Chapter 12 – Acid-Base Chemistry

Introduction

The terms acid and base have been used for several hundred years. Acids were substances that had a sour taste, were corrosive, and reacted with substances called bases. Substances that had a bitter taste, made skin slippery on contact, and reacted with acids were called bases. However, these simple definitions had to be refined as the chemical properties of acids and bases became better understood. The first chemical definition of acids and bases was made by Svante Arrhenius. An Arrhenius acid is a substance that produces H¹⁺ ions when it is dissolved in water, and an Arrhenius base is a substance that produces OH^1– ions when dissolved in water. In this theory, an acid ionizes in water much as an ionic substance, and the equilibrium constant for the reaction is called the acid ionization constant. For example, the ionization of the Arrhenius acid HCl in water is represented as follows: Neutralization is the reaction of an acid and a base to produce water and a salt. NaCl is a salt. Note that the cation of a salt is derived from the base and the anion from the acid. Arrhenius acid-base theory is very limited because its definitions are restricted to behavior in water. Consequently, broader definitions for these very important classes of compounds were developed. In this chapter, we examine the Lewis and the Brønsted-Lowry theories of acid-base chemistry. The Lewis theory is the broadest and is discussed first.

12.1 Lewis Acids and Bases

Introduction

The broadest definition of acids and bases is that of Lewis. By this definition, a large number of reactions can be classified as acid-base reactions. In this section, we introduce Lewis acids and bases and the use of curved arrows to show the mechanism of a Lewis acid-base reaction. These topics will be used again in Chapter 13, Organic Chemistry.

Prerequisites

• •
  5.6 Determining Lewis Structures (Draw Lewis structures.)
• •
  5.4 Lewis Symbols of the Elements (Identify lone pairs in a Lewis structure.)
• •
  6.1 Molecular Shapes (Determine the number of electron regions around each atom in a Lewis structure.)

Objectives

• •
  Define a Lewis acid and a Lewis base.
• •
  Describe a Lewis acid-base reaction.
• •
  Identify Lewis acids and bases.
• •
  Explain how curved arrows are used to show the mechanism of a Lewis acid-base reaction.
• •
  Distinguish between an electron transfer and a Lewis acid-base reaction.

12.1-1. Definitions

• •
  A Lewis acid is a substance that has an empty orbital that it can use to share a lone pair to form a bond.
• •
  A Lewis base is a substance that has a lone pair that it can share in a covalent bond.
• •
  A Lewis acid-base reaction is the conversion of the lone pair on the base and the empty orbital of the acid into a covalent bond between the acid and the base.

The product of a Lewis acid-base reaction is a covalent bond between the acid and the base. Both bonding electrons come from the base, so it is a coordinate covalent bond. A curved arrow from the lone pair to the atom with the empty orbital is used to show that the lone pair will become the bonding pair between the two atoms.

12.1-2. Lewis Acids and Bases

Lewis Bases

• •
  A Lewis base must contain at least one lone pair of electrons.
• •
  All anions are Lewis bases, but not all Lewis bases are anions.
• •
  The lone pair is frequently, but not always, located on oxygen or nitrogen atoms.
• •
  The strength of a base is increased by electron density.

The strength of the base depends upon the electron density in the region of the lone pair, the greater the electron density the stronger the base. Consequently, the strength of a base depends upon the groups around the lone pair. For example, consider the relative base strengths of the following, which are basic due to the lone pairs on the oxygen atom. CH₃O^1– is the strongest base because the CH₃ group pushes electron density onto the oxygen atom. ClO^1– is the weakest because the electronegative chlorine atom removes electron density from the oxygen. The top row of Figure 12.2 shows some Lewis bases that are molecules. In each case the lone pair resides on a nitrogen or oxygen atom, a common occurrence in Lewis bases that are molecules. Anions are also Lewis basic. The chloride anion is a very weak Lewis base, while the hydrogen sulfide ion (HS^1–) and the acetate ion (C₂H₃O₂^1–) are common weak Lewis bases.

Lewis Acids

Lewis acids are often more difficult to identify. The following should help.

• •
  A Lewis acid must be able to accommodate an additional electron region (the new bond), so, if it obeys the octet rule, a Lewis acidic atom must have less than four regions.
• •
  Attack by a lone pair is facilitated by positive charge, so Lewis acidity is strengthened by positive charge.
• •
  All cations are Lewis acids, but not all Lewis acids are cations.

The Lewis acidic sites in Figure 12.3, each of which contains less than four electron regions, are shown in red. AlCl₃ is electron deficient because aluminum has only six valence electrons. Molecules with electron deficient atoms are strong Lewis acids. SO₃ and CO₂ are not electron deficient, but the central atom in each has less than four electron regions (three around S and two around C), so they are Lewis acids. Their acidity is strengthened by positive formal charge. Cations such as Ag¹⁺ and H¹⁺ that have fairly low-energy empty orbitals are also good Lewis acids.

12.1-3. Lewis Acidity and Basicity and Orbital Energy

The bond between two atoms is covalent only when the interacting orbitals have similar energies because large energy separations favor ionic bonds. Thus, the formation of a coordinate covalent bond in a Lewis acid-base reaction is facilitated when the energy of the empty orbital of the Lewis acid is close to that of the lone pair of the Lewis base. The energies of lone pairs are typically lower than those of empty orbitals, so the strongest interactions occur when the energy of the lone pair is high for a lone pair and the energy of the empty orbital is low for an empty orbital. For example, consider the cases of Na¹⁺ and Ag¹⁺ as shown in the figure. The energy of the empty orbital of Ag¹⁺ is much lower than that of Na¹⁺; i.e., the energy of the empty orbital of Ag¹⁺ is low for an empty orbital. Thus, the empty orbital on Ag¹⁺ is sufficiently close to that of the lone pair on the Br^1– ion that the Ag–Br bond is covalent. However, the energy of the empty orbital on Na¹⁺ is so high that the Na–Br bond is ionic. Thus, Ag¹⁺ is a sufficiently strong Lewis acid to react with Br^1– ion, but the acidity of Na¹⁺ is so weak that it does not. Indeed, Na¹⁺ is such a weak Lewis acid (its orbitals are so high in energy) that it does not function as an acid in aqueous solutions. In general, H¹⁺ and cations of metals with high effective nuclear charge (metals such as Ag and Pb that lie low and to the right of the periodic table) have empty orbitals that are relatively low in energy, so they are Lewis acidic, but the cations of metals on the left side of the periodic table are such weak Lewis acids that their acidity can be ignored in most cases. We conclude the following.

