Definitions of Acids and Bases

So far in the story, we defined acids as substances that dissolve in water to produce H⁺ ions, whereas bases were defined as substances that dissolve in water to produce OH⁻ ions. In fact, this is only one possible set of definitions. Although the general properties of acids and bases have been known for more than a thousand years, the definitions of acid and base have changed dramatically as scientists have learned more about them. In ancient times, an acid was any substance that had a sour taste (e.g., vinegar or lemon juice), caused consistent color changes in dyes derived from plants (e.g., turning blue litmus paper red), reacted with certain metals to produce hydrogen gas and a solution of a salt containing a metal cation, and dissolved carbonate salts such as limestone (CaCO₃) with the evolution of carbon dioxide. In contrast, a base was any substance that had a bitter taste, felt slippery to the touch, and caused color changes in plant dyes that differed diametrically from the changes caused by acids (e.g., turning red litmus paper blue). Although these definitions were useful, they were entirely descriptive.

Image Credit: Lemon-By Bordercolliez (Own work) [CC0], via Wikimedia Commons. Soap-By Maksim, https://creativecommons.org/licenses/by-sa/3.0/ via Wikimedia Commons

Polyprotic Acids

Acids differ in the number of protons they can donate. For example, monoprotic acidsA compound that is capable of donating one proton per molecule. are compounds that are capable of donating a single proton per molecule. Monoprotic acids include HF, HCl, HBr, HI, HNO₃, and HNO₂. All carboxylic acids that contain a single −CO₂H group, such as acetic acid (CH₃CO₂H), are monoprotic acids, dissociating to form RCO₂⁻ and H⁺ (Section 4.1 "Aqueous Solutions"). Polyprotic acidsA compound that can donate more than one proton per molecule. can donate more than one proton per molecule. For example, H₂SO₄ can donate two H⁺ ions in separate steps, so it is a diprotic acidA compound that can donate two protons per molecule in separate steps., and H₃PO₄, which is capable of donating three protons in successive steps, is a triprotic acidA compound that can donate three protons per molecule in separate steps. (Equation 4.20, Equation 4.21, and Equation 4.22):

In chemical equations such as these, a double arrow is used to indicate that both the forward and reverse reactions occur simultaneously, so the forward reaction does not go to completion. Instead, the solution contains significant amounts of both reactants and products. Over time, the reaction reaches a state in which the concentration of each species in solution remains constant. The reaction is then said to be in equilibriumThe point at which the rates of the forward and reverse reactions become the same, so that the net composition of the system no longer changes with time. - the topic of future chapters.

Strengths of Acids and Bases

We will not discuss the strengths of acids and bases quantitatively until we explore equilibrium in more depth. Qualitatively, however, we can state that strong acidsAn acid that reacts essentially completely with water to give ${\text{H}}^{+}$ and the corresponding anion. react essentially completely with water to give H⁺ and the corresponding anion. Similarly, strong basesA base that dissociates essentially completely in water to give ${\text{OH}}^{-}$ and the corresponding cation. dissociate essentially completely in water to give OH⁻ and the corresponding cation. Strong acids and strong bases are both strong electrolytes. In contrast, only a fraction of the molecules of weak acidsAn acid in which only a fraction of the molecules react with water to produce ${\text{H}}^{+}$ and the corresponding anion. and weak basesA base in which only a fraction of the molecules react with water to produce ${\text{OH}}^{-}$ and the corresponding cation. react with water to produce ions, so weak acids and weak bases are also weak electrolytes. Typically less than 5% of a weak electrolyte dissociates into ions in solution, whereas more than 95% is present in undissociated form.

In practice, only a few strong acids are commonly encountered: HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄ (H₃PO₄ is only moderately strong). The most common strong bases are ionic compounds that contain the hydroxide ion as the anion; three examples are NaOH, KOH, and Ca(OH)₂. Common weak acids include HCN, H₂S, HF, oxoacids such as HNO₂ and HClO, and carboxylic acids such as acetic acid. The ionization reaction of acetic acid is as follows:

Although acetic acid is very soluble in water, almost all of the acetic acid in solution exists in the form of neutral molecules (less than 1% dissociates), as we stated in Section 4.1 "Aqueous Solutions". Sulfuric acid is unusual in that it is a strong acid when it donates its first proton (Equation 4.24) but a weak acid when it donates its second proton (Equation 4.25) as indicated by the single and double arrows, respectively:

Consequently, an aqueous solution of sulfuric acid contains H⁺(aq) ions and a mixture of HSO₄⁻(aq) and SO₄²⁻(aq) ions but no H₂SO₄ molecules.

