 6.11 4.83
    Zn2+ 4.87 2.78

    1,10-phenanthroline

    The chemical structure of 1,10-phenanthroline is shown.

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Fe2+ 20.7 (\(\beta_3\))
    Mn2+ (\(\mu = 0.1 \text{ M}\)) 4.0 3.3 3.0
    Cu2+ (\(\mu = 0.1 \text{ M}\)) 7.08 6.64 6.08
    Ni2+ 8.6 8.1 7.6
    Fe3+ 13.8 (\(\beta_3\))
    Ag+ (\(\mu = 0.1 \text{ M}\)) 5.02 7.04
    Zn2+ 6.2 [5.9] [5.2]

    Thiosulfate

    \(\ce{S2O3^{2-}}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Ag+ (T = 20 °C) 8.82 4.85 0.53

    Thiocyanate

    \(\ce{SCN-}\)

    log \(K_1\) log \(K_2\) log \(K_3\) log \(K_4\) log \(K_5\) log \(K_6\)
    Mn2+ 1.23
    Fe2+ 1.31
    Co2+ 1.71
    Ni2+ 1.76
    Cu2+ 2.33
    Fe3+ 3.02
    Ag+ 4.8 3.43 1.27 0.2
    Zn2+ 1.33 0.58 0.09 –0.4
    Cd2+ 1.89 0.89 0.02 –0.5
    Hg2+ 17.26 (\(\beta_2\)) 2.71 1.83

    This page titled 16.12: Formation Constants is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey.

    • Was this article helpful?