# 8.26: Brønsted-Lowry Acids and Bases: Quantifying Acid/Base Concentrations in a Neutral Solution

Learning Objectives
• Quantify the concentrations of hydronium ions and hydroxide ions that are present in a neutral solution.

As will be discussed in the remaining sections of this chapter, chemists have derived two equations that can be used to calculate the amounts of acid and base that are present in a solution.  In order to establish a standard, or reference, value to which all subsequently-collected quantitative data could be compared, chemists initially studied a "solution" of "pure" liquid water, H2O.  Because no acidic or basic solutes were dissolved in this "solution," which was, therefore, classified as "neutral," scientists expected to detect only a single chemical, water, H2O.  Instead, these researchers discovered that very small amounts of acid and base were present in all of the water samples that were tested.  This unexpected result can be explained by predicting the products that are generated during the autoionization of water, in which a proton, H+1, is spontaneously transferred from one water molecule, which acts as a Brønsted-Lowry acid, to another water molecule, which, therefore, is classified as a Brønsted-Lowry base.  The Brønsted-Lowry acid/base equation that symbolically-represents this reaction was developed in the previous section of this chapter and is reproduced below.

$$\ce{H_2O}$$ $$\left( l \right)$$$$\ce{H_2O}$$ $$\left( l \right)$$ $$\longrightleftharpoons$$ $$\ce{OH^{–1}}$$ $$\left( aq \right)$$ + $$\ce{H_3O^{+1}}$$ $$\left( aq \right)$$

Because the conjugate products that are generated during this reaction are found in all aqueous solutions that contain basic or acidic solutes, chemists chose to determine the amounts of base and acid that are contained in a solution by measuring the quantities of hydroxide ions, OH–1, and hydronium ionsH3O+1, respectively, that are present in that solution.  Since the equation that is shown above is balanced, the coefficients that are associated with the chemical formulas for the hydroxide ion, OH–1, and the hydronium ionH3O+1, can be used to determine the stoichiometric ratio in which these ions are produced.  Because the coefficients that correspond to both of these formulas are unwritten "1"s, the basic hydroxide ion, OH–1, and the acidic hydronium ionH3O+1, are generated in a one-to-one molar ratio, as shown below.  Therefore, since the acid/base equation that is shown above symbolically-represents the autoionization of "pure" water, this mathematical relationship indicates that a neutral solution must contain equal molar amounts of basic and acidic ions.

mol OH–1 = mol H3O+1

However, since the Brønsted-Lowry solutes that are being investigated are, by definition, contained in solutions, the measured amounts of hydroxide ions, OH–1, and hydronium ionsH3O+1, must be reported as concentrations.  As stated in Chapter 7, mass percent, volume percent, and mass/volume percent concentration calculations are typically simplified and presented as "end-result" values.  In contrast, molarities are molar quantities and, therefore, can be related to the other molar standards that have been presented in this textbook, including the stoichiometric relationship that is indicated above.  Recall that the molarity of a solution is defined as the ratio of the molar amount of solute, "nsolute," that is present in a solution, relative to the volume of the solution, "Vsolution," as a whole.  The equation that is used to calculate the molarity of a solution is reproduced below.

$$\text{Molarity}$$ = $$\dfrac{ \rm{n_{solute} \; (\rm{mol})}}{\rm{V_{solution} \; (\rm{L})}}$$

This equation can be modified to more heavily-emphasize the identity of the solute by replacing the "Molarity" variable with the chemical formula of that solute, enclosed in square brackets.  Therefore, the following equations can be used to calculate the molarity of hydroxide ions, OH–1,

$$\rm{[OH^{–1}]}$$ = $$\dfrac{ \rm{n_{hydroxide} \; (\rm{mol})}}{\rm{V_{solution} \; (\rm{L})}}$$

and hydronium ionsH3O+1,

$$\rm{[H_3O^{+1}]}$$ = $$\dfrac{ \rm{n_{hydronium} \; (\rm{mol})}}{\rm{V_{solution} \; (\rm{L})}}$$

respectively, that are present in a solution.

As stated above, during the autoionization of water, the basic hydroxide ion, OH–1, and the acidic hydronium ionH3O+1, are generated in an equal, one-to-one molar ratio.  Furthermore, because this Brønsted-Lowry acid/base reaction occurs in a single "solution," these ions are present in equal volumes of solution.  Therefore, since the quantities in the numerators and the denominators in the equations that are shown above have equivalent values, the molarity of hydroxide ions, OH–1, must be equal to the molarity of hydronium ionsH3O+1, in a neutral solution.  Equating these variables to the experimentally-determined molarity of hydronium ionsH3O+1, 1.00 x 10–7 M, results in the equality string that is shown below.

$$\rm{[OH^{–1}]}$$ $$\rm{[H_3O^{+1}]}$$ $${1.00 \times 10^{–7} M}$$

Because the concentrations of acid and base that are detected in "pure" water samples are very small, the corresponding measured values are most easily-reported in scientific notation.  Finally, as will be discussed in the following section of this chapter, the molarities of hydroxide ions, OH–1, and hydronium ionsH3O+1, in a non-neutral solution can be compared to determine whether the amount of acid or the quantity of base predominates in and, therefore, dictates the characteristics of, that solution.  For nearly-neutral solutions, the measurements that correspond to the amounts of acid and base that are present are first distinguishable at the third significant digit.  As a result, chemists required that the coefficients in the reported concentrations, which are usually rounded quantities, be recorded to the hundredths place.