The most common weak base is ammonia, which reacts with water to form small amounts of hydroxide ion:

Most of the ammonia (>99%) is present in the form of NH₃(g). Amines, which are organic analogues of ammonia, are also weak bases, as are ionic compounds that contain anions derived from weak acids (such as S²⁻).

Table 4.3 "Common Strong Acids and Bases" lists some common strong acids and bases. Acids other than the six common strong acids are almost invariably weak acids. The only common strong bases are the hydroxides of the alkali metals and the heavier alkaline earths (Ca, Sr, and Ba); any other bases you encounter are most likely weak. Remember that there is no correlation between solubility and whether a substance is a strong or a weak electrolyte! Many weak acids and bases are extremely soluble in water.

The Hydronium Ion

Because isolated protons are very unstable and hence very reactive, an acid never simply “loses” an H⁺ ion. Instead, the proton is always transferred to another substance, which acts as a base in the Brönsted-Lowry definition. Thus in every acid–base reaction, one species acts as an acid and one species acts as a base. Occasionally, the same substance performs both roles, as you will see later. When a strong acid dissolves in water, the proton that is released is transferred to a water molecule that acts as a proton acceptor or base, as shown for the dissociation of sulfuric acid:

Technically, therefore, it is imprecise to describe the dissociation of a strong acid as producing H⁺(aq) ions, as we have been doing. The resulting H₃O⁺ ion, called the hydronium ionThe ${\text{H}}_{\text{3}}{\text{O}}^{+}$ ion, represented as ${\text{H}}^{+}\left(\text{aq}\right).$, is a more accurate representation of H⁺(aq). For the sake of brevity, however, in discussing acid dissociation reactions, we will often show the product as H⁺(aq) (as in Equation 4.23) with the understanding that the product is actually the H₃O⁺(aq) ion.

Conversely, bases that do not contain the hydroxide ion accept a proton from water, so small amounts of OH⁻ are produced, as in the following:

Again, the double arrow indicates that the reaction does not go to completion but rather reaches a state of equilibrium. In this reaction, water acts as an acid by donating a proton to ammonia, and ammonia acts as a base by accepting a proton from water. Thus water can act as either an acid or a base by donating a proton to a base or by accepting a proton from an acid. Substances that can behave as both an acid and a base are said to be amphotericWhen substances can behave as both an acid and a base..

The products of an acid–base reaction are also an acid and a base. In Equation 4.27, for example, the products of the reaction are the hydronium ion, here an acid, and the hydrogen sulfate ion, here a weak base. In Equation 4.28, the products are NH₄⁺, an acid, and OH⁻, a base. The product NH₄⁺ is called the conjugate acidThe substance formed when a Br�nsted–Lowry base accepts a proton. of the base NH₃, and the product OH⁻ is called the conjugate baseThe substance formed when a Br�nsted–Lowry acid donates a proton. of the acid H₂O. Thus all acid–base reactions actually involve two conjugate acid–base pairsAn acid and a base that differ by only one hydrogen ion. All acid–base reactions involve two conjugate acid–base pairs, the Br�nsted–Lowry acid and the base it forms after donating its proton, and the Br�nsted–Lowry base and the acid it forms after accepting a proton.; in Equation 4.28, they are NH₄⁺/NH₃ and H₂O/OH⁻.

