# 8.12: Arrhenius Acids and Bases: Using Solution Equations to Classify Solutes as Arrhenius Acids or Arrhenius Bases

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

Learning Objectives
• Write a solution equation that represents the electrolyte behavior of a solute.
• Use a solution equation to classify a solute as an Arrhenius acid or an Arrhenius base.
• Define salt.

Sections 8.8, 8.9, and 8.11 presented and applied three patterns that were used to write the chemical formulas and names of hydrohalogenated, "HX," and polyatomic, "HNPoly," Arrhenius acids and metal hydroxide, "M(OH)Y," Arrhenius bases, respectively.  Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ion, OH–1, donor in water.  However, these patterns were developed solely based on the ion symbols, H+1 and OH–1, that are referenced in the definitions of Arrhenius acids and bases, respectively, and do not address the defined requirement that these ions be donated in water.  Therefore, while the chemical formulas that were developed from these patterns contain the types of ions that must be present in Arrhenius acids and bases, since the dissociative behaviors of the corresponding molecules were not analyzed, these compounds cannot be definitively classified as Arrhenius acids or bases.  Because the complete definitions of Arrhenius acids and bases were not utilized to develop the "HX," "HNPoly," and "M(OH)Y" patterns, applying these symbolisms to classify a particular chemical as an Arrhenius acid or an Arrhenius base is a "shortcut."  Furthermore, since using a "shortcut" to analyze information occasionally generates misleading or erroneous results, as exemplified by the "Group A/B valence electron" and the "Reverse Criss-Cross Method" "shortcuts" that were presented in Sections 2.7 and 3.10, respectively, any acid/base classification that results from comparing these patterns to a particular chemical formula must be independently-verified through an alternative process, in order to be accepted by the scientific community.

Based on the criteria that are described in the previous paragraph, both the types of ions that are present in a compound and the dissociative behavior of that compound in an aqueous solution must be analyzed, in order to classify a substance as an Arrhenius acid or an Arrhenius base.  Recall that the solution equations that were presented in Chapter 7 are, by definition, symbolic representations of the dissociative behaviors of solutes.  Therefore, in order to definitively classify a chemical as an Arrhenius acid or an Arrhenius base through a scientifically-sound, verifiable process, the solution equation for a particular chemical must be written, and the generated symbolic information must then be compared to the chemical and behavioral criteria that are established in the definitions of Arrhenius acids and Arrhenius bases.

For example, use a solution equation to classify HNO3, which exhibits the characteristics of a strong electrolyte when dissolved in water, as an Arrhenius acid or an Arrhenius base.

Because the given chemical formula, HNO3, contains one hydrogen and a nitrate ion, NO3–1, which is a polyatomic anion, the corresponding molecule can be classified as a polyatomic, or "HNPoly," Arrhenius acid.  However, because the "HNPoly" pattern is a "shortcut," in order to definitively classify HNO3 as an Arrhenius acid, a solution equation for this chemical must be written, and the generated symbolic information must be compared to the chemical and behavioral criteria that are established in the definition of an Arrhenius acid.

In order to apply the strong electrolyte solution equation pattern that was presented in Section 7.6, each substance that is referenced in the given statement must first be classified as a solute or a solvent.  Because the indicator word "in" is present in the given statement, the chemical that is mentioned after this word, water, H2O, is the solvent in this solution, and the remaining substance, HNO3, is the solute, "by default."

A "forward," or left-to-right, arrow is utilized in the solution equation for a strong electrolyte, the chemical formula of the solvent, water, H2O, is written over this arrow, and the chemical formula of the solute, HNO3, is written on the left side of the arrow.  Because a strong electrolyte completely dissociates into its constituent cations and anions as it dissolves, the ion symbol for each of these particles is written on the right side of the arrow.  The anionic component of HNO3 is the nitrate ion, NO31, which is a polyatomic anion.  The remaining element that is present in the given solute, hydrogen, H, does not typically ionize.  However, because the given statement explicitly indicates that HNO3 exhibits the characteristics of a strong electrolyte, which must, by definition, dissociate into cations and anions during the solvation process, the hydrogen that is present in HNO3 must ionize to form a cation, H+1.  Finally, in order to indicate that the cation and anion are unique particles, a plus sign is used to separate their symbols.  The information that is described in this paragraph is reflected in the solution equation that is shown below.

