# 8.19: Brønsted-Lowry Acids and Bases: Writing Acid/Base Equations that Represent Non-Aqueous Proton Transfers

Learning Objectives
• Develop a Brønsted-Lowry acid/base equation that represents the absorption of a proton by a non-aqueous solvent.

As stated previously, when a Brønsted-Lowry acid dissociates, the hydrogen ion, H+1, that is produced is extremely unstable and, consequently, is immediately absorbed by a nearby solvent molecule.  After observing this phenomenon, Brønsted and Lowry defined an acid/base reaction as the transfer of a proton, H+1, from a solute particle, which is categorized as a Brønsted-Lowry acid, to a solvent molecule, which is classified as a Brønsted-Lowry base.  Section 8.18 presented and applied the process for transforming a solution equation into a Brønsted-Lowry acid/base equation, which symbolically represents the synergistic relationship that exists between a Brønsted-Lowry acid and a Brønsted-Lowry base.

Because "H2O" was written over the arrow in the solution equations that were presented in Section 8.18, water is the solvent that was used to prepare the homogeneous mixtures that are represented by those equations.  Therefore, the resultant Brønsted-Lowry acid/base equations, which were developed by restructuring the given solution equations, represent the generation and subsequent absorption of protons, H+1, in aqueous solutions.  However, because Brønsted and Lowry did not explicitly identify the solvent in which their acids must be dissolved, an alternative solvent, such as nitrogen trihydride, NH3, which is more commonly-known as "ammonia," or ethanol, C2H5OH, could be used to solvate a Brønsted-Lowry acid.  Because these solvents can also absorb the proton, H+1, that is generated upon the dissociation of a Brønsted-Lowry acid, solution equations and, subsequently, Brønsted-Lowry acid/base equations, can be written to represent these non-aqueous solutions, as will be exemplified in the following paragraphs.

For example, develop a Brønsted-Lowry acid/base equation by restructuring the following balanced solution equation.  Balance the final Brønsted-Lowry equation by writing coefficients, as necessary.  (States of matter are not required.)

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

As stated previously, when a Brønsted-Lowry acid dissociates, the hydrogen ion, H+1, that is produced is immediately absorbed by a solvent molecule, which is classified as a Brønsted-Lowry base.  In order for this proton, H+1, transfer to occur, a solute particle must exist in close physical proximity to a solvent molecule.  Because a solution is, by definition, a homogenous mixture, solute and solvent molecules are evenly-distributed, relative to one another, when present in the same solution.  However, because the chemical formula of the solute, acetic acid, HC2H3O2, is written on the left side of the arrow in the given solution equation, and the formula of the solvent, nitrogen trihydride, NH3, is written above this arrow, the format of the solution equation that is shown above does not reflect that these solute and solvent molecules exist with one another in solution.  Therefore, in order to indicate that solute molecules are uniformly-dispersed among solvent molecules in a homogeneous mixture, the chemical formula of the solvent, NH3, must be moved from its current position in the given solution equation to the left side of the arrow.  A plus sign must be used to separate the formulas of these chemicals, as shown below.

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

While the equation that is shown above accurately reflects that solute and solvent molecules exist in the same chemical environment in a solution, this equation is not balanced.  Because a new chemical formula was introduced on the left side of the solution equation arrow, the relative quantity of atoms and ions on the left and right sides of this equation cannot be balanced through the incorporation of coefficients.  However, recall that, by definition, the solvent is the chemical that is present in the greatest amount in a given solution.  Consequently, after the appropriate quantity of solute particles have dissociated, and the protonsH+1, that are produced have been absorbed by an equal number of solvent molecules, excess solvent molecules are still present in the resultant solution.  Therefore, the chemical formula of the solvent, NH3, should also be written on the right side of the arrow.  Again, a plus sign must be used to separate this formula from those that were already present, as shown below.  Because the chemical formula of the solvent is now written on both sides of the arrow, the resultant equation is balanced.

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

Finally, as stated above, the purpose of a Brønsted-Lowry acid/base equation is to symbolically-represent the transfer of a proton, H+1, from a solute particle to a solvent molecule.  Therefore, in order to represent the absorption of a hydrogen ion, H+1, by a nearby solvent molecule, the formulas of these chemicals must be combined.  While the chemical formula of the solvent, NH3, is written on both sides of the arrow in the equation that is shown above, the hydrogen ion, H+1, is only symbolized on the right side of this equation.  As explained above, in order to indicate that two chemicals exist in the same environment and, consequently, can interact with one another, the formulas of those substances must be written on the same side of the arrow in an equation.  Therefore, the ion symbol of the proton, H+1, is combined with the solvent formula, NH3, on the right side of the equation, as shown below.

$$\ce{HC_2H_3O_2}$$ + $$\ce{NH_3}$$ $$\longrightarrow$$ $$\ce{NH_4^{+1}}$$ + $$\ce{C_2H_3O_2^{–1}}$$

The formula of the chemical that is generated by combining these substances is derived by adding both the subscripts that are associated with each constituent element and the overall charges of the particles.  Therefore, because the solvent in the given solution is nitrogen trihydride, NH3, which is more commonly-known as "ammonia," combining this chemical with a hydrogen ion, H+1, generates a particle that contains four hydrogens, H, one nitrogen, N, and a net +1 charge and, therefore, is symbolized as NH4+1.  The name of this ion, the ammonium ion, is derived by combining a prefix, "ammo-," that indicates the identity of the solvent, ammonia, with a suffix, "-ium ion," that indicates that this particle bears a net positive charge.

