Equilibrium: Bronsted-Lowry Acids and Bases

When dissolved in water, acids transfer the acidic proton to water to varying extents according to the following generic reaction:

The strength of the acid relative to H₃O⁺ is indicated by the size of the equilibrium constant, K_a. Acids with K_a >>1 are strong acids, for which reaction (1) proceeds essentially completely to the right. Perchloric acid, HClO₄, is an example of a strong acid. Acids with K_a < 1 are weak acids. Formic acid, HCOOH, is an example of a weak acid. For weak acids, relatively few HA molecules transfer a proton to water, resulting in relatively small concentrations of H₃O⁺ and A^- in solution. Acids with K_a < 10^-14 are very weak acids; they have no measurable tendency to transfer a proton to water. Examples of very weak acids are NH₃, H₂, and CH₄.

Reaction (1) is called a proton transfer reaction, because it depicts the transfer of a proton, H⁺, from HA to H₂O. Proton transfer processes are the focus of the Bronsted-Lowry theory of acids and bases, according to which an acid is a proton donor, and a base is a proton acceptor. Note in (1) that loss of a proton from the acid, HA, results in a species, A^-, that is a proton acceptor. Thus when an acid reacts, it becomes a base! The closely related pair of species, HA and A^-, is referred to as a conjugate acid-base pair. They are related via addition or loss of a proton, as in (2):

Water and hydronium ion, H₃O⁺, are also a conjugate pair. Any proton transfer process involves two conjugate acid-base pairs, as shown below:

If HA is a stronger acid than HB, the reaction will proceed primarily to the right. If HB is the stronger acid, reaction will proceed primarily to the left.

We can achieve a couple of interesting results by rearranging and manipulating the equilibrium constant expression for the proton transfer process, (1).

This arrangement of the expression shows us that the ratio of the base ("deprotonated" form, A-) to acid ("protonated" form, HA) forms of HA depends on, first, how strong the acid is (K_a); and on what the concentration of H₃O⁺ happens to be. If [H₃O⁺] is large, there are lots of protons around, which tends to shift (2) to the left in favor of the conjugate acid form. Thus the value of R (= [A^-]/[HA]) is small. If [H₃O⁺] is small, there is a paucity of protons, shifting (2) to the right and favoring the conjugate base, A^-. Thus R is large. A very interesting situation is that in which the hydronium ion concentration is equal to the value of K_a for the acid. In this circumstance, the value of R is precisely 1; that is, the concentrations of conjugate acid and base are equal in the solution.

A commonly seen version of (4) can be developed by, first, taking the common logarithm of both sides of (4):

rearranging to isolate -log[H₃O⁺] on the left side:

and, finally, recognizing that -log[H₃O⁺] is pH:

Here we have generalized the concept of pH to any quantity, X, so that pX = -log X. Thus pK_a is simply the negative of the log of K_a for the acid.

Equation (5) is called the Henderson-Hasselbalch equation. It leads directly to the following very useful general statements:

The equilibrium established when a weak acid reacts with water according to 2 can be explored using a procedure called titration, involving the following steps:

• A precisely known volume of acid solution is measured out. Such a precisely known volume is called an aliquot, and may be measured using a volumetric pipet, an item of glassware which, when filled with the solution of interest, delivers precisely the indicated volume of solution. Convenient pipet sizes for aliquot measurement range from 1.00 to 25.00 mL.
• To the aliquot of acid solution, a solution of base of precisely known concentration (called standard base) is added from another item of precision glassware called a buret. This process is the actual titration. The substance added from the buret, in this case the base, is called the titrant. Addition of titrant is continued until the moles of OH^- added is precisely equal to the moles of H⁺ in the acid. The point of the titration where moles OH^- added = moles H⁺ in acid is called the equivalence point.
• From the volume of base added and its known concentration, we calculate the concentration of acid in the original solution.

The buret is a graduated (i.e., marked) glass tube fitted with a stopcock (a valve) at the bottom. The tube, or barrel, has a capacity of 25 mL. Graduation marks completely encircling the barrel correspond to whole numbers of milliliters. Between any 2 of these marks are 9 additional marks corresponding to tenths of a milliliter (0.10 mL). These marks are separated by a distance of approximately 1 mm. To read the level of liquid in a buret, locate the bottom of the liquid meniscus curve, which normally will fall between two of the 0.1-mL marks. To estimate hundredths of a milliliter, assess the position of the meniscus between the two 0.1-mL marks. For example, suppose the meniscus falls about 40% of the way between the marks corresponding to 2.2 and 2.3 mL. The liquid level would then be read as 2.24 mL. The volume of liquid delivered from the buret in a titration is the difference between the liquid levels at the end and at the start of the titration.

Titration involves a very important practical problem: how is the equivalence point detected? Unless we can detect the equivalence point, we will not know when to stop adding titrant. Clearly, the pH of the solution must change as the titration proceeds. At the beginning of the process, before base is added, the pH of the solution is fairly low because it contains acid. As titration proceeds, acid is neutralized by the added base, and pH rises. Addition of base after all of the acid has been neutralized produces a basic solution, with a high pH. During the titration, then, pH runs the gamut from low to high. We can detect the equivalence point from the manner in which the pH change occurs.

Two methods are commonly used to detect the equivalence point in a titration. In the first, an instrument called a pH meter is used to monitor the pH of the solution as base is added during the titration. In this method, we successively add small volumes of base, measure pH after each addition, and plot the titration curve, from which we may find V_base at the inflection point (the equivalence point). Moles of acid in the original aliquot is calculated as follows:

The second method for detecting the equivalence point is to use an appropriate indicator, a weak acid that exhibits different colors in its protonated and deprotonated forms. The indicator is chosen so that it changes color at the pH of the equivalence point for the acid to be titrated. In this experiment we will make use of 2 common indicators, phenolphthalein and methyl red.