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There are three definitions for acids and bases. The Arrhenius definition of an acid is a substance that produces H⁺ in water; a base is a substance that produces OH^– in water. The Brønsted–Lowry definition defines an acid as a proton donor (H⁺ donor) and a base as a proton (H⁺) acceptor. Since an Arrhenius acid donates H⁺ water and an Arrhenius base accepts H⁺ from water, anything that is an Arrhenius acid is also a Brønsted–Lowry acid, although the reverse is not true. A third definition is the Lewis definition. Lewis acids accept a lone pair of electrons from a Lewis base. Since H⁺ reacts with the lone pair on a base, the Lewis definition includes Arrhenius and Brønsted–Lowry acids and bases. Again, the reverse is not true.

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Technically, whether a substance is an acid or a base depends on the reaction. However, substances are generally classified as an acid or base based on the reaction of that substance in (with) water. Normally, this can be determined from its formula. Inorganic acids tend to have hydrogen as the first element in its formula. Organic acids tend to have formulas ending in "COOH" (carboxylic acids). Nonmetal oxides also react with water as acids. Bases are normally metal hydroxides or organic nitrogen compounds (amines) or ammonia (NH₃), which is a special case of an amine.

Acids can be either strong or weak. A strong acid will completely ionize in water with one product being H⁺(aq) or H₃O⁺(aq). H⁺ and H₃O⁺ are two ways of writing the same idea. Because the most common isotope of hydrogen has no neutrons, H⁺ is often also called a proton. Because H⁺ only exists connected to water, some believe that only H₃O⁺ is appropriate. Others use whichever notation is convenient. Weak acids still produce H₃O⁺, but in an incomplete (equilibrium) reaction. There are seven strong acids: hydrochloric (HCl), hydrobromic (HBr), hydroiodic (HI), nitric (HNO₃), perchloric (HClO₄), chloric (HClO₃), and sulfuric (H₂SO₄). The easiest way to tell the difference between weak and strong acids is to memorize the strong acids. All other acids are weak.

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Stronger acids produce higher concentrations of H₃O⁺. The strength of a weak acid depends on the degree of ionization, which is the amount of acid that ionizes in water. The equilibrium constant for a weak acid with water is called the acid–ionization constant, or K_a. Since the ions are products of the reaction, larger K_a values represent stronger acids. Strong acids do not have K_as, since they completely react, rather than react in equilibrium, with water. In addition, all strong acids are the same strength, as they each ionize 100%. Therefore the product of the ionization, H⁺, is the strongest acid that can exist in water. The fact that strong acids are of the same strength is called the leveling effect of water.

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The relative strength of acids with similar chemical structures can be predicted. For oxoacids, acids containing oxygen as well as hydrogen and another element, substances with more oxygen atoms, but the same otherwise, will be stronger. Similarly, if the substances differ by only the central atom, more electronegative atoms are (generally) stronger acids.

Polyprotic acids have more than one H⁺ that is acidic (reacts with a base). For polyprotic acids, reaction of the first proton is K_a1; that of the second is K_a2; and so forth. With polyprotic acids, the second ionization is always weaker than the first (K_a1 > K_a2). The third ionization (if there is one) will be weaker than the second (K_a2 > K_a3).

Sulfuric acid is a special case of both a strong acid and a polyprotic acid. The first acidic H⁺ is a strong acid and reacts completely with water. The second H⁺ reacts in equilibrium with water (a weak acid). However, HSO₄^– is one of the strongest common weak acids.

Bases can also be strong or weak. Like a strong acid, strong bases completely ionize in water. The difference is that bases produce OH^– instead of H₃O⁺. There are only a few strong bases. Like acids, it is easer to memorize the strong bases and recognize that all other bases are weak. The strong bases are hydroxide salts of the group I metals, calcium, strontium, or barium. In water, salts simply dissolve into their component ions. These bases are strong because they are completely soluble in water. Other hydroxide salts are not soluble so they cannot react completely and are therefore weak bases. The nitrogen bases react with water by taking an H⁺ from the water (the H⁺ bonds to the lone pair on the nitrogen), leaving OH^– as a product. The equilibrium constant for this reaction is K_b. With a leveling effect parallel to that of acids, the strongest base that can exist in water is hydroxide ion.

When it reacts with acid, water acts as a base. When it reacts with a base, water acts as an acid. Substances that can act as either an acid or a base are called amphoteric. Water can also undergo an acid–base reaction with itself, called autoionization.

H₂O + H₂O H₃O⁺ + OH^–         (Equation 16. 9)

Since water is also the solvent in this reaction, the equilibrium constant expression is

K_w = [H₃O⁺][OH^–]          (Equation 16.11)

and the value of the equilibrium constant, K_w, is 1.0 x 10^–14 at 25 °C (room temperature). Therefore the concentration of H₃O⁺ and of OH^– in pure water at room temperature is 1.0 x 10^–7 M. Acid–base reactions in water can shift this equilibrium. Therefore in any aqueous solution, if you know the concentration of either H₃O⁺ or OH^–, the other can be determined from the K_w expression.

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An alternate way of expressing concentration is with a p–function, which is the negative log of the molarity. Therefore,

pH = –log[H₃O⁺]         (Equation 16.12)

and

pOH = –log[OH^–]         (Equation 16.13)

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The K_w expression can be rewritten as

pH + pOH = pK_w = 14.00         (Equation 16.14)

where pK_w is, like pH and pOH, a p–function

pK_w = –log K_w

K_a and K_b values can also be written as p–functions (pK_a and pK_b).

The advantage of p–functions is that scientific notation is not required. However, it is important to recognize that each p–unit is a change by a factor of 10 and that lower p–function numbers represent higher values.

