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Bjerrum plot

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A Bjerrum plot (named after <a href="Niels_Bjerrum" title="Niels Bjerrum">Niels Bjerrum</a>), sometimes also known as a Sillén diagram (after Lars Gunnar Sillén), or a Hägg diagram (after <a href="Gunnar_H%C3%A4gg" title="Gunnar Hägg">Gunnar Hägg</a>)<a href="#cite_note-1">[1]</a> is a <a href="Chart" title="Chart">graph</a> of the <a href="Concentration" title="Concentration">concentrations</a> of the different species of a <a href="Acid#Polyprotic_acids" title="Acid">polyprotic acid</a> in a <a href="Solution_(chemistry)" title="Solution (chemistry)">solution</a>, as a function of <a href="PH" title="PH">pH</a>,<a href="#cite_note-Andersen-2">[2]</a> when the solution is at <a href="Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a>. Due to the many <a href="Orders_of_magnitude" class="mw-redirect" title="Orders of magnitude">orders of magnitude</a> spanned by the concentrations, they are commonly plotted on a <a href="Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a>. Sometimes the ratios of the concentrations are plotted rather than the actual concentrations. Occasionally H+ and OH− are also plotted.

Most often, the carbonate system is plotted, where the polyprotic acid is <a href="Carbonic_acid" title="Carbonic acid">carbonic acid</a> (a <a href="Diprotic_acid" class="mw-redirect" title="Diprotic acid">diprotic acid</a>), and the different species are dissolved <a href="Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a>, <a href="Carbonic_acid" title="Carbonic acid">carbonic acid</a>, <a href="Bicarbonate" title="Bicarbonate">bicarbonate</a>, and <a href="Carbonate" title="Carbonate">carbonate</a>. In acidic conditions, the dominant form is CO2; in <a href="Base_(chemistry)" title="Base (chemistry)">basic</a> (alkaline) conditions, the dominant form is CO2− 3; and in between, the dominant form is HCO− 3. At every pH, the concentration of carbonic acid is assumed to be negligible compared to the concentration of dissolved CO 2, and so is often omitted from Bjerrum plots. These plots are very helpful in solution chemistry and natural water chemistry. In the example given here, it illustrates the response of seawater pH and carbonate speciation due to the input of man-made CO 2 emission by the fossil fuel combustion.<a href="#cite_note-wolfgladrow2007-3">[3]</a>

The Bjerrum plots for other polyprotic acids, including <a href="Silicic_acid" title="Silicic acid">silicic</a>, <a href="Boric_acid" title="Boric acid">boric</a>, <a href="Sulfuric_acid" title="Sulfuric acid">sulfuric</a> and <a href="Phosphoric_acid" title="Phosphoric acid">phosphoric</a> acids, are other commonly used examples.<a href="#cite_note-Andersen-2">[2]</a>

<div class="mw-heading mw-heading2"><h2 id="Bjerrum_plot_equations_for_carbonate_system">Bjerrum plot equations for carbonate system</h2></div>

If <a href="Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a>, <a href="Carbonic_acid" title="Carbonic acid">carbonic acid</a>, <a href="Hydron_(chemistry)" class="mw-redirect" title="Hydron (chemistry)">hydrogen ions</a>, <a href="Bicarbonate" title="Bicarbonate">bicarbonate</a> and <a href="Carbonate" title="Carbonate">carbonate</a> are all dissolved in <a href="Water" title="Water">water</a>, and at <a href="Chemical_equilibrium" title="Chemical equilibrium">chemical equilibrium</a>, their equilibrium <a href="Concentration" title="Concentration">concentrations</a> are often assumed to be given by:

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}[]\left[{\textrm {CO}}_{2}\right]_{\text{eq}}&={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\\[3pt]\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}&={\frac {K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\\[3pt]\left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}&={\frac {K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\end{aligned}}}</annotation>

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</math><img src="./5add9ed036f12c906f0c0d313c8891e0db78d00b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.838ex; width:51.786ex; height:26.843ex;" alt="{\displaystyle {\begin{aligned}[]\left[{\textrm {CO}}_{2}\right]_{\text{eq}}&={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\\[3pt]\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}&={\frac {K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\\[3pt]\left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}&={\frac {K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}},\end{aligned}}}" loading="lazy"></dd></dl>

where the subscript 'eq' denotes that these are equilibrium concentrations, K1 is the <a href="Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> for the reaction CO 2 + H 2O ⇌ H+ + HCO− 3 (i.e. the first <a href="Acid_dissociation_constant" title="Acid dissociation constant">acid dissociation constant</a> for carbonic acid), K2 is the <a href="Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> for the reaction HCO− 3 ⇌ H+ + CO2− 3 (i.e. the second <a href="Acid_dissociation_constant" title="Acid dissociation constant">acid dissociation constant</a> for carbonic acid), and DIC is the (unchanging) total <a href="Concentration" title="Concentration">concentration</a> of <a href="Total_inorganic_carbon" title="Total inorganic carbon">dissolved inorganic carbon</a> in the system, i.e. [CO2] + [HCO− 3] + [CO2− 3]. K1, K2 and DIC each have units of a <a href="Concentration" title="Concentration">concentration</a>, e.g. <a href="Mole_(unit)" title="Mole (unit)">mol</a>/<a href="Litre" title="Litre">L</a>.