12.1-4. Oxidants and Acids

Oxidizing agents and Lewis acids are both characterized by empty valence orbitals that are low in energy, while reducing agents and Lewis bases both have high-energy electrons. Consequently, many Lewis acids are also oxidants and many Lewis bases are also reductants. Indeed, oxidants and Lewis acids are often defined as electron acceptors, and reductants and Lewis bases as electron donors. The obvious question becomes, "What determines whether electrons are transferred or shared when a lone pair comes into contact with an empty orbital?" As has been the case so often in our study of chemistry, the answer lies in their relative energies: electrons do whatever is most efficient at increasing their electrical potential in order to lower their energy. If the energy of the empty orbital is lower than that of the lone pair, the electrons simply transfer from the reductant to the more positive electrical potential on the oxidant in a redox reaction. However, if the empty orbital is at higher energy, the electrons lower their energy by forming a covalent bond between an acid and a base, which increases their electrical potential by exposing them to part of the nuclear charge on the acid. The example of H¹⁺, which is both an oxidant and an acid, is considered in Figure 12.5. If H¹⁺ encounters a zinc atom, it behaves as an oxidant and accepts the higher energy electrons from the reductant zinc. However, electrons will not flow from a Br^1– ion to the higher energy orbital on H¹⁺, so the lone pair on Br^1– ion lowers its energy by forming an H–Br covalent bond. Br^1– is a base in the presence of H¹⁺, but it is a reductant in the presence of something like Cl₂ that has an empty orbital at lower energy (2 Br^1– + Cl₂ → Br₂ + 2 Cl^1–).

12.1-5. Curved Arrows in Lewis Acid-Base Reactions

Curved arrows always start on an electron pair and end on an atom, but their meaning depends upon whether the electron pair is a lone pair or a bonding pair.

Start of a Curved Arrow	End of a Curved Arrow	Reactant	Product	Effect
lone pair on atom B	atom A			The lone pair becomes an A–B bond.
A–B bonding pair	atom A			The A–B bond becomes a lone pair on atom A.

Table 12.1

Curved arrows will be used extensively in this chapter and the next chapter to explain the mechanisms of Lewis acid-base reactions.

12.1-6. Examples of Metals as Lewis Acids

Ag¹⁺ ions have relatively low-energy empty orbitals, so they are good Lewis acids. Cl^1– ions have lone pairs, so they are Lewis bases. In Figure 12.6a, a curved arrow from Cl^1– to Ag¹⁺ is used to show the conversion of a lone pair on the Cl^1– ion into the AgCl bond in this Lewis acid-base reaction. Silver ions also react with ammonia. Note that the red lone pair on the nitrogen in each ammonia is converted into a red Ag–N bond in Figure 12.6b. In Figure 12.6c, the aluminum atom of AlCl₃ has only six valence electrons and three electron regions surrounding it, so AlCl₃ is a strong Lewis acid. Note that during this reaction, Al goes from three electron regions and sp² hybridization to four electron regions and sp³ hybridization. The hybridization change from sp² to sp³ results in a geometry change from trigonal planar to tetrahedral. The following animation shows the geometry change. We conclude the following.

12.1-7. Curved Arrows in a Mechanism–an Example

The Lewis acid-base reaction between SO₃ and H₂O to form H₂SO₄ is the reaction that is the primary cause of acid rain. The oxygen atom of the water molecule contains two lone pairs, so water is a Lewis base, while the sulfur atom in SO₃ has only three electron regions, which makes SO₃ Lewis acidic. As shown in Figure 12.7a, a lone pair on the oxygen atom in water is shared with the sulfur atom to form a new S–O bond. Simultaneously, the the pi electrons in the S=O bond are converted into a lone pair on the oxygen (curved arrow from the bond to the atom), and the hybridization of the sulfur atom goes from sp² to sp³ (from trigonal planar to tetrahedral). The resulting structure places positive formal charge on the oxygen atom, which is eliminated by transferring a proton from that oxygen atom to one that carries negative formal charge. The proton transfer is accomplished with two acid-base reactions with the solvent. In the first, a proton is transferred from the oxygen atom with positive formal charge to a solvent molecule (water) as shown in Figure 12.7b. In the final step, a proton is transferred from the solvent to an oxygen atom with negative formal charge as shown in Figure 12.7c. The H₃O¹⁺ produced in step 2 and the OH^1– produced in this step would then undergo proton transfer reactions to produce 2 H₂O. The final product has the correct structure of sulfuric acid.

12.1-8. Comparing Redox and Lewis Acid-Base Reactions

Compare the definitions of the reactants involved in Lewis acid-base and redox reactions.

• •
  Reductant: a substance that can transfer electrons to another substance. Good reducing agents are characterized by high-energy electrons.
• •
  Lewis base: a substance that can donate an electron pair to a covalent bond with another substance. Good Lewis bases are characterized by high-energy electron pairs.
• •
  Oxidant: a substance that can accept electrons from another substance. Good oxidizing agents are characterized by low-energy, empty orbitals.
• •
  Lewis acid: a substance that can accept an electron pair into an empty orbital to form a covalent bond. Good Lewis acids are characterized by low-energy, empty orbitals.

The only difference between the two reaction types is that one transfers, while the other shares electrons between the two reactants.

12.2 Brønsted Acids

Introduction

Although the Lewis definition is the broadest, the Brønsted-Lowry (or simply Brønsted) definition is the most frequently used acid-base definition in aqueous solutions. In this section, we define Brønsted acids and bases and introduce Brønsted acid-base reactions.

Prerequisites

• •
  10.5 Electrolytes (Differentiate between strong electrolytes and nonelectrolytes based upon the ability of their aqueous solutions to conduct electricity.)

Objectives

• •
  Write the name of an acid from its formula or the formula from its name.

12.2-1. Brønsted Definition

A Brønsted acid is a proton donor, a Brønsted base is a proton acceptor, and a Brønsted acid-base reaction is a proton transfer from the acid to the base. Thus, the electron pair is the point of reference in Lewis theory, while the proton is the point of reference in Brønsted theory. The Brønsted definition is a special case of the Lewis definition. In each, a base contains a lone pair that it shares with the acid to form a covalent bond. Any Brønsted base is a Lewis base and vice versa. However, a Lewis acid is any species that can accept a lone pair, but the lone pair acceptor must be a proton in the Brønsted definition, and the substance that contains the proton is a Brønsted acid.