Neutralization Reactions

A neutralization reactionA chemical reaction in which an acid and a base react in stoichiometric amounts to produce water and a salt. is one in which an acid and a base react in stoichiometric amounts to produce water and a saltThe general term for any ionic substance that does not have ${\text{OH}}^{-}$ as the anion or ${\text{H}}^{+}$ as the cation., the general term for any ionic substance that does not have OH⁻ as the anion or H⁺ as the cation. If the base is a metal hydroxide, then the general formula for the reaction of an acid with a base is described as follows: Acid plus base yields water plus salt. For example, the reaction of equimolar amounts of HBr and NaOH to give water and a salt (NaBr) is a neutralization reaction:

If we write the complete ionic equation for the reaction in Equation 4.29, we see that Na⁺(aq) and Br⁻(aq) are spectator ions and are not involved in the reaction:

The overall reaction is therefore simply the combination of H⁺(aq) and OH⁻(aq) to produce H₂O, as shown in the net ionic equation:

The net ionic equation for the reaction of any strong acid with any strong base is identical to Equation 4.31.

The strengths of the acid and the base generally determine whether the reaction goes to completion. The reaction of any strong acid with any strong base goes essentially to completion, as does the reaction of a strong acid with a weak base, and a weak acid with a strong base. Examples of the last two are as follows:

Sodium acetate is written with the organic component first followed by the cation, as is usual for organic salts. Most reactions of a weak acid with a weak base also go essentially to completion. One example is the reaction of acetic acid with ammonia:

An example of an acid–base reaction that does not go to completion is the reaction of a weak acid or a weak base with water, which is both an extremely weak acid and an extremely weak base.

In some cases, the reaction of an acid with an anion derived from a weak acid (such as HS⁻) produces a gas (in this case, H₂S). Because the gaseous product escapes from solution in the form of bubbles, the reverse reaction cannot occur. Therefore, these reactions tend to be forced, or driven, to completion. Examples include reactions in which an acid is added to ionic compounds that contain the HCO₃⁻, CN⁻, or S²⁻ anions, all of which are driven to completion (Figure 4.14 "The Reaction of Dilute Aqueous HNO₃"):

Figure 4.14 The Reaction of Dilute Aqueous HNO₃ with a Solution of Na₂CO₃

Note the vigorous formation of gaseous CO₂. Image Credit: Highland Community College

The reactions in Equation 4.37 are responsible for the rotten egg smell that is produced when metal sulfides come in contact with acids.

Antacid in Space. Expedition 43 Commander and NASA astronaut Terry Virts creates a sphere of bubbles in the station's microgravity environment using drinking water and an antacid tablet. Image catalogued by Johnson Space Center of the United States National Aeronautics and Space Administration (NASA) under Photo ID: ISS043-E-276537. Public Domain, Courtesy NASA/JPL-Caltech. .

One of the most familiar and most heavily advertised applications of acid–base chemistry is antacids, which are bases that neutralize stomach acid. The human stomach contains an approximately 0.1 M solution of hydrochloric acid that helps digest foods. If the protective lining of the stomach breaks down, this acid can attack the stomach tissue, resulting in the formation of an ulcer. Because one factor that is believed to contribute to the formation of stomach ulcers is the production of excess acid in the stomach, many individuals routinely consume large quantities of antacids. The active ingredients in antacids include sodium bicarbonate and potassium bicarbonate (NaHCO₃ and KHCO₃; Alka-Seltzer); a mixture of magnesium hydroxide and aluminum hydroxide [Mg(OH)₂ and Al(OH)₃; Maalox, Mylanta]; calcium carbonate (CaCO₃; Tums); and a complex salt, dihydroxyaluminum sodium carbonate [NaAl(OH)₂CO₃; original Rolaids]. Each has certain advantages and disadvantages. For example, Mg(OH)₂ is a powerful laxative (it is the active ingredient in milk of magnesia), whereas Al(OH)₃ causes constipation. When mixed, each tends to counteract the unwanted effects of the other. Although all antacids contain both an anionic base (OH⁻, CO₃²⁻, or HCO₃⁻) and an appropriate cation, they differ substantially in the amount of active ingredient in a given mass of product.

The pH Scale

One of the key factors affecting reactions that occur in dilute solutions of acids and bases is the concentration of H⁺ and OH⁻ ions. The pH scaleA logarithmic scale used to express the hydrogen ion $({\text{H}}^{+})$ concentration of a solution, making it possible to describe acidity or basicity quantitatively. provides a convenient way of expressing the hydrogen ion (H⁺) concentration of a solution and enables us to describe acidity or basicity in quantitative terms.