A Bjerrum plot is obtained by using these three equations to plot these three species against pH = −log10 [H+]eq, for given K1, K2 and DIC. The fractions in these equations give the three species' relative proportions, and so if DIC is unknown, or the actual concentrations are unimportant, these proportions may be plotted instead.

These three equations show that the curves for CO2 and HCO− 3 intersect at [H+]eq = K1, and the curves for HCO− 3 and CO2− 3 intersect at [H+]eq = K2. Therefore, the values of K1 and K2 that were used to create a given Bjerrum plot can easily be found from that plot, by reading off the concentrations at these points of intersection. An example with linear Y axis is shown in the accompanying graph. The values of K1 and K2, and therefore the curves in the Bjerrum plot, vary substantially with temperature and salinity.<a href="#cite_note-4">[4]</a>

<div class="mw-heading mw-heading2"><h2 id="Chemical_and_mathematical_derivation_of_Bjerrum_plot_equations_for_carbonate_system">Chemical and mathematical derivation of Bjerrum plot equations for carbonate system</h2></div>

Suppose that the reactions between <a href="Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a>, <a href="Hydron_(chemistry)" class="mw-redirect" title="Hydron (chemistry)">hydrogen ions</a>, <a href="Bicarbonate" title="Bicarbonate">bicarbonate</a> and <a href="Carbonate" title="Carbonate">carbonate</a> <a href="Ions" class="mw-redirect" title="Ions">ions</a>, all dissolved in <a href="Water" title="Water">water</a>, are as follows:

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</style><table role="presentation" class="numblk" style="margin-left: 1.6em;"><tbody><tr><td class="nowrap">CO 2 + H 2O ⇌ H+ + HCO− 3</td> <td></td> <td class="nowrap">1</td></tr></tbody></table>

Note that reaction <a href="#math_1">1</a> is actually the combination of two <a href="Elementary_reaction" title="Elementary reaction">elementary reactions</a>:

Assuming the <a href="Mass_action_law" class="mw-redirect" title="Mass action law">mass action law</a> applies to these two reactions, that water is <a href="Abundance_(chemistry)" class="mw-redirect" title="Abundance (chemistry)">abundant</a>, and that the different chemical species are always well-mixed, their <a href="Rate_equation" title="Rate equation">rate equations</a> are

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {{\textrm {d}}\left[{\textrm {CO}}_{2}\right]}{{\textrm {d}}t}}&=-k_{1}\left[{\textrm {CO}}_{2}\right]+k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {H}}^{+}\right]}{{\textrm {d}}t}}&=k_{1}\left[{\textrm {CO}}_{2}\right]-k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right]+k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]-k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {HCO}}_{3}^{-}\right]}{{\textrm {d}}t}}&=k_{1}\left[{\textrm {CO}}_{2}\right]-k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right]-k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]+k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {CO}}_{3}^{2-}\right]}{{\textrm {d}}t}}&=k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]-k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right]\end{aligned}}}</annotation>

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</math><img src="./c1442fcc0083a438f6687e70dc8943f3952234c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.005ex; width:79.88ex; height:25.009ex;" alt="{\displaystyle {\begin{aligned}{\frac {{\textrm {d}}\left[{\textrm {CO}}_{2}\right]}{{\textrm {d}}t}}&=-k_{1}\left[{\textrm {CO}}_{2}\right]+k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {H}}^{+}\right]}{{\textrm {d}}t}}&=k_{1}\left[{\textrm {CO}}_{2}\right]-k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right]+k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]-k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {HCO}}_{3}^{-}\right]}{{\textrm {d}}t}}&=k_{1}\left[{\textrm {CO}}_{2}\right]-k_{-1}\left[{\textrm {H}}^{+}\right]\left[{\textrm {HCO}}_{3}^{-}\right]-k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]+k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right],\\{\frac {{\textrm {d}}\left[{\textrm {CO}}_{3}^{2-}\right]}{{\textrm {d}}t}}&=k_{2}\left[{\textrm {HCO}}_{3}^{-}\right]-k_{-2}\left[{\textrm {H}}^{+}\right]\left[{\textrm {CO}}_{3}^{2-}\right]\end{aligned}}}" loading="lazy"></dd></dl>

where [ ] denotes <a href="Concentration" title="Concentration">concentration</a>, t is time, and K1 and k−1 are appropriate <a href="Proportionality_(mathematics)" title="Proportionality (mathematics)">proportionality</a> constants for reaction <a href="#math_1">1</a>, called respectively the forwards and reverse <a href="Reaction_rate_constant" title="Reaction rate constant">rate constants</a> for this reaction. (Similarly K2 and k−2 for reaction <a href="#math_2">2</a>.)