12.2-2. Aqueous Solutions of Acids and Base

In the Brønsted definition, acids transfer a proton to water, which is a weak Brønsted base, to produce hydronium ions (H₃O¹⁺). It is the concentration of H₃O¹⁺ that dictates how acidic an aqueous solution is. Thus, if the above reaction with water is extensive, the concentration of H₃O¹⁺ is relatively high as essentially all of the HX is converted to H₃O¹⁺. Such acids are strong acids. If its reaction with water is not extensive,the concentration of H₃O¹⁺ is relatively low as only a small portion of the acid is converted into H₃O¹⁺, and such acids are called weak acids. Similar considerations can be made for bases. It is the hydroxide ion concentration that determines the basicity of an aqueous solution. Thus, a strong base, such as KOH, is one that is converted extensively into hydroxide ions in water: KOH → K¹⁺ + OH^1–. A weak base, such as fluoride ion, reacts only slightly with water to produce hydroxide ions:

F¹⁻ + H₂O HF + OH¹⁻.

12.2-3. Acids and Bases are Electrolytes

If HX is a strong acid, then it is converted completely into H₃O¹⁺ and X^1– ions in water. The presence of these ions makes the acid a strong electrolyte. However, if HX does not react completely with water, then only small concentrations of the ions are produced. In this case, HX is a weak electrolyte. Similarly, strong bases are strong electrolytes and weak bases are weak electrolytes. Recall from Section 10.5 that electricity is conducted through a solution of an electrolyte but not through a solution of a nonelectrolyte. Indeed, the brightness of the light is indicative of the ion concentration in solution. Consider the following possibilities for an acid or base.

	The light bulb does not glow, so there are no ions in solution. The fact that HX produces no ions in solution indicates that HX is a nonelectrolyte. An aqueous solution is represented as HX to show that the molecules do not ionize in water.
	The light shines brightly, which means that the concentration of H3O1+ ions in solution is relatively high. Acids that ionize completely in water to produce high concentrations of H3O1+ ions are called strong acids. An aqueous solution is represented as H3O1+ + X1– to show that the molecules ionize completely in water.
	The light shines, so HX is an electrolyte, but the intensity of the light is much less than for a strong acid. The dimness of the light indicates that the H3O1+ ion concentration is low. Thus, only a fraction of the HX molecules in water ionize. Acids that ionize only partially in water are called weak acids. An aqueous solution is represented as HX because HX is the predominant species in solution.

Table 12.2: Determining the Relative Concentrations of H₃O¹⁺ Ions in a 0.1 M of HX

12.2-4. Examples

pure H2O		Water is a nonelectrolyte and represented as H2O. There are ions in water, but their concentrations are very small.
0.10 M HNO3		Nitric acid is a strong acid, and its aqueous solution is represented as H3O1+(H1+) + NO31–. The following reaction is so extensive that there are essentially no nitric acid molecules in solution. Recall that extensive reactions are expressed with single arrows as in the following. HNO3 + H2O → H3O1+ + NO31–
0.10 M KOH		KOH ionizes completely in water and is a strong electrolyte. It is a strong base because one of the ions that it produces is the OH1– ion. Thus, aqueous KOH is written as K1+ + OH1–.
0.10 M CH3OH		CH3OH is a nonelectrolyte. It is neither an acid nor a base—it is an alcohol (wood alcohol). An aqueous solution of methanol is written as CH3OH.
0.10 M HNO2		The light bulb glows dimly, so nitrous acid is a weak acid and its aqueous solutions are represented as HNO2, not as hydronium ion and nitrite ion, to show the predominant form. The following reaction is not extensive (only about 5% of the HNO2 molecules react), so double arrows are used. HNO2 + H2O H3O1+ + NO21–
0.10 M NH3		The light bulb glows dimly, so NH3 is a weak electrolyte. About 1% of the ammonia molecules react with water to produce ions, so an aqueous solution is represented as NH3 molecules, not as the ions. Double arrows are used in the reaction. NH3 + H2O NH41+ + OH1– The proton is transferred from water to ammonia, so NH3 is a weak base.

Table 12.3

12.2-5. Brønsted Acids

In order for HX to be acidic, the H–X bond must break to produce H¹⁺ and X^1– ions, but that can happen only if it is a polar bond. Thus, a hydrogen atom must be covalently bound to a highly electronegative atom to be acidic. There are a great number of compounds with hydrogen atoms covalently bound to atoms that are not very electronegative, but these compounds are not Brønsted acids. The most common examples are organic compounds because the C–H bond is not polar (C and H have very similar electronegativities). For example, the C–H bonds in CH₄ do not produce H¹⁺ when they break, so CH₄ cannot be a Brønsted acid. The H–Cl bond is very polar, so breaking the H–Cl bond does produce H¹⁺ ions, which makes HCl a Brønsted acid. For example, the chemical formulas of the hydrogen sulfate ion and perchloric acid are written as HSO₄^1– and HClO₄ to demonstrate that they are acids, while the formulas of methane and ammonia are written CH₄ and NH₃ to indicate that they have no acidic protons. However, writing the formulas this way can be misleading because it often places the proton next to an atom to which it is not bound. The acidic protons in HSO₄^1– and HClO₄ are both attached to oxygen atoms. Acetic acid is written HC₂H₃O₂ to indicate that it is an acid that has only one acidic proton. Once again, the acidic proton is also bound to an oxygen atom, not the carbon, while the other hydrogen atoms are attached to the carbon and are not acidic. Consequently, acetic acid is often written as CH₃COOH, which indicates an O–H bond and better represents the true structure of the acid. Similarly, H₂SO₄ contains two O–H bonds but no S–H bonds.

12.2-6. Binary Acids and Oxoacids

Binary Acids

Binary acids have a proton and only one other element. HCl, HBr, and HI are strong acids, but HF is a weak acid. Note: these acids plus NH₄¹⁺, H₂S, and H–CN are the only acids that we deal with that do not have O–H bonds.

• •
  Note that HCN is not a binary acid because it contains atoms from three different elements. However, HCN is a gas and its name (hydrogen cyanide) ends in -ide, so it is treated as a binary compound.

Oxoacids

Most acidic protons are bound to an oxygen atom. Such acids are called oxoacids. The acidic protons are shown in blue in Figure 12.12.

Naming Acids

12.2-7. Binary Acids

The pure compounds that produce binary acids are named using the rules outlined in Section 4.6 until they are dissolved in water. For example, HCl is hydrogen chloride and H₂S is hydrogen sulfide. However, when these substances are dissolved in water, they produce acidic solutions that are named in the following manner.

• •
  Replace hydrogen with hydro.
• •
  Change the -ide ending to -ic.
• •
  Add the word acid.

