Name: stepwise ionization of polyprotic acids
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 3 min 38 s
Channel: JoVE

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Polyprotic Acids

Monoprotic acids, like hydrofluoric acid, contain a single ionizable proton. In contrast, polyprotic acids contain two or more ionizable protons. For example, sulfurous acid has two ionizable protons, and phosphoric acid has three.
A polyprotic acid loses each of its protons sequentially, and each reaction has its own Ka.
It is easier to remove a proton from a neutral molecule than a negatively charged one because the negative charge increases the strength of the bond between the proton and the anion.
Therefore, for phosphoric acid, the Ka for the removal of the first proton, Ka1, is higher than the second one, Ka2, which is higher than Ka3.
The pH of a polyprotic acid can be estimated using only the first reaction if Ka1 is at least one thousand times larger than its subsequent Ka&#8217;s.
For example, the pH of a 0.050 molar ascorbic acid solution can be determined using its Ka1 and an ICE table.
When dissolved in water, ascorbic acid dissociates into hydronium and ascorbate ions. The Ka1 for this reaction is 8 &#215; 10&#8722;5, and it is equal to the concentration of hydronium times the concentration of ascorbate monoanion, divided by the concentration of ascorbic acid.
An ICE table can be prepared for this reaction with the initial and equilibrium concentrations. Due to the small value of x, 0.050 minus x is approximately equal to 0.050.
Substituting these values into the expression for Ka1, the value for x is equal to 0.0020 molar, which is only 4% of the initial concentration of ascorbic acid. Thus, the approximation is valid.
The pH of the solution equals 2.70.
The concentration of ascorbate dianion formed in the second step of the reaction can also be calculated using Ka2 and an ICE table.
Ka2 is equal to 1.6 &#215; 10&#8722;12, and it can be expressed as the concentration of hydronium times the concentration of ascorbate dianion divided by the concentration of ascorbate monoanion.
For this reaction, the ICE table is filled in with the initial concentration of ascorbate monoanion and hydronium from the first reaction, 0.002 molar. Due to the small value of x, it can be omitted from the equilibrium concentrations of ascorbate monoanion and hydronium.
After substituting these values in the Ka2 expression and solving, x is 1.6 &#215;10&#8722;12 molar.
Since x is less than 5% of 0.002 molar, the approximation is valid.
As the concentration of hydronium ions that were generated during the second step of ascorbic acid dissociation is negligible, the first ionizable proton determines the pH of the solution.