At any equilibrium, the concentrations are unchanging, hence the left hand sides of these equations are zero. Then, from the first of these four equations, the ratio of reaction <a href="#math_1">1</a>'s rate constants equals the ratio of its equilibrium concentrations, and this ratio, called K1, is called the <a href="Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> for reaction <a href="#math_1">1</a>, i.e.

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<annotation encoding="application/x-tex">{\displaystyle K_{1}={\frac {k_{1}}{k_{-1}}}={\frac {[{\textrm {H}}^{+}]_{\text{eq}}[{\textrm {HCO}}_{3}^{-}]_{\text{eq}}}{[{\textrm {CO}}_{2}]_{\text{eq}}}}}</annotation>

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</math><img src="./69c301ab3a171a441322b64efdcace69f4df6935.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:30.682ex; height:6.843ex;" alt="{\displaystyle K_{1}={\frac {k_{1}}{k_{-1}}}={\frac {[{\textrm {H}}^{+}]_{\text{eq}}[{\textrm {HCO}}_{3}^{-}]_{\text{eq}}}{[{\textrm {CO}}_{2}]_{\text{eq}}}}}" loading="lazy"></td> <td></td> <td class="nowrap">3</td></tr></tbody></table>

where the subscript 'eq' denotes that these are equilibrium concentrations.

Similarly, from the fourth equation for the <a href="Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> K2 for reaction <a href="#math_2">2</a>,

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<annotation encoding="application/x-tex">{\displaystyle K_{2}={\frac {k_{2}}{k_{-2}}}={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}\left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}}{\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}}}}</annotation>

</semantics>

</math><img src="./6ff6c9f84badea89a7aa2da977c83c67c089c190.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:31.053ex; height:8.343ex;" alt="{\displaystyle K_{2}={\frac {k_{2}}{k_{-2}}}={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}\left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}}{\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}}}}" loading="lazy"></td> <td></td> <td class="nowrap">4</td></tr></tbody></table>

Rearranging <a href="#math_3">3</a> gives

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<annotation encoding="application/x-tex">{\displaystyle \left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}={\frac {K_{1}\left[{\textrm {CO}}_{2}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}}</annotation>

</semantics>

</math><img src="./41aae30e778a3799a81429d28e8056bcc9dbb70a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:25.136ex; height:7.676ex;" alt="{\displaystyle \left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}={\frac {K_{1}\left[{\textrm {CO}}_{2}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}}" loading="lazy">        </td> <td></td> <td class="nowrap">5</td></tr></tbody></table>

and rearranging <a href="#math_4">4</a>, then substituting in <a href="#math_5">5</a>, gives

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<annotation encoding="application/x-tex">{\displaystyle \left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}={\frac {K_{2}\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}={\frac {K_{1}K_{2}\left[{\textrm {CO}}_{2}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}}</annotation>

</semantics>

</math><img src="./1aadffeab48abc57051954b43d1a7f93f7b9db92.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:44.714ex; height:8.676ex;" alt="{\displaystyle \left[{\textrm {CO}}_{3}^{2-}\right]_{\text{eq}}={\frac {K_{2}\left[{\textrm {HCO}}_{3}^{-}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}={\frac {K_{1}K_{2}\left[{\textrm {CO}}_{2}\right]_{\text{eq}}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}}" loading="lazy">        </td> <td></td> <td class="nowrap">6</td></tr></tbody></table>

The total <a href="Concentration" title="Concentration">concentration</a> of <a href="Total_inorganic_carbon" title="Total inorganic carbon">dissolved inorganic carbon</a> in the system is given by substituting in <a href="#math_5">5</a> and <a href="#math_6">6</a>:

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\textrm {DIC}}&=\left[{\textrm {CO}}_{2}\right]+\left[{\textrm {HCO}}_{3}^{-}\right]+\left[{\textrm {CO}}_{3}^{2-}\right]\\&=\left[{\textrm {CO}}_{2}\right]_{\text{eq}}\left(1+{\frac {K_{1}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}+{\frac {K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}\right)\\&=\left[{\textrm {CO}}_{2}\right]_{\text{eq}}\left({\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}\right)\end{aligned}}}</annotation>