Formula	Name as Pure Substance		Formula	Name as Aqueous Solution
HF(g)	hydrogen fluoride		HF(aq)	hydrofluoric acid
HCl(g)	hydrogen chloride		HCl(aq)	hydrochloric acid
HI(g)	hydrogen iodide		Hl(aq)	hydroiodic acid
HCN(g)	hydrogen cyanide		HCN(aq)	hydrocyanic acid
H2S(g)	hydrogen sulfide		H2S(aq)	hydrosulfuric acid

Table 12.4: Names of Some Common Binary Acids

12.2-8. Polyatomic Acids

Polyatomic acids are derived from polyatomic ions and are named by

• •
  changing the -ate ending of the polyatomic ion to -ic or
• •
  changing the -ite ending of the polyatomic ion to -ous and
• •
  adding the word acid.

If the acid is also an ion, its name is unchanged. For example, the HPO₄^2– and H₂PO₄^1– ions are the monohydrogen phosphate ion and dihydrogen phosphate ion, respectively. In an older, but still common, method, ions with acidic protons are named by using the prefix 'bi' instead of the word 'hydrogen.' Thus, HSO₄^1– is either hydrogen sulfate or bisulfate.

Ion Formula	Ion Name		Acid Formula	Acid Name
C2H3O21–	acetate ion		HC2H3O2	acetic acid
SO32–	sulfite ion		H2SO3	sulfurous acid
SO42–	sulfate ion		H2SO4	sulfuric acid
NO21–	nitrite ion		HNO2	nitrous acid
NO31–	nitrate ion		HNO3	nitric acid
ClO1–	hypochlorite ion		HClO	hypochlorous acid
ClO21–	chlorite ion		HClO2	chlorous acid
ClO31–	chlorate ion		HClO3	chloric acid
ClO41–	perchlorate ion		HClO4	perchloric acid
PO43–	phosphate ion		H3PO4	phosphoric acid

Table 12.5: Acids Derived from Polyatomic Anions

12.2-9. Acid Naming Exercise

12.3 Brønsted Acid-Base Reactions

Introduction

Brønsted acid-base reactions all involve transferring a single proton from the acid to the base. In this section, we see how to predict the products of a Brønsted acid-base reaction.

Objectives

• •
  Identify the conjugate base of an acid.
• •
  Identify the conjugate acid of a base.
• •
  Describe a Brønsted acid-base reaction in terms of the proton transfer.

12.3-1. Conjugate Base

After the acid loses a proton, it becomes a base because the species it becomes can gain the proton back. The loss of a single proton converts an acid into its conjugate base. It is important to realize that an acid and its conjugate base differ by one, and only one proton. All Brønsted reactions involve the transfer of a single proton. Thus, the acid is always converted to it conjugate base in a Brønsted reaction. The charge on the conjugate base is always lower than that on the acid by one because the acid loses H¹⁺.

12.3-2. Conjugate Acid

After the base gains a proton, it becomes an acid because the species it becomes can donate the proton back. The gain of a single proton converts a base into its conjugate acid. All Brønsted reactions involve the transfer of a single proton. Thus, the base is always converted into its conjugate acid in a Brønsted reaction. The charge on the conjugate acid is always greater than that on the base by one because the base gains H¹⁺. A base and an acid that differ by one, and only one proton, are said to be a conjugate acid-base pair.

12.3-3. Brønsted Acid-Base Reactions

Brønsted acid-base reactions convert the reacting acid into its conjugate base and the reacting base into its conjugate acid. The chemical equation for a Brønsted acid-base reaction consists of two conjugate acid-base pairs and nothing else. Consider the following proton transfer reaction: HCN + NH₃ → CN^1– + NH₄¹⁺. The proton transfer converts the reacting acid (HCN) into its conjugate base (CN^1–) and the reacting base (NH₃) into its conjugate acid (NH₄¹⁺). The products of an acid-base reaction are also an acid and a base, so the substances on the right of the chemical equation also react to produce those on the left: CN^1– + NH₄¹⁺ → HCN + NH₃. In this particular reaction, the probability that a collision between the acid and the base results in an acid-base reaction is about the same in either direction. The fact that the back reaction is important is demonstrated with the use of double arrows in the chemical equation: HCN + NH₃ CN^1– + NH₄¹⁺.

12.4 Extent of Proton Transfer

Introduction

Not all acids and bases react very well with one another, and the degree to which they do react is referred to as the extent of proton transfer. If the extent of proton transfer is great, the reaction is usually written with a single arrow, but if the transfer is not extensive, the reaction is written with double arrows.

Prerequisites

• •
  9.11 Equilibrium and the Equilibrium Constant

Objectives

• •
  Write the chemical equation for the reaction of a strong acid, a weak acid, or a weak base with water.

12.4-1. Comparing Conjugate Acid-Base Strengths

The strength of an acid is related to the ease with which it donates its proton to become its conjugate base, and the strength of a base is related to its ability to accept a proton to become its conjugate acid. If A^1– is a strong base, then it must bind a proton strongly when it forms HA, and if its proton is bound strongly, then HA must be a weak acid. We conclude that the strength of a base varies inversely with the strength of its conjugate acid, i.e., strong acids have weak conjugate bases and vice versa. Consider the following acid-base reaction. If HA is the stronger of the two acids, then A^1– must be the weaker of the two bases due to the inverse relationship between conjugate acid-base strengths. This means that the stronger acid is always on the same side of the chemical equation as the stronger base. Similarly, the weaker acid and base are also on the same side of the equation. Consequently, there are only three possible combinations in Brønsted acid-base reactions:

• 1
  stronger acid + stronger base → weaker base + weaker acid
• 2
  reacting and produces acids of comparable strengths and reacting and produced bases of comparable strengths
• 3
  weaker acid + weaker base → stronger base + stronger acid

12.4-2. Extent as a Function of Relative Acid Strengths

• •
  Forward Reaction: stronger acid + stronger base is extensive.
• •
  Reverse Reaction: weaker acid + weaker base produces little of the stronger acid and base.
• •
  Equilibrium: almost exclusively the weaker acid and base, which are the products in this reaction type.
• •
  A single arrow typically used to indicate that very little of the limiting reactant is present at equilibrium.

• •
  Forward Reaction: moderate acid + moderate base produces moderate amounts of products.
• •
  Reverse Reaction: moderate acid + moderate base produces moderate amounts of reactants.
• •
  Equilibrium: moderate amounts of all species.
• •
  All species present in significant amounts at equilibrium, so reaction is not extensive and double arrows should be used.

• •
  Forward Reaction: weaker acid + weaker base produces little of the stronger base and stronger acid.
• •
  Reverse Reaction: stronger acid + stronger base react extensively to produce weaker acid and base.
• •
  Equilibrium: almost exclusively the weaker acid and base, which are the reactants in this reaction type.
• •
  Little product, but some product is formed as there is some reaction, and double arrows would have to be used when writing the chemical equation.