___ $$\ce{HNO_3}$$ $$\overset{\ce{H_2O}}{\longrightarrow}$$ ___ $$\ce{H^{+1}}$$ + ___ $$\ce{NO_3^{–1}}$$

Since the left and right sides of this solution equation contain equal amounts of hydrogen ions, H+1, and nitrate ions, NO31, the solution equation that is shown above is balanced and, therefore, is the chemically-correct representation of the dissociation of HNO3 in water.

Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ionOH1, donor in water.  Therefore, in order to be classified as an Arrhenius acid, both the types of ions that are present in the given soluteHNO3and the dissociative behavior of HNO3 in an aqueous solution must be analyzed.

• Because an Arrhenius acid must be dissolved in an aqueous solution, water must be the solvent that is used to prepare an Arrhenius solution.  As stated above, the chemical formula of the solvent must be written over the arrow in a solution equation.  Therefore, because "H2O," the chemical formula of water, occupies this position in the solution equation that is shown above, the requirement that an Arrhenius acid be dissolved in an aqueous solution is satisfied.
• Additionally, an Arrhenius chemical must donate, or produce, a particular type of ion.  Therefore, a solute can only be classified as an Arrhenius acid if a proton, H+1, is written on the right, or product, side of the arrow in a solution equation.  Because a hydrogen ion, H+1, is present on the right side of the solution equation that is shown above, a proton is produced, or donated, during the dissociation of HNO3.

Based on the analysis that is described in the previous paragraphs, the indicated solute, HNO3, can be definitively classified as an Arrhenius acid.  This definition-driven assignment aligns with the "shortcut" conclusion that was established above.

Exercise $$\PageIndex{1}$$

Use a solution equation to classify Fe(OH)2, which exhibits the characteristics of a weak electrolyte when dissolved in water, as an Arrhenius acid or an Arrhenius base.

Because the given chemical formula, Fe(OH)2, contains iron, Fe, which is a metal, and two hydroxide ions, OH–1, the corresponding molecule is a metal hydroxide, M(OH)Y, and, therefore, can be classified as an Arrhenius base.  However, because the "M(OH)Y" pattern is a "shortcut," in order to definitively classify Fe(OH)2 as an Arrhenius base, a solution equation for this chemical must be written, and the generated symbolic information must be compared to the chemical and behavioral criteria that are established in the definition of an Arrhenius base.

In order to apply the weak electrolyte solution equation pattern that was presented in Section 7.7, each substance that is referenced in the given statement must first be classified as a solute or a solvent.  Because the indicator word "in" is present in the given statement, the chemical that is mentioned after this word, water, H2O, is the solvent in this solution, and the remaining substance, Fe(OH)2, is the solute, "by default."

An equilibrium arrow is utilized in the solution equation for a weak electrolyte, the chemical formula of the solvent, water, H2O, is written over this arrow, and the chemical formula of the solute, Fe(OH)2, is written on the left side of the arrow.  Because a weak electrolyte partially dissociates into its constituent cations and anions as it dissolves, the ion symbol for each of these particles is written on the right side of the arrow.  The cationic component of Fe(OH)2 is the iron (II) ion, Fe+2, which is a transition metal cation, and the anionic component of this solute is the hydroxide ion, OH1, which is a polyatomic anion.  Finally, in order to indicate that the cation and anion are unique particles, a plus sign is used to separate their symbols.  The information that is described in this paragraph is reflected in the unbalanced solution equation that is shown below.

___ $$\ce{Fe(OH)_2}$$ $$\overset{\ce{H_2O}}{\longrightleftharpoons}$$ ___ $$\ce{Fe^{+2}}$$ + ___ $$\ce{OH^{–1}}$$

Since the left and right sides of this solution equation contain equal amounts of iron (II) ions, Fe+2, that ion is balanced.  However, the hydroxide ion, OH1, is not balanced, and, therefore, a coefficient of 2 should be written in the "blank" that corresponds to this ion on the right side of the arrow, as shown below.  Because all of the components in the following solution equation are balanced, this equation is the chemically-correct representation of the dissociation of Fe(OH)2 in water.