</semantics>

</math><img src="./0dc88df668fddf6b88c748bdca159ef65c6ce956.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -10.338ex; width:49.907ex; height:21.843ex;" alt="{\displaystyle {\begin{aligned}{\textrm {DIC}}&=\left[{\textrm {CO}}_{2}\right]+\left[{\textrm {HCO}}_{3}^{-}\right]+\left[{\textrm {CO}}_{3}^{2-}\right]\\&=\left[{\textrm {CO}}_{2}\right]_{\text{eq}}\left(1+{\frac {K_{1}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}}}+{\frac {K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}\right)\\&=\left[{\textrm {CO}}_{2}\right]_{\text{eq}}\left({\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}}\right)\end{aligned}}}" loading="lazy"></dd></dl>

Re-arranging this gives the equation for CO 2:

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<annotation encoding="application/x-tex">{\displaystyle \left[{\textrm {CO}}_{2}\right]_{\text{eq}}={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}}}</annotation>

</semantics>

</math><img src="./34824e22e8fecb8cea2ecfbf0d2e7f1f2379d9df.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:47.542ex; height:9.176ex;" alt="{\displaystyle \left[{\textrm {CO}}_{2}\right]_{\text{eq}}={\frac {\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}}{\left[{\textrm {H}}^{+}\right]_{\text{eq}}^{2}+K_{1}\left[{\textrm {H}}^{+}\right]_{\text{eq}}+K_{1}K_{2}}}\times {\textrm {DIC}}}" loading="lazy"></dd></dl>

The equations for HCO− 3 and CO2− 3 are obtained by substituting this into <a href="#math_5">5</a> and <a href="#math_6">6</a>.

<ul><li><a href="Charlot_equation" title="Charlot equation">Charlot equation</a></li>

<li><a href="Gran_plot" title="Gran plot">Gran plot</a> (also known as Gran titration or the Gran method)</li>

<li><a href="Henderson%E2%80%93Hasselbalch_equation" title="Henderson–Hasselbalch equation">Henderson–Hasselbalch equation</a></li>

<li><a href="Hill_equation_(biochemistry)" title="Hill equation (biochemistry)">Hill equation (biochemistry)</a></li>

<li><a href="Ion_speciation" title="Ion speciation">Ion speciation</a></li>

<li><a href="Fresh_water" title="Fresh water">Fresh water</a></li>

<li><a href="Seawater" title="Seawater">Seawater</a></li>

<li><a href="Thermohaline_circulation" title="Thermohaline circulation">Thermohaline circulation</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFTogni2022" class="citation journal cs1">Togni, Antonio (2022-05-25). <a rel="nofollow" class="external text" href="https://chimia.ch/chimia/article/view/2022_481">"Teaching Acid-Base Equilibria by Using Log-log Diagrams: Chemical Education"</a>. CHIMIA. 76 (5): 481. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2533%2Fchimia.2022.481">10.2533/chimia.2022.481</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/20.500.11850%2F557050">20.500.11850/557050</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2673-2424">2673-2424</a>.</cite>

</li>

<li id="cite_note-Andersen-2">^ <a href="#cite_ref-Andersen_2-0">a</a> <a href="#cite_ref-Andersen_2-1">b</a> <cite id="CITEREFAndersen2002" class="citation journal cs1">Andersen, C. B. (2002). "Understanding carbonate equilibria by measuring alkalinity in experimental and natural systems". Journal of Geoscience Education. 50 (4): 389–403. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002JGeEd..50..389A">2002JGeEd..50..389A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5408%2F1089-9995-50.4.389">10.5408/1089-9995-50.4.389</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17094010">17094010</a>.</cite>

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<li id="cite_note-wolfgladrow2007-3"><a href="#cite_ref-wolfgladrow2007_3-0">^</a> <cite id="CITEREFD.A._Wolf-Gladrow2007" class="citation journal cs1">D.A. Wolf-Gladrow (2007). <a rel="nofollow" class="external text" href="http://www.soest.hawaii.edu/oceanography/faculty/zeebe_files/Publications/WolfGladrowMarChem07.pdf">"Total alkalinity: the explicit conservative expression and its application to biogeochemical processes"</a> (PDF). Marine Chemistry. 106 (1): 287–300. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007MarCh.106..287W">2007MarCh.106..287W</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.marchem.2007.01.006">10.1016/j.marchem.2007.01.006</a>.</cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> Mook W (2000) Chemistry of carbonic acid in water. In 'Environmental Isotopes in the Hydrological Cycle: Principles and Applications' pp. 143-165. (INEA / UNESCO: Paris). <a rel="nofollow" class="external autonumber" href="http://www-naweb.iaea.org/napc/ih/documents/global_cycle/vol%20I/cht_i_09.pdf">[1]</a> Retrieved 30 November 2013.

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