12.4-3. Relative Acid Strength Exercise

12.4-4. Equilibrium Constant Expression

We now examine the equilibrium mixture that results from mixing equal amounts of HA and B^1– as a function of the relative acid strengths of HA and HB.

HA >> HB; K >> 1

Stronger Acid		Stronger Base		Weaker Base		Weaker Acid
HA	+	B1–	→	A1–	+	HB

At equilibrium, [A^1–][HB] >> [HA][B^1–], so K >> 1, consistent with an extensive reaction. Note: A^1– is the weaker base and HB is the weaker acid!

HA ~ HB; K ~ 1

Acid		Base		Base		Acid
HA	+	B1–		A1–	+	HB

[A^1–][HB] ~ [HA][B^1–] at equilibrium, so K ~ 1 when the reacting and produced acids are of similar strengths.

HA << HB; K << 1

Weaker Acid		Weaker Base		Stronger Base		Stronger Acid
HA	+	B1–		A1–	+	HB

At equilibrium, [HA][B^1–] >> [A^1–][HB], so K << 1, consistent with a reaction that in not extensive. Note that HA is the weaker acid and B^1– is the weaker base. In each case where the acid strengths are much different, the product of the equilibrium concentrations of the weaker acid and base are always much greater than the product of the concentrations of the stronger acid and base. That is, the equilibrium mixture is dominated by the weaker acid and base.

12.4-5. Single vs. Double Arrows

When K >> 1, the amount of product formed can be determined without use of the equilibrium constant because the equilibrium concentration of at least one of the reactants will be negligible. Reactions of this type are frequently written with single arrows (→) rather than the double equilibrium arrows to emphasize that the reverse reaction occurs only to a negligible extent. Although the value of K at which the reverse reaction can be ignored varies with the concentrations of the reactants, we will use a value of ~1000 in our discussions. Thus, a single arrow can be used for reactions in which

K > ~1000.

If

K < 1000,

the reverse reaction cannot be ignored, and the value of K must be used when determining the amount of product that is formed. Equations for reactions of this type should be written with double arrows () to emphasize the importance of the reverse reaction. An example of each case is provided in the following table.

HF + ClO1− → F1− + HOCl	K = [F1−][HOCl] [HF][OCl1−] = 2 × 104	K >> 1 so, The reaction (or proton transfer) is extensive. The reacting acid (HF) is a much stronger acid than the produced acid (HClO). The equilibrium concentrations of F1– and HClO are much greater than those of HF + OCl1–. The reaction is frequently written with a single arrow.
HF + NO21− F1− + HNO2	K = [F1−][HNO2] [HF][NO21−] = 2	K ~ 1 so, The reaction is not extensive in either direction. The strengths of the reacting and produced acids are comparable. The equilibrium concentrations of reactants and products are similar. The reaction is written with double arrows.
HCN + F1− CN1− + HF	K = [CN1−][HF] [HCN][F1−] = 6 × 10−7	K << 1 so, The forward reaction is not extensive, but the reverse reaction is. The reacting acid (HCN) is much weaker than the produced acid (HF). The equilibrium concentrations of HF and F1– are much greater than those of CN1– and HF. The reaction is written with double arrows.

Table 12.6

12.4-6. Proton Transfer Exercise

Acid-Base Reactions Involving Water

12.4-7. The Role of Water

All of the remaining acid-base reactions in this chapter occur in water, which can act as both as an acid and a base. Thus, the reaction with water is an important consideration in acid-base chemistry. The general reaction of an acid and water can be represented as the following.

• •
  Strong acids: Strong acids react extensively with water. In order for the reaction to be extensive, HA must be a stronger acid than H₃O¹⁺. In other words, any acid stronger than hydronium ion is considered to be a strong acid.
• •
  Weak acids: Weak acids do not react extensively with water. Thus, weak acids are weaker acids than H₃O¹⁺ ions.

12.4-8. Strong Acids in Water

The strong acids are those that are stronger than H₃O¹⁺. Thus, their reaction with water is one where the reacting acid is stronger than the produced acid, i.e., the reaction is so extensive that it is usually written with a single arrow. The common strong acids are HClO₄, HCl, HBr, HI, HNO₃, and H₂SO₄. Hydronium ion is the strongest acid that can exist in water because any acid stronger than hydronium reacts extensively with the water to produce hydronium ion. This effect is known as the leveling effect because the strengths of the strong acids are all leveled to that of hydronium ion. Due to the leveling effect, strong acids are all represented by H₃O¹⁺ in acid-base reactions in water. The conjugate bases of the strong acids are all too weak to react as Brønsted bases in aqueous solution. Thus, the ClO₄^1–, Cl^1–, Br^1–, I^1–, and NO₃^1– ions should be treated as spectator ions in aqueous Brønsted acid-base reactions. The HSO₄^1– does not react as a Brønsted base in water, but it can react as a weak acid. Hydrochloric acid, which is an aqueous solution of HCl, is a strong acid, but there are essentially no HCl molecules in hydrochloric acid solution because the above reaction is so extensive. Hydronium ion is a strong acid, but chloride ion is such a weak Brønsted base that it can be ignored in Brønsted acid-base reactions. Consequently, hydrochloric acid is represented as H₃O¹⁺ + Cl^1– ions in aqueous solutions.

12.4-9. Weak Acids in Water

Weak acids are those acids weaker than H₃O¹⁺. Thus, their reaction with water is one in which the produced acid is stronger than the reacting acid, i.e., the following reaction is not extensive. The reverse reaction between hydronium ion and the conjugate base of the weak acid is the extensive reaction, so

K < 1.

The reactions are written with double arrows to emphasize the importance of the back reaction. The concentration of HA is much greater than that of A^1– or H₃O¹⁺ in a solution of a weak acid. Consequently, weak acids are represented by the formula of the acid not by H₃O¹⁺ in acid-base reactions. The example of hydrofluoric acid is considered below. The hydronium ion is a much stronger acid than HF, so the reverse reaction is much more extensive than the forward reaction. Consequently, K < 1, and very little HF reacts. Less than 10% of the HF molecules in a typical HF solution react to produce H₃O¹⁺ ions, so the solution is represented by HF not by H₃O¹⁺.

12.4-10. Bases in Water

Water is also used as the reference acid in determining relative base strengths. The reaction of a base (A^1–, the conjugate base of HA) with water can be represented as follows: A^1– + H₂O HA + OH^1–.