___ $$\ce{Fe(OH)_2}$$ $$\overset{\ce{H_2O}}{\longrightleftharpoons}$$ ___ $$\ce{Fe^{+2}}$$ + 2 $$\ce{OH^{–1}}$$

Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ionOH1, donor in water.  Therefore, in order to be classified as an Arrhenius base, both the types of ions that are present in the given soluteFe(OH)2and the dissociative behavior of Fe(OH)2 in an aqueous solution must be analyzed.
• Because an Arrhenius base must be dissolved in an aqueous solution, water must be the solvent that is used to prepare an Arrhenius solution.  As stated above, the chemical formula of the solvent must be written over the arrow in a solution equation.  Therefore, because "H2O," the chemical formula of water, occupies this position in the solution equation that is shown above, the requirement that an Arrhenius base be dissolved in an aqueous solution is satisfied.
• Additionally, an Arrhenius chemical must donate, or produce, a particular type of ion.  Therefore, a solute can only be classified as an Arrhenius base if a hydroxide ionOH1, is symbolized on the right, or product, side of a solution equation arrow.  Because a hydroxide ionOH1, is present on the right side of the solution equation that is shown above, a hydroxide ion is produced, or donated, during the dissociation of Fe(OH)2.
Based on the analysis that is described in the previous paragraphs, the indicated solute, Fe(OH)2, can be definitively classified as an Arrhenius base.  This definition-driven assignment aligns with the "shortcut" conclusion that was established above.
Exercise $$\PageIndex{2}$$

Use a solution equation to classify HC2H3O2, which exhibits the characteristics of a strong electrolyte when dissolved in nitrogen trihydride, as an Arrhenius acid or an Arrhenius base.

Because the given chemical formula, HC2H3O2, contains one hydrogen and an acetate ion, C2H3O2–1, which is a polyatomic anion, the corresponding molecule can be classified as a polyatomic, or "HNPoly," Arrhenius acid.  However, because the "HNPoly" pattern is a "shortcut," in order to definitively classify HC2H3O2 as an Arrhenius acid, a solution equation for this chemical must be written, and the generated symbolic information must be compared to the chemical and behavioral criteria that are established in the definition of an Arrhenius acid.

In order to apply the strong electrolyte solution equation pattern that was presented in Section 7.6, each substance that is referenced in the given statement must first be classified as a solute or a solvent.  Because the indicator word "in" is present in the given statement, the chemical that is mentioned after this word, nitrogen trihydride, NH3, is the solvent in this solution, and the remaining substance, HC2H3O2, is the solute, "by default."

A "forward," or left-to-right, arrow is utilized in the solution equation for a strong electrolyte, the chemical formula of the solvent, nitrogen trihydride, NH3, is written over this arrow, and the chemical formula of the solute, HC2H3O2, is written on the left side of the arrow.  Because a strong electrolyte completely dissociates into its constituent cations and anions as it dissolves, the ion symbol for each of these particles is written on the right side of the arrow.  The anionic component of HC2H3O2 is the acetate ion, C2H3O21, which is a polyatomic anion.  The remaining element that is present in the given solute, hydrogen, H, does not typically ionize.  However, because the given statement explicitly indicates that HC2H3O2 exhibits the characteristics of a strong electrolyte, which must, by definition, dissociate into cations and anions during the solvation process, the hydrogen that is present in HC2H3O2 must ionize to form a cation, H+1.  Finally, in order to indicate that the cation and anion are unique particles, a plus sign is used to separate their symbols.  The information that is described in this paragraph is reflected in the solution equation that is shown below.

___ $$\ce{HC_2H_3O_2}$$ $$\overset{\ce{NH_3}}{\longrightarrow}$$ ___ $$\ce{H^{+1}}$$ + ___ $$\ce{C_2H_3O_2^{–1}}$$

Since the left and right sides of this solution equation contain equal amounts of hydrogen ions, H+1, and acetate ions, C2H3O21, the solution equation that is shown above is balanced and, therefore, is the chemically-correct representation of the dissociation of HC2H3O2 in nitrogen trihydride.

Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ionOH1, donor in water.  Therefore, in order to be classified as an Arrhenius acid, both the types of ions that are present in the given soluteHC2H3O2and the dissociative behavior of HC2H3O2 in an aqueous solution must be analyzed.