In a Brønsted–Lowry acid–base equilibrium reaction, the transfer of H⁺ occurs in both directions. Therefore the product of the reaction between an acid and a base is an acid and a base. Thus when an acid reacts in an acid–base reaction, the loss of H⁺ creates a base called its conjugate base. Similarly, the gain of a proton by a base creates its conjugate acid. Two substances differing by only one H⁺ are a conjugate acid–base pair.

There is an inverse relationship between the strength of conjugate acid–base pairs. The stronger the acid, the weaker its conjugate base and vice versa. This relationship is quantitatively expressed in Equation 16.17, where

K_aK_b = K_w = 1.0 x 10^–14         (Equation 16.17)

This equation requires that the acid and base be a conjugate acid–base pair.

Since the conjugate base has lost an H⁺ ion, it normally has a negative charge. Consequently, most anions act as bases. Exceptions are Cl^–, Br^–, I^–, NO₃^–, ClO₄^–, ClO₃^–, and SO₄^2–. These conjugate bases of the strong acids are such weak bases that they will not react with water.

Similarly, most cations act as acids. This is most obvious with the nitrogen bases, where the hydrogen bonded to the nitrogen creates the conjugate acid of the nitrogen base. Less obviously, metal ions can also act as bases. Metal ions normally bond to several water molecules in aqueous solutions. An H⁺ can be removed from one of the water molecules (leaving an OH^– bonded to the water), increasing the overall concentration of H₃O⁺. The cations associated with the strong bases (group I metal ions, Ca²⁺, Sr²⁺, and Ba²⁺) do not react with water.

When a metal ion acts as a Lewis acid, it may bond with more than one Lewis base. The Lewis bases in this type of reaction are called ligands. The compound formed by this reaction is often a complex ion. The equilibrium constant for this reaction, the formation of a complex ion, is called a formation constant, K_f.

Ionic compounds, salts, dissociate into their component ions in water. Soluble salts dissociate completely. The ions may then undergo further reaction with water as acids or bases or form complex ions. Most salts are not soluble in water. These dissociate in an equilibrium reaction to their component ions. The equilibrium constant for this reaction is called the solubility product (or solubility product constant), K_sp. Because the concentration of ions is so small, further reactions are unimportant.

A mixture of an acid and its conjugate base (or a base and its conjugate acid) forms a buffer solution. Buffers resist pH change with the addition of water, small amounts of acid, or small amounts of base. Considering Le Chatelier's principle, the addition of conjugate base, a product of the equilibrium, makes the amount of H₃O⁺ produced by the reaction much smaller than the acid alone. This is an example of the common–ion effect. Because the reaction only occurs to a small extent ("x is small"), the concentration of acid and base is not significantly affected by the equilibrium. Thus the K_a expression can then be rearranged to the Henderson–Hasselbalch equation:

pH

=

pKa

+

log

[base] [acid]

(Equation 16.20)

With this equation it is easy to observe that diluting the solution would dilute the acid and base concentrations by the same factor, and not change the pH. The presence of base ensures that a small amount of additional acid is neutralized. Likewise, a small amount of additional base is neutralized by the acid. The amount of acid (or base) neutralized a buffer without significant pH change is called the buffer capacity. Higher concentrations of acid will neutralize larger amounts of base, as higher concentrations of base neutralize more acid. Therefore buffer capacity is maximized with high concentrations of acid and base. Since the acid and base concentrations are part of a log term, large changes in concentration are required to change pH significantly. Since both need to be present in significant concentration (so that both acid and base can be neutralized), the most efficient buffers are designed so that the acid and base concentrations are about equal and the pH pK_a.

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Acid–base indicators are a special type of weak acid or weak base. What makes these substances special is that the acid is one color and its conjugate base is a different color. Since the concentration of acid or base is controlled by pH, the color of an indicator solution is pH dependent. The Henderson–Hasselbalch equation (which is just a rearrangement of K_a) shows that when pH = pK_a, the acid and base concentrations are equal. Thus the color will be a mixture of both the acid and base forms. (For example, if an indicator has a yellow acid form and a blue basic form, the solution will be green when pH = pK_a.) Since there is at least 10 times higher acid concentration than base, the acid form and color predominate at pH < pK_a – 1.0. Likewise, the basic form and color predominate at pH > pK_a + 1.0.

By using a strong acid or a strong base as a reactant, as an acid–base reaction can be forced to completion. In a complete reaction, stoichiometry (Chapter 4) can be used to relate reactants and products to each other. A titration is an experiment where the volume of reactant solution (titrant) needed to react exactly with some amount of another reactant is measured. This volume is called the equivalence point. Although regular stoichiometry can be used, if both reactants are solutions, a convenient equation to relate volume (V) and concentration (M) is

MAVA

=

1 X

MBVB         (Equation 16.25)

where A = acid, B = base, and X is the stoichiometric ratio of moles acid per moles base.

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The progress of an acid–base titration can be followed with a titration curve, a graph of pH versus volume of titrant. The pH of the reaction mixture is measured as titrant is added to the other reactant. Before titrant is added, the pH depends on the reactant. After some titrant is added, the concentration of reactant is reduced (due to both reaction and dilution) and the conjugate acid or base of the reactant is created. Consequently, if the reactant is a weak acid or weak base, a buffer is created. Half way to the equivalence point, the moles of acid and moles of base are equal, and the Henderson–Hasselbalch equation shows that pH = pK_a. Even if the reactant is a weak base, the pH = pK_a of its conjugate acid. At the equivalence point, only the conjugate acid or base is present in the reaction mixture. Since the product of the reaction of a weak base is its conjugate acid, the pH at the equivalence point is weakly acidic. Likewise, the pH of a weak acid at the equivalence point is slightly basic. After the equivalence point, more titrant is added, but it does not react. Therefore the pH will be determined by the titrant.

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