• •
  Strong Bases: A^1– is a strong base if the above reaction is extensive, which is the case when the base is a stronger base than hydroxide ion.
• •
  Weak Bases: A^1– is a weaker base than hydroxide ion, so it does not react extensively with water.

O^2– and NH₂^1– are strong bases. However, OH^1– is the strongest base that can exist in water because the above reaction is extensive when A^1– is a strong base. Metal hydroxides are the most common strong bases. All anions are bases because an anion can always accept a proton. However some bases are molecular and the common example of ammonia is considered below. The above reaction is not extensive in the forward direction, which is demonstrated with the use of double arrows, because ammonia is a weak base. Only about 1% of NH₃ molecules in a typical aqueous solution react with water to produce NH₄¹⁺ + OH^1–, so an aqueous solution of ammonia is represented as NH₃.

12.5 Acid and Base Strengths

Introduction

We have now seen that the extent of an acid-base reaction depends upon the relative strengths of the reacting and produced acids. In this section, we show how the relative strengths of acids are measured and tabulated.

Prerequisites

• •
  4.4 Oxidation States
• •
  5.1 The Covalent Bond

Objectives

• •
  Relate acid strength of HA to the strength of the H–A bond.
• •
  Explain why the acid strength of HA also depends upon the electronegativity of A.
• •
  Predict the stronger of two acids with comparable bond strengths from the electronegativity of the atom to which the H is bound.
• •
  Rate the relative strengths a series of oxoacids (HOX) based on the electron withdrawing or donating abilities of X.

12.5-1. Bond Strengths

Knowledge of the relative acid strengths of the reacting and produced acids allow us to predict the extent of reaction, so we now examine the factors that dictate those strengths. The acid strength of HA is related to the ease with which the H–A bond is broken. If the H–A bond is weaker, then HA gives up the proton more easily and is a stronger acid, but if the bond is stronger, then it does not give up the proton as readily and is a weaker acid. Other factors being equal, we can conclude the following.

12.5-2. Bond Breaking

Bond energies are not sufficient to explain relative acid strengths because the tabulated values are for the bonds in the gas phase, not in solution. In addition, the bonding pair is divided between the bound atoms to produce atoms, not ions. The bond energy process is compared to the solution process for HF, HCl, and CH₄ in Figures 12.15a and 12.15b. Note that the H–C bond is not polar, so it cannot break to produce ions, which is why hydrogen atoms attached to carbon are not acidic. We conclude that the hydrogen atom must be attached to an atom that is more electronegative than carbon in order to be acidic.

12.5-3. Electronegativity

Breaking the H–A bond in an acid-base reaction produces the ions, and ion formation is favored by large electronegativity differences between the bound atoms. Thus, acid strengths also increase as the electronegativity of the atom to which the hydrogen is bound increases.

12.5-4. Oxoacid Strengths

Oxoacids are acids in which the acidic hydrogen is attached to an oxygen atom. The strength of the oxoacid H–O–X depends upon the strength of the H–O bond. Anything that withdraws electron density from the H–O bond, weakens the bond and makes the acid stronger. Thus, the strength of the acid increases with increases in the electronegativity or oxidation state of X.

• •
  If X is highly electronegative, it withdraws electron density of the O–H bond, which weakens the bond and makes the acid stronger. Thus, H₂SO₄ is a stronger acid than H₂SeO₄ because S is more electronegative than Se.
• •
  The ability of X to withdraw electron density from the O–H bond also increases as its oxidation state increases. Thus, H₂SO₄ is a stronger acid than H₂SO₃ because the oxidation state of S is higher in H₂SO₄.

In Table 12.7, we consider four compounds with the general X–OH, where X = H, CH₃, Cl, and ClO. There are two lone pairs and a proton on the oxygen atom, so XOH can function as either an acid or a base depending upon the properties of X.

HOH	H–O–H (water) is both a very weak acid and a very weak base. In fact its acid and base strengths are equal.
HOCH3	CH3 groups are electron donating, so the oxygen atom is more electron rich than in water. Consequently, CH3OH is a better base than water. Alternatively, the added electron density in the O–H bond strengthens the bond, which makes CH3OH a weaker acid than water.
HOCl	Cl is electron withdrawing and is more electronegative than H. Removing electron density from OH has two effects: the oxygen is not as electron rich, so HOCl is a weaker base, and the O–H bond is weakened, so HOCl is a stronger acid. Thus, HOCl is a stronger acid and weaker base than water.
HOClO	OClOH (HClO2) is the strongest acid and weakest base in this group. This is because the additional oxygen atom removes even more electron density than the single Cl, so it is a stronger acid than HOCl. Alternatively, the oxidation state of Cl goes from +1 in HClO to +3 in HClO2. The increase in oxidation state withdraws electron density from OH, which makes it a weaker base and a stronger acid.

Table 12.7

12.5-5. Example

12.6 Acid Dissociation Constant, K_a

Introduction

The extent of an acid-base reaction depends upon the strengths of the reacting and produced acids, and the acid dissociation constants of the acids give us those relative strengths.

Prerequisites

• •
  9.11-2. Examples of Equilibrium Constant Expressions (Write the equilibrium constant expression for a reaction that involves both aqueous solutes liquid water.)
• •
  9.11 Equilibrium and the Equilibrium Constant

Objectives

• •
  Write the acid dissociation constant expression for an Arrhenius acid and the chemical equation to which it applies.
• •
  Rate the relative acid strengths of series of Arrhenius acids given their acid dissociation constants.
• •
  Write the acid dissociation constant expression for a Brønsted acid and the chemical equation to which it applies.
• •
  Rate the relative acid strengths of series of Brønsted acids given their acid dissociation constants.
• •
  Determine the equilibrium constant for an acid-base reaction from the acid dissociation constants of the reacting and produced acids.

12.6-1. Arrhenius Definition

An Arrhenius acid is a substance that contains H atoms and produces H¹⁺ in water, and an Arrhenius base is a substance that contains OH and produces OH^1– in water. All Arrhenius acids and bases are also Brønsted acids and bases, but the Brønsted definition is slightly broader, so not all Brønsted acids and bases are classified as Arrhenius acids and bases. For example, NH₃ is a Brønsted base but not an Arrhenius base. Arrhenius acids "ionize" in water to produce H¹⁺ rather than react with it to produce H₃O¹⁺. The extent of the reaction is dictated by the strength of the acid and is measured by the equilibrium constant, which is called the acid dissociation or acid ionization constant and given the symbol K_a.

12.6-2. Brønsted K_a

Brønsted Definition of Acid Strength

Brønsted acids do not dissociate in water, they react with it, so the equilibrium reaction becomes

HA + H₂O H₃O¹⁺ + A^1–.