polyprotic acids

Acids are classified by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO3, and HCN that contain one ionizable hydrogen atom in each molecule are called monoprotic acids. Their reactions with water are:
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Monoprotic acids: Reactions with water</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">HCl (aq) + H2O (l) &#10230; H3O+ (aq) + Cl&#8722; (aq)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">HNO3 (aq) + H2O (l) &#10230; H3O+ (aq) + NO3&#8722; (aq)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">HCN (aq) + H2O (l) &#8652; H3O+ (aq) + CN&#8722; (aq)</td>
		</tr>
	</tbody>
</table>
Even though it contains four hydrogen atoms, acetic acid, CH3CO2H, is also monoprotic because only the hydrogen atom from the carboxyl group (COOH) reacts with bases:
<img alt="Acetic acid ionization reaction equation; chemical equilibrium; acid-base reaction diagram." src="/files/ftp_upload/11405/11405_Figure%201.svg" style="height: 125px;" data-altupdatedat="1754904545000" data-alt="Acetic acid ionization equation; static equilibrium; chemical reaction diagram; proton transfer." />
Similarly, monoprotic bases are bases that will accept a single proton.
Diprotic acids contain two ionizable hydrogen atoms per molecule; ionization of such acids occurs in two steps. The first ionization always takes place to a greater extent than the second ionization. For example, sulfuric acid, a strong acid, ionizes as follows:
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">Diprotic acid: Sulfuric acid (H2SO4)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1st ionization</td>
			<td style="color: black; border: 1px solid black; text-align: center;">H2SO4 (aq) + H2O (l) &#8652; H3O+ (aq) + HSO4&#8722; (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Ka1 = more than 102; complete dissociation</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2nd ionization</td>
			<td style="color: black; border: 1px solid black; text-align: center;">HSO4&#8722; (aq) + H2O (l) &#8652; H3O+ (aq) + SO42&#8722; (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Ka2 = 1.2 &#215; 10&#8722;2</td>
		</tr>
	</tbody>
</table>
This stepwise ionization process occurs for all polyprotic acids. Carbonic acid, H2CO3, is an example of a weak diprotic acid. The first ionization of carbonic acid yields hydronium ions and bicarbonate ions in small amounts.
First ionization: H2CO3 (aq) + H2O (l) &#8652; H3O+ (aq) + HCO3&#8722; (aq)
<img alt="Chemical synthesis process, arrow diagram, organic chemistry, illustrating reaction mechanism steps." src="/files/ftp_upload/11405/11405_Equation_1.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Kirchhoff's circuit laws, schematic diagram showing voltage, current, and resistance symbols." />
The bicarbonate ion can also act as an acid. It ionizes and forms hydronium ions and carbonate ions in even smaller quantities.
Second ionization: HCO3&#8722; (aq) + H2O (l) &#8652; H3O+ (aq) + CO32&#8722; (aq)
<img alt="Free body diagram, static equilibrium equations: &#931;Fx=0, &#931;Fy=0, showing forces on an object." src="/files/ftp_upload/11405/11405_Equation_2.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram, &#931;Fx=0, &#931;Fy=0, beam balancing on supports, forces and moments analysis." />
KH2CO3 is larger than KHCO3&#8722; by a factor of 104, so H2CO3 is the dominant producer of hydronium ion in the solution. This means that little of the HCO3&#8722; formed by the ionization of H2CO3 ionizes to give hydronium ions (and carbonate ions), and the concentrations of H3O+ and HCO3&#8722; are practically equal in a pure aqueous solution of H2CO3.
If the first ionization constant of a weak diprotic acid is larger than the second by a factor of at least 20, it is appropriate to treat the first ionization separately and calculate concentrations resulting from it before calculating concentrations of species resulting from subsequent ionization. This approach is demonstrated in the following example exercise.
Ionization of a Diprotic Acid
&#8220;Carbonated water&#8221; contains a palatable amount of dissolved carbon dioxide. The solution is acidic because CO2 reacts with water to form carbonic acid, H2CO3. What are [H3O+], [HCO3&#8722;], and [CO32&#8722;] in a saturated solution of CO2 with an initial [H2CO3] = 0.033?
<img alt='&#60;span lang="en"&#62;Static equilibrium diagram: beam, forces &#931;F=0, &#931;M=0; shows torque balance, tension analysis.&#60;/span&#62;' src="/files/ftp_upload/11405/11405_Equation_3.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Capacitor circuit diagram, series configuration, three capacitors (C1, C2, C3) with equivalent capacitance." />
As indicated by the ionization constants, H2CO3 is a much stronger acid than HCO3&#8722;, so the stepwise ionization reactions may be treated separately.Using the provided information, an ICE table for this first ionization step is prepared:
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;">H2CO3 (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">H3O+ (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">HCO3&#8722; (aq)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Initial concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.033</td>
			<td style="color: black; border: 1px solid black; text-align: center;">~0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Change (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">&#8722;x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Equilibrium concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.033 &#8722; x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
		</tr>
	</tbody>
</table>
Substituting the equilibrium concentrations into the equilibrium equation gives
<img alt="Biomolecular structure illustration of DNA helix with base pairs; depiction of genetic coding." src="/files/ftp_upload/11405/11405_Equation_4.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Chemical reaction mechanism diagram showing electrophilic addition of hydrogen bromide to propene." />
Assuming x &#60;&#60; 0.033 and solving the simplified equation yields
<img alt="Protein electrophoresis, diagram; technique for protein separation by size and charge, analysis method." src="/files/ftp_upload/11405/11405_Equation_5.png" style="height: 50px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; &#931;Fx=0, MA=0, showing forces, moments, and fulcrum for balance analysis." />
The ICE table defined x as equal to the bicarbonate ion molarity and the hydronium ion molarity:
<img alt="Moment of force calculation with cross product formula: M = r &#215; F, diagram of vectors r and F." src="/files/ftp_upload/11405/11405_Equation_6.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Molecular orbital diagram for carbon dioxide, linear geometry, showing bonding and antibonding orbitals." />
Using the bicarbonate ion concentration computed above, the second ionization is subjected to a similar equilibrium calculation: HCO3&#8722; (aq) + H2O (l) &#8652; H3O+ (aq) + CO32&#8722; (aq)
<img alt="DNA transcription diagram with gene editing symbols, keywords: DNA&#8594;RNA, molecular biology." src="/files/ftp_upload/11405/11405_Equation_7.png" style="height: 180px;" data-altupdatedat="1754904545000" data-alt="Chromatography system diagram; illustrates DNA separation process with column and solvent flow." />
To summarize: at equilibrium [H2CO3] = 0.033 M; [H3O+] = 1.2 &#215; 10&#8722;4; [HCO3&#8722;] = 1.2 &#215; 10&#8722;4 M; and [CO32&#8722;] = 4.7 &#215; 10&#8722;11 M.
A triprotic acid is an acid that has three ionizable H atoms. Phosphoric acid is one example:
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">Triprotic acid: Phosphoric acid (H3PO4)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1st ionization</td>
			<td style="color: black; border: 1px solid black; text-align: center;">H3PO4 (aq) + H2O (l) &#8652; H3O+ (aq) + H2PO4&#8722; (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">Ka1 = 7.5 &#215; 10&#8722;3</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2nd ionization</td>
			<td style="color: black; border: 1px solid black; text-align: center;">H2PO4&#8722; (aq) + H2O (l) &#8652; H3O+ (aq) + HPO42&#8722; (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Ka2 = 6.2 &#215; 10&#8722;8</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">3rd ionization</td>
			<td style="color: black; border: 1px solid black; text-align: center;">HPO42&#8722; (aq) + H2O (l) &#8652; H3O+ (aq) + PO43&#8722; (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Ka3 = 4.2 &#215; 10&#8722;13</td>
		</tr>
	</tbody>
</table>
As for the diprotic acid examples, each successive ionization reaction is less extensive than the former, reflected in decreasing values for the stepwise acid ionization constants. This is a general characteristic of polyprotic acids and successive ionization constants often differ by a factor of about 105 to 106.
This set of three dissociation reactions may appear to make calculations of equilibrium concentrations in a solution of H3PO4 complicated. However, because the successive ionization constants differ by a factor of 105 to 106, large differences exist in the small changes in concentration accompanying the ionization reactions. This allows the use of math-simplifying assumptions and processes, as demonstrated in the examples above. Polyprotic bases are capable of accepting more than one hydrogen ion. The carbonate ion is an example of a diprotic base, because it can accept two protons, as shown below. Similar to the case for polyprotic acids, note the ionization constants decrease with ionization step. Likewise, equilibrium calculations involving polyprotic bases follow the same approaches as those for polyprotic acids.
<img alt="Spectroscopy diagram illustrating light absorption and emission pathways; energy transitions depicted." src="/files/ftp_upload/11405/11405_Equation_8.png" style="height: 90px;" data-altupdatedat="1754904545000" data-alt="Chemical equilibrium reaction formula; dynamic equilibrium diagram; educational chemistry content." />
This text is adapted from<a href="https://openstax.org/books/chemistry-2e/pages/14-5-polyprotic-acids"> Openstax, Chemistry 2e, Section 14.5: Polyprotic Acids</a>.