Because an Arrhenius acid must be dissolved in an aqueous solution, water must be the solvent that is used to prepare an Arrhenius solution.  As stated above, the chemical formula of the solvent must be written over the arrow in a solution equation.  However, because "H2O," the chemical formula of water, does not occupy this position in the solution equation that is shown above, the requirement that an Arrhenius chemical be dissolved in an aqueous solution is not satisfied.  Therefore, the indicated solute, HC2H3O2, cannot be classified as either an Arrhenius acid or an Arrhenius base.  This definition-driven assignment does not align with the "shortcut" conclusion that was established above. Since using a "shortcut" to analyze information occasionally generates misleading or erroneous results, the conclusion that is established from applying the "solution equation" process to analyze the information in the given statement is accepted by the scientific community as the correct acid/base classification for HC2H3O2 in nitrogen trihydride.
Exercise $$\PageIndex{3}$$

Use a solution equation to classify ammonium carbonate, which exhibits the characteristics of a strong electrolyte when dissolved in water, as an Arrhenius acid or an Arrhenius base.

Because the given chemical, ammonium carbonate, (NH4)2CO3, contains two ammonium ions, NH4+1, which are polyatomic cations, and a carbonate ion, CO3–2, which is a polyatomic anion, none of the previously-discussed patterns, "HX," "HNPoly," or "M(OH)Y," can be applied to classify this chemical as an Arrhenius acid or an Arrhenius base.  However, because these patterns are "shortcuts," in order to definitively classify ammonium carbonate, (NH4)2CO3, as an Arrhenius acid or an Arrhenius base, a solution equation for this chemical must be written, and the generated symbolic information must be compared to the chemical and behavioral criteria that are established in the definitions of an Arrhenius acid and an Arrhenius base.

In order to apply the strong electrolyte solution equation pattern that was presented in Section 7.6, each substance that is referenced in the given statement must first be classified as a solute or a solvent.  Because the indicator word "in" is present in the given statement, the chemical that is mentioned after this word, water, H2O, is the solvent in this solution, and the remaining substance ammonium carbonate(NH4)2CO3, is the solute, "by default."

A "forward," or left-to-right, arrow is utilized in the solution equation for a strong electrolyte, the chemical formula of the solvent, water, H2O, is written over this arrow, and the chemical formula of the solute, ammonium carbonate(NH4)2CO3, is written on the left side of the arrow.  Because a strong electrolyte completely dissociates into its constituent cations and anions as it dissolves, the ion symbol for each of these particles is written on the right side of the arrow.  The cationic component of ammonium carbonate(NH4)2CO3, is the ammonium ion, NH4+1, which is a polyatomic cation, and the anionic component of this solute is the carbonate ion, CO32, which is a polyatomic anion.  Finally, in order to indicate that the cation and anion are unique particles, a plus sign is used to separate their symbols.  The information that is described in this paragraph is reflected in the solution equation that is shown below.

___ $$\ce{(NH_4)_2CO_3}$$ $$\overset{\ce{H_2O}}{\longrightarrow}$$ ___ $$\ce{NH_4^{+1}}$$ + ___ $$\ce{CO_3^{–2}}$$

Since the left and right sides of this solution equation contain equal amounts of carbonate ions, CO32, that ion is balanced.  However, the ammonium ion, NH4+1, is not balanced, and, therefore, a coefficient of 2 should be written in the "blank" that corresponds to this ion on the right side of the arrow, as shown below.  Because all of the components in the following solution equation are balanced, this equation is the chemically-correct representation of the dissociation of ammonium carbonate(NH4)2CO3 in water.

___ $$\ce{(NH_4)_2CO_3}$$ $$\overset{\ce{H_2O}}{\longrightarrow}$$ 2 $$\ce{NH_4^{+1}}$$ + ___ $$\ce{CO_3^{–2}}$$

Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ionOH1, donor in water.  Therefore, in order to be classified as an Arrhenius acid or an Arrhenius base, both the types of ions that are present in the given soluteammonium carbonate(NH4)2CO3and the dissociative behavior of ammonium carbonate(NH4)2CO3, in an aqueous solution must be analyzed.
• Because an Arrhenius chemical must be dissolved in an aqueous solution, water must be the solvent that is used to prepare an Arrhenius solution.  As stated above, the chemical formula of the solvent must be written over the arrow in a solution equation.  Therefore, because "H2O," the chemical formula of water, occupies this position in the solution equation that is shown above, the requirement that an Arrhenius chemical be dissolved in an aqueous solution is satisfied.
• Additionally, an Arrhenius chemical must donate, or produce, a particular type of ion.  Therefore, if a proton, H+1, is written on the right, or product, side of the arrow in a solution equation, the corresponding solute can be classified as an Arrhenius acid.  In contrast, a solute can be categorized as an Arrhenius base if a hydroxide ionOH1, is symbolized on the product, side of a solution equation arrow.  However, because neither of these ions is present on the right side of the solution equation that is shown above, neither a proton, H+1, nor a hydroxide ionOH1, is produced, or donated, during the dissociation of ammonium carbonate(NH4)2CO3.
Based on the analysis that is described in the previous paragraphs, the indicated solute, ammonium carbonate(NH4)2CO3, cannot be classified as either an Arrhenius acid or an Arrhenius base.  This definition-driven assignment aligns with the "shortcut" conclusion that was established above.  Because the given solute, ammonium carbonate(NH4)2CO3, does ionize in water, but does not produce protons, H+1, or hydroxide ionsOH1, upon its dissociation, this type of solute is classified as a salt.  This type of electrolyte will be further discussed in a later section of this chapter.
Exercise $$\PageIndex{4}$$