The equilibrium constant for the reaction is the following. Water is the solvent and considered to be a pure liquid, so it enters the equilibrium expression as 1 (one). Note that this is the same dissociation constant (K_a) as given for Arrhenius acids except that H₃O¹⁺ appears instead of H¹⁺, but H₃O¹⁺ and H¹⁺ are just two way of representing the same species in the two different theories. The important thing to remember is that acids with large K_a values are stronger than acids with smaller K_a values, regardless of whether the acid is treated as an Arrhenius acid or as a Brønsted acid. HCl is a strong acid (K_a >> 1). There are essentially no HCl molecules in a 0.1 M solution of HCl. The reverse reaction can be ignored when calculating the concentration of H₃O¹⁺ or Cl^1– because K_a is so large. Consequently, the reaction is usually indicated with a single arrow. HClO is a weak acid. In a 0.1 M solution of HClO, [H₃O¹⁺] = 10^–4 M. The reverse reaction is important in determining the concentrations of H¹⁺ and Cl^1–, so the double equilibrium arrows are used when writing the K_a equation. H₂SO₃ is a weak diprotic (contains two protons) acid. In a 0.1 M solution of H₂SO₃, [H₃O¹⁺] = 0.04 M. The importance of the reverse reaction is indicated with the double arrows. Note that only one proton is removed in the K_a equation. The conjugate base of H₂SO₃ is HSO₃^1–, which is also an acid with its own K_a (1.0 × 10^–7). HS^1– is a very weak acid. In a 0.1 M solution of HS^1–, [H₃O¹⁺] = 10^–7 M. Hydronium ion is the strongest acid that can exist in water. HCl is a stronger acid, but it cannot exist in water because it reacts so extensively with the water.

12.6-3. Determining K for an Acid-Base Reaction

The equilibrium constant for any acid-base reaction can be determined from the K_a values of the reacting and produced acids as shown in Equation 12.1. Recall that we are using the general guideline that acid-base reactions in which K > ~1000 are so extensive that the back reaction can be ignored in calculations, and they can be written with single arrows. This means that the reacting acid must be about 1000 times stronger than the produced acid if an acid-base reaction is considered to be so extensive that the back reaction can be ignored in calculations.

12.6-4. Determining K Exercise

12.6-5. Predicting Extent Exercise

12.7 Solutions of Weak Bases

Introduction

Water is also an acid, so it can react with weak bases to produce hydroxide ion and the conjugate acid of the weak base.

12.7-1. Most Anions are Weak Bases

Consider the reaction of hypochlorite ion, a weak base, with water: ClO^1– + H₂O(l) HClO(aq) + OH^1–. The reaction of a base with water breaks an O–H bond in water in a process called hydrolysis. Most weak bases are found as salts, so salts such as KClO, NaF, KCN, and LiNO₂ all form basic solutions in water because their anions react with water to produce hydroxide ion.

12.8 Acid Base Table

Introduction

Acid-base reactions are extensive when the reacting acid is stronger than the produced acid. Acid strengths are measured by the acid dissociation constants for the acids. Combining these two facts, we can now write equations for acid-base reactions and determine if they are extensive.

Objectives

• •
  Predict whether an acid-base reactions is extensive based on the positions of the acid and base in the acid-base table.
• •
  Identify the reactants to be used in a net equation for an acid-base reaction.
• •
  Use the acid base table to write equations for acid-base reactions and to determine the equilibrium constant for the reaction.
• •
  Decide whether an acid-base reaction is better represented with a single or a double arrow.

12.8-1. Using an Acid-Base Table Video

12.8-2. Using the Acid-Base Table to Write Chemical Equations

12.8-3. Acid-Base Table

Acid base reactions are extensive when the reacting acid is stronger than the produced acid, and the relative acid strengths can be deduced from the acid dissociation constants. Consequently, tables of acids and their K_a values are common. The acid-base table used in the text includes the acid, its K_a, and its conjugate base. Thus, both the reactants and the products of an acid-base reaction can be found in the table. The acid-base table used in this text is given in the Acid-Base Table resource. It lists the acids in the left column, their K_as in the center column, and their conjugate bases in the right column. Acid strengths decrease and base strengths increase going down the table. This arrangement puts the strongest acid (HClO₄) in the upper left corner and the strongest base (O^2– ion) in the lower right corner. Therefore, consider the following. The following examples show how the relative positions of the acid and base allow us to predict whether an acid-base reaction is extensive. HA is a stronger acid than HB, so it lies above HB in the acid-base table. B^1– is a stronger base than A^1–, so it lies below A^1– in the acid-base table. Reaction of the stronger acid (HA) with the stronger base (B^1–) is favorable (K > 1). Note that this arrangement guarantees that the reacting acid is stronger than the produced acid. If the reacting acid is well above the reacting base (or produced acid), the reaction is so extensive that it can be written with a single arrow. For example,

HF + OH^1– → F^1– + H₂O.

Reaction of the weaker acid (HB) with the weaker base (A^1–) is not extensive. Note that the reacting acid is below (weaker than) the produced acid. Only a small fraction of the acid is converted to its conjugate base (B^1–), and only a small fraction of the base is converted to its conjugate acid (HA). The back reaction of the stronger acid and base is important in determining the concentrations of B^1– and HA, so the net equation is usually written with double arrows. For example, HCN + F^1– CN^1– + HF.

12.8-4. Acid-Base Table Examples

We now use the acid-base table to write chemical equations for the acid-base reactions that result when the following solutions are mixed and use Equation 12.1

K =

Ka of reacting acid

Ka of produced acid

to determine their equilibrium constants. We use the relative positions of the reactants in the table and the equilibrium constants to indicate whether the reactions are extensive. Remember that the acid strengths increase going up the table, but base strengths increase going down the table. View the Acid-Base Table resource.

Hydrogen chloride gas is bubbled into water.

The relative reactant positions and their K_a values from the table in the resources are given in Figure 12.17a. Note that the reactant is hydrogen chloride, not hydrochloric acid, so the reacting acid is HCl. The reacting base is then water. The products of the reaction are Cl^1–, the conjugate base of the reacting acid, and H₃O¹⁺, the conjugate acid of the reacting base. The acid is above the base, so we expect a favorable reaction. Note that the K_a values of the strong acids are given simply as << 1 because they are so large that they cannot be determined accurately. We use Equation 12.1

K =

Ka of reacting acid

Ka of produced acid

to determine that the value of the equilibrium constant is very large, so a single arrow should be used. Thus, dissolving

HCl(g)

in water produces hydrochloric acid, which is a solution of hydronium and chloride ions.