Acids are classified by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO3, and HCN that contain one ...

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stepwise ionization of polyprotic acids

Polyprotic acids lose hydrogen ions in steps. The number of ionizable protons in a molecule determines whether an acid is monoprotic, diprotic, or triprotic. This video also shows that polyprotic bases can accept more than one proton.

Monoprotic acids have one ionizable hydrogen atom per molecule. Examples include HCl, HNO3, and HCN. Their reactions with water form hydronium ions and the matching anion. Acetic acid, CH3CO2H, is also monoprotic because only the hydrogen in the carboxyl group reacts with bases. Monoprotic bases accept a single proton.

Diprotic acids have two ionizable hydrogen atoms, so they ionize in two steps. The first ionization is greater than the second. Sulfuric acid is a strong example, with complete first dissociation and a much smaller second dissociation. Carbonic acid, H2CO3, is a weak diprotic acid with the same stepwise pattern. Its first ionization forms hydronium and bicarbonate ions, and its second ionization converts bicarbonate into carbonate in even smaller amounts.

For carbonic acid, the first ionization constant is much larger than the second. In a pure aqueous solution of H2CO3, H3O+ and HCO3− are practically equal, while only a tiny amount of CO3 2− forms. When the first ionization constant is at least 20 times larger than the second, the two steps can be treated separately in equilibrium calculations. The example of saturated CO2 in water uses an ICE table for the first step, then a second equilibrium calculation for bicarbonate.