Use a solution equation to classify HF, which exhibits the characteristics of a weak electrolyte when dissolved in water, as an Arrhenius acid or an Arrhenius base.

Because the given chemical formula, HF, contains one hydrogen and one fluoride ion, F–1, which is a halide anion, the corresponding molecule can be classified as a hydrohalogenated, or "HX," Arrhenius acid.  However, because the "HX" pattern is a "shortcut," in order to definitively classify HF as an Arrhenius acid, a solution equation for this chemical must be written, and the generated symbolic information must be compared to the chemical and behavioral criteria that are established in the definition of an Arrhenius acid.

In order to apply the weak electrolyte solution equation pattern that was presented in Section 7.7, each substance that is referenced in the given statement must first be classified as a solute or a solvent.  Because the indicator word "in" is present in the given statement, the chemical that is mentioned after this word, water, H2O, is the solvent in this solution, and the remaining substance, HF, is the solute, "by default."

An equilibrium arrow is utilized in the solution equation for a weak electrolyte, the chemical formula of the solvent, water, H2O, is written over this arrow, and the chemical formula of the solute, HF, is written on the left side of the arrow.  Because a weak electrolyte partially dissociates into its constituent cations and anions as it dissolves, the ion symbol for each of these particles is written on the right side of the arrow.  The anionic component of HF is a fluoride ion, F1.  The remaining element that is present in the given solute, hydrogen, H, does not typically ionize.  However, because the given statement explicitly indicates that HF exhibits the characteristics of a weak electrolyte, which must, by definition, partially dissociate into cations and anions during the solvation process, the hydrogen that is present in HF must ionize to form a cation, H+1.  Finally, in order to indicate that the cation and anion are unique particles, a plus sign is used to separate their symbols.  The information that is described in this paragraph is reflected in the solution equation that is shown below.

___ $$\ce{HF}$$ $$\overset{\ce{H_2O}}{\longrightleftharpoons}$$ ___ $$\ce{H^{+1}}$$ + ___ $$\ce{F^{–1}}$$

Since the left and right sides of this solution equation contain equal amounts of hydrogen ions, H+1, and fluoride ions, F1, the solution equation that is shown above is balanced and, therefore, is the chemically-correct representation of the dissociation of HF in water.

Recall that an Arrhenius acid is defined as a proton, H+1, donor in water, and an Arrhenius base is defined as a hydroxide ionOH1, donor in water.  Therefore, in order to be classified as an Arrhenius acid, both the types of ions that are present in the given solute, HFand the dissociative behavior of HF in an aqueous solution must be analyzed.
• Because an Arrhenius acid must be dissolved in an aqueous solution, water must be the solvent that is used to prepare an Arrhenius solution.  As stated above, the chemical formula of the solvent must be written over the arrow in a solution equation.  Therefore, because "H2O," the chemical formula of water, occupies this position in the solution equation that is shown above, the requirement that an Arrhenius acid be dissolved in an aqueous solution is satisfied.
• Additionally, an Arrhenius chemical must donate, or produce, a particular type of ion.  Therefore, a solute can only be classified as an Arrhenius acid if a proton, H+1, is written on the right, or product, side of the arrow in a solution equation.  Because a hydrogen ion, H+1, is present on the right side of the solution equation that is shown above, a proton is produced, or donated, during the dissociation of HF.
Based on the analysis that is described in the previous paragraphs, the indicated solute, HF, can be definitively classified as an Arrhenius acid.  This definition-driven assignment aligns with the "shortcut" conclusion that was established above.