Solutions of hydrocyanic acid and potassium nitrite are mixed.

We identify HCN as the reacting acid, K¹⁺ as a spectator ion, and the NO₂^1– ion as the reacting base. The reactants and their K_a values as determined from the acid-base table are given in Figure 12.17b. The reacting acid is below the reacting base, so little proton transfer is expected. Using Equation 12.1

K =

Ka of reacting acid

Ka of produced acid

, we determine that the equilibrium constant is only 1.0 × 10^–6, so very little product would form and double arrows would have to be used in the chemical equation.

A solution of potassium hypochlorite is added to hydrochloric acid.

We identify the K¹⁺ ion as a spectator ion and the ClO^1– ion as the reacting base. HCl is leveled to H₃O¹⁺ + Cl^1– in water, so H₃O¹⁺ is the reacting acid, while Cl^1– is also a spectator ion. We retrieve the reacting acid and base from the acid-base table as shown in Figure 12.17c. The acid is well above the base, so an extensive proton transfer is expected, and using Equation 12.1

K =

Ka of reacting acid

Ka of produced acid

, we determine that K = 2.9 × 10⁷. Thus, the reaction can be written with a single arrow.

Ammonia is added to water.

We identify NH₃ as the reacting base and H₂O as the reacting acid. The relative positions and K_a values of the reactants as given in the acid-base table are shown in Figure 12.17d. The base is well above the acid, so little proton transfer is expected. Indeed, K = 1.8 × 10^–5 for the reaction, so double arrows should be used for the reaction of this weak base with water.

Hydrofluoric acid is added to a solution of potassium hydrogen sulfide.

HF is the reacting acid and K¹⁺ is a spectator ion. The HS^1– ion has a proton and is an anion, so it can behave as either and acid or a base, but the HF will not react with another acid, so HS^1– is the reacting base in this reaction. The acid is above the base so the transfer is favorable with an equilibrium constant of 7.2 × 10³, so a single arrow can be used in the net equation to show that essentially all of at least one of the reactants disappears.

12.8-5. Identifying the Reactants

Identifying the reacting species is the first thing you must do when writing the net ionic equation for an acid-base equation. Remember the following:

• •
  Strong acids are written as H₃O¹⁺ and weak acids as the formula of the acid.
• •
  Most bases and a few acids are anions, but they are usually found as salts. However, the cation is usually a spectator ion in these cases. Thus, the base in a solution of KF is the F^1– ion.
• •
  NH₄¹⁺ is an acid, but it is normally found as a salt. Be careful with the anion because anions are also bases. If the anion is the conjugate base of a strong acid, it is a spectator ion in an acid-base reaction, otherwise, the anion may be a reactive base.
• •
  Anions with acidic protons, such as HSO₃^–, are amphiprotic. They behave like acids in the presence of bases, but they function as bases in the presence of acids.

12.8-6. Net Equations

12.9 _pH and _pK_a

Introduction

The hydronium ion concentration is an important property of an aqueous solution, but it can be very small, so it is often given on the p-scale to avoid writing exponents.

Objectives

• •
  Write the expression for the ion product constant of water and give its value at 25 °C.
• •
  Determine the hydronium (or hydroxide) ion concentration in aqueous solution given the hydroxide (or hydronium) ion concentration.
• •
  Define pK_a and determine relative acid strengths based on the acid pK_a.

12.9-1. The Ion Product Constant of Water

Water is both a very weak acid and a very weak base, so it can react with itself. Remember that water is the solvent and is treated as a pure liquid, so it enters the equilibrium expression as unity to produce the following equilibrium constant expression. The equilibrium constant for the reaction is called the ion product constant of water and given the symbol K_w. The value given for the equilibrium constant is the value at 25 °C. Equation 12.2 can be used to determine either [H₃O¹⁺] or [OH^1–] if the other is known. In pure water, the hydronium and hydroxide ion concentrations are the same because they are produced in a 1:1 ratio from water. Consequently, in pure water at 25 °C, the following is true. Solutions for which Equation 12.3 is valid are called neutral; solutions in which [H₃O¹⁺] > [OH^1–] are called acidic; and solutions in which [H₃O¹⁺] < [OH^1–] are called basic or alkaline.

12.9-2. pH

The hydronium ion concentration is an important characteristic of the solution, but it is normally a small number. To avoid the use of exponentials in discussions of hydronium ion concentrations, we define pH. The exponent of [H₃O¹⁺] is usually negative, so the sign of log [H₃O¹⁺] is usually negative. The negative sign in Equation 12.4 assures that the pH is usually positive. Because of the negative sign, a high pH implies a low hydronium ion concentration, and a low pH implies a high hydronium ion concentration. Equation 12.2

K_w = [H₃O¹⁺][OH¹⁻] = 1.0 × 10⁻¹⁴

can be rearranged as follows to show how the hydronium ion concentration, and therefore the pH, of a basic solution can be determined. Equation 12.5 shows that solutions with high hydroxide ion concentrations have low hydronium ion concentrations, so a high pH also implies a high hydroxide ion concentration and a low pH implies a low hydroxide ion concentration. A neutral solution is one in which

[H₃O¹⁺] = [OH¹⁻] = 1.0 × 10⁻⁷ M,

so the pH of a neutral solution is determined to be

pH = −log(1.0 × 10⁻⁷) = 7.0.

The hydronium ion concentration is greater in an acidic solution, so the pH of an acidic solution is less than 7.0. The hydronium ion concentration is less in a basic solution, so the pH of a basic solution is greater than 7.0. These conclusions are summarized in the following table.

Solution pH	Solution Type
above 7	basic
equal to 7	neutral
below 7	acidic

Table 12.8: Solution Type Versus pH

12.9-3. Hydronium Ion Concentration Exercise

12.9-4. pH Exercises

12.9-5. pK_a

The K_a of an acid is a commonly used property of acids because it describes the acid strength, but it is frequently given as the pK_a to avoid using negative exponents in discussions of acid strength. The pK_a of an acid is the negative base 10 logarithm of the K_a. Acids with high pK_as are weak acids because of the negative sign in the pK_a definition. The following table lists some acids, their K_as and their pK_as.

Acid	Ka	pKa
HF	7.2 × 10–4	3.14
HOCl	3.5 × 10–8	7.46
HCN	4.0 × 10–10	9.40

Table 12.9

Note that the pK_a increases as the acid strength decreases.

12.9-6. pK_a Exercise

12.9-7. Selecting the Solution with the Lower pH Exercise

12.10 Exercises and Solutions

Select the links to view either the end-of-chapter exercises or the solutions to the odd exercises.

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