At equilibrium in that example, [H2CO3] is 0.033 M, [H3O+] is 1.2 × 10−4 M, [HCO3−] is 1.2 × 10−4 M, and [CO3 2−] is 4.7 × 10−11 M. This shows why the first ionization dominates the solution. It also shows how stepwise calculations can simplify polyprotic acid problems.

Triprotic acids have three ionizable hydrogen atoms. Phosphoric acid, H3PO4, is one example. Its three ionization steps produce H2PO4−, then HPO4 2−, and finally PO4 3−. Each successive ionization is less extensive than the one before it. The stepwise acid ionization constants decrease, often by a factor of about 10^5 to 10^6.

That large difference in ionization constants makes equilibrium work easier. Even though a triprotic acid has three dissociation reactions, the small concentration changes can still be handled with simplifying assumptions. Polyprotic bases follow the same idea. The carbonate ion is a diprotic base because it can accept two protons, and its ionization constants also decrease with each step.

Stepwise Ionization of Polyprotic Acids

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Polyprotic acids lose hydrogen ions in steps. The number of ionizable protons in a molecule determines whether an acid is monoprotic, diprotic, or triprotic. This video also shows that polyprotic bases can accept more than one proton. Monoprotic acids have one ionizable hydrogen atom per molecule. Examples include HCl, HNO3, and HCN. Their reactions with water form hydronium ions and the matching anion. Acetic acid, CH3CO2H, is also monoprotic because only the hydrogen in the carboxyl group...

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Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

Carry out investigations to compare physical and chemical properties of matter.

PS.PSc.1.3

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

Use models to interpret the data presented in Bohr diagrams and electron dot diagrams for neutral atoms of elements 1 through 18.

PS.PSc.1.4

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

Use models to compare representations of atoms, ions, and isotopes.

PS.PSc.1.5

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

Use the Periodic Table as a model to predict the relative properties (metallic/nonmetallic character, ionic charge, and reactivity) and arrangement of elements based on the pattern of valence electrons in the outermost energy levels of atoms.

PS.PSc.1.6

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Dr&#xFC;de called the ...

Construct an explanation to classify the type of chemical bond that occurs (covalent, ionic, or metallic) in a given substance.

PS.PSc.2.1

Nomenclature of Alkanes

In the late 19th-century, the number of new chemical compounds discovered increased tremendously. Hence, the necessity arose to develop a naming system ...

Nomenclature of Alkenes

The IUPAC naming system for alkenes replaces -an- with -en- in the corresponding parent alkanes. Accordingly, a simple alkene replaces the -ane suffix of ...

Nomenclature of Alkynes

Alkynes are unsaturated hydrocarbons characterized by the presence of carbon-carbon triple bonds and have a general formula CnH2n-2. The nomenclature of ...

structure-and-nomenclature-of-alcohols-and-phenols

Structure and Nomenclature of Alcohols and Phenols

Overview 
Alcohols are one of the most important functional groups in organic chemistry. The name of alcohol comes from the hydrocarbon from which it is ...

Structure and Nomenclature of Ethers

Structure and Bonding
Ethers are organic compounds with an ether functional group which is characterized by an oxygen atom connected to two &#8212; ...

IUPAC Nomenclature of Aldehydes

Aldehydes are named based on the systematic nomenclature rules set by the IUPAC. For acyclic aldehydes, the longest carbon chain containing the aldehydic ...

IUPAC Nomenclature of Ketones

Like aldehydes, ketones are named using IUPAC rules; in this case, by replacing &#8220;e&#8221; in the name of the longest hydrocarbon chain with ...

IUPAC Nomenclature of Carboxylic Acids

IUPAC names of carboxylic acids are systematically derived following a few rules discussed below.
For acyclic saturated monocarboxylic acids, the longest ...

nomenclature-of-aromatic-compounds-with-a-single-substituent

Nomenclature of Aromatic Compounds with a Single Substituent

Benzene is the simplest aromatic hydrocarbon or arene. The IUPAC names for simple monosubstituted benzene derivatives are derived by adding the ...

nomenclature-of-aromatic-compounds-with-multiple-substituents

Nomenclature of Aromatic Compounds with Multiple Substituents

When more than one substituent is present on the benzene ring, the IUPAC nomenclature depends on the number of substituents present.
For disubstituted ...

Use models to apply International Union of Pure and Applied Chemistry (IUPAC) conventions to name and write formulas for simple compounds.

PS.PSc.2.2

Understand types, properties, and structure of matter.

Stepwise Ionization of Polyprotic Acids

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