Because all of the components in the final equation that is shown above are balanced, this equation is the chemically-correct representation of the Brønsted-Lowry acid/base reaction that occurs between acetic acid, HC2H3O2, which, as the solute, is a Brønsted-Lowry acid, and nitrogen trihydride, NH3, which is the solvent, and, therefore, the Brønsted-Lowry base, in the corresponding solution.  A Brønsted-Lowry acid/base equation will always be balanced, as-written, if the restructuring process that is described above is correctly applied to the chemicals that are present in a given solution equation.  Additionally, the molecules on the left and right sides of the reaction arrow can be written in any order, as long as their positions relative to the arrow remain constant.  Finally, recall that a "forward," or left-to-right, arrow indicates that a strong electrolyte has completely dissociated and that an equilibrium arrow represents the "forward" dissociation and "reverse" recombination processes that occur simultaneously during the solvation of a weak electrolyte.  Therefore, because only the relative locations of the chemical formulas in a solution equation, not the relative strengths of the associated molecules, are changed during the development of a Brønsted-Lowry acid/base equation, the type of arrow that is written in the final Brønsted-Lowry acid/base equation must be identical to the arrow that was given in the initial solution equation.

Exercise $$\PageIndex{1}$$

Develop a Brønsted-Lowry acid/base equation by restructuring the following balanced solution equation.  Balance the final Brønsted-Lowry equation by writing coefficients, as necessary.  (States of matter are not required.)

$$\ce{H_2O}$$ $$\overset{\ce{C_2H_5OH}}{\longrightleftharpoons}$$ $$\ce{H^{+1}}$$ + $$\ce{OH^{–1}}$$

As stated previously, when a Brønsted-Lowry acid dissociates, the hydrogen ion, H+1, that is produced is immediately absorbed by a solvent molecule, which is classified as a Brønsted-Lowry base.  In order for this proton, H+1, transfer to occur, a solute particle must exist in close physical proximity to a solvent molecule.  However, because the chemical formula of the solute, water, H2O, is written on the left side of the arrow in the given solution equation, and the formula of the solvent, ethanol, C2H5OH, is written above this arrow, the format of the solution equation that is shown above does not reflect that these solute and solvent molecules exist with one another in solution.  Therefore, the chemical formula of the solvent, C2H5OH, must be moved from its current position in the given solution equation to the left side of the arrow, and a plus sign must be used to separate the formulas of these chemicals, as shown below.

$$\ce{H_2O}$$ + $$\ce{C_2H_5OH}$$ $$\longrightleftharpoons$$ $$\ce{H^{+1}}$$ + $$\ce{OH^{–1}}$$

While the equation that is shown above accurately reflects that solute and solvent molecules exist in the same chemical environment in a solution, this equation is not balanced.  Recall that, by definition, the solvent is the chemical that is present in the greatest amount in a given solution.  Consequently, after the appropriate quantity of solute particles have dissociated, and the protonsH+1, that are produced have been absorbed by an equal number of solvent molecules, excess solvent molecules are still present in the resultant solution.  Therefore, the chemical formula of the solvent, C2H5OH, should also be written on the right side of the arrow.  Again, a plus sign must be used to separate this formula from those that were already present, as shown below.  Because the chemical formula of the solvent is now written on both sides of the arrow, the resultant equation is balanced.

$$\ce{H_2O}$$ + $$\ce{C_2H_5OH}$$ $$\longrightleftharpoons$$ $$\ce{H^{+1}}$$ + $$\ce{OH^{–1}}$$ + $$\ce{C_2H_5OH}$$

Finally, as stated above, the purpose of a Brønsted-Lowry acid/base equation is to symbolically-represent the transfer of a proton, H+1, from a solute particle to a solvent molecule.  Therefore, in order to represent the absorption of a hydrogen ion, H+1, by a nearby solvent molecule, the formulas of these chemicals must be combined.  As explained above, the formulas of two chemicals that exist in the same environment and, consequently, interact with one another, must be written on the same side of the arrow in an equation.  Therefore, the ion symbol of the proton, H+1, is combined with the solvent formula, C2H5OH, on the right side of the equation that is shown above.  The formula of the chemical that is generated by combining these substances is derived by adding both the subscripts that are associated with each constituent element and the overall charges of the particles.  Therefore, because the solvent in the given solution is ethanol, C2H5OH, combining this chemical with a hydrogen ion, H+1, generates an ion that contains two carbons, C, seven hydrogens, H, one oxygen, O, and a net +1 charge.  Because the proton, H+1, bonds with the oxygen, O, that is present in ethanol, the resultant ion is symbolized as C2H5OH2+1, as shown below.

$$\ce{H_2O}$$ + $$\ce{C_2H_5OH}$$ $$\longrightleftharpoons$$ $$\ce{C_2H_5OH_2^{+1}}$$ + $$\ce{OH^{–1}}$$

Because all of the components in the final equation that is shown above are balanced, this equation is the chemically-correct representation of the Brønsted-Lowry acid/base reaction that occurs between water, H2O, which, as the solute, is a Brønsted-Lowry acid, and ethanol, C2H5OH, which is the solvent, and, therefore, the Brønsted-Lowry base, in the corresponding solution.  The molecules on the left and right sides of the reaction arrow can be written in any order, as long as their positions relative to the arrow remain constant.  Finally, because only the relative locations of the chemical formulas in a solution equation, not the relative strengths of the associated molecules, are changed during the development of a Brønsted-Lowry acid/base equation, the type of arrow that is written in the final Brønsted-Lowry acid/base equation must be identical to the arrow that was given in the initial solution equation.