Pure liquid water contains extremely low but measurable concentrations of H₃O⁺(aq) and OH⁻(aq) ions produced via an autoionization reaction, in which water acts simultaneously as an acid and as a base:

The concentration of hydrogen ions in pure water is only 1.0 × 10⁻⁷ M at 25°C. Because the autoionization reaction produces both a proton and a hydroxide ion, the OH⁻ concentration in pure water is also 1.0 × 10⁻⁷ M. Pure water is a neutral solutionA solution in which the total positive charge from all the cations is matched by an identical total negative charge from all the anions., in which [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M.

The pH scale describes the hydrogen ion concentration of a solution in a way that avoids the use of exponential notation; pHThe negative base-10 logarithm of the hydrogen ion concentration: $\text{pH}=-\text{log}[{\text{H}}^{+}].$ is defined as the negative base-10 logarithm of the hydrogen ion concentration:pH is actually defined as the negative base-10 logarithm of hydrogen ion activity. As you will learn in a more advanced course, the activity of a substance in solution is related to its concentration. For dilute solutions such as those we are discussing, the activity and the concentration are approximately the same.

Conversely,

(If you are not familiar with logarithms or using a calculator to obtain logarithms and antilogarithms, consult Essential Skills 3 in Section 4.10 "Essential Skills 3 ".)

Because the hydrogen ion concentration is 1.0 × 10⁻⁷ M in pure water at 25°C, the pH of pure liquid water (and, by extension, of any neutral solution) is

Adding an acid to pure water increases the hydrogen ion concentration and decreases the hydroxide ion concentration because a neutralization reaction occurs, such as that shown in Equation 4.31. Because the negative exponent of [H⁺] becomes smaller as [H⁺] increases, the pH decreases with increasing [H⁺]. For example, a 1.0 M solution of a strong monoprotic acid such as HCl or HNO₃ has a pH of 0.00:

Conversely, adding a base to pure water increases the hydroxide ion concentration and decreases the hydrogen ion concentration. Because the autoionization reaction of water does not go to completion, neither does the neutralization reaction. Even a strongly basic solution contains a detectable amount of H⁺ ions. For example, a 1.0 M OH⁻ solution has [H⁺] = 1.0 × 10⁻¹⁴ M. The pH of a 1.0 M NaOH solution is therefore

For practical purposes, the pH scale runs from pH = 0 (corresponding to 1 M H⁺) to pH 14 (corresponding to 1 M OH⁻), although pH values less than 0 or greater than 14 are possible.

We can summarize the relationships between acidity, basicity, and pH as follows:

• If pH = 7.0, the solution is neutral.
• If pH < 7.0, the solution is acidic.
• If pH > 7.0, the solution is basic.

Keep in mind that the pH scale is logarithmic, so a change of 1.0 in the pH of a solution corresponds to a tenfold change in the hydrogen ion concentration. The foods and consumer products we encounter daily represent a wide range of pH values, as shown in Figure 4.15 "A Plot of pH versus [H".

Figure 4.15 A Plot of pH versus [H⁺] for Some Common Aqueous Solutions

Although many substances exist in a range of pH values (indicated in parentheses), they are plotted using typical values.

Tools have been developed that make the measurement of pH simple and convenient (Figure 4.16 "Two Ways of Measuring the pH of a Solution: pH Paper and a pH Meter"). For example, pH paper consists of strips of paper impregnated with one or more acid–base indicatorsAn intensely colored organic molecule whose color changes dramatically depending on the pH of the solution., which are intensely colored organic molecules whose colors change dramatically depending on the pH of the solution. Placing a drop of a solution on a strip of pH paper and comparing its color with standards give the solution’s approximate pH. A more accurate tool, the pH meter, uses a glass electrode, a device whose voltage depends on the H⁺ ion concentration.

Figure 4.16 Two Ways of Measuring the pH of a Solution: pH Paper and a pH Meter

Note that both show that the pH is between 1 and 2, but the pH meter gives a more precise value. Image Credit: Highland Community College, Freeport, IL.