Acids and Bases

Nature of Acids and Bases

Acids and bases will neutralize one another to form liquid water and a salt.

Acids

Acids have long been recognized as a distinctive class of compounds whose aqueous solutions exhibit the following properties:

• A characteristic sour taste.
• Changes the color of litmus from blue to red.
• Reacts with certain metals to produce gaseous H₂.
• Reacts with bases to form a salt and water.

Acidic solutions have a pH less than 7, with lower pH values corresponding to increasing acidity. Common examples of acids include acetic acid (in vinegar), sulfuric acid (used in car batteries), and tartaric acid (used in baking).

There are three common definitions for acids:

• Arrhenius acid: any substances that increases the concentration of hydronium ions (H₃O⁺) in solution.
• Brønsted-Lowry acid: any substance that can act as a proton donor.
• Lewis acid: any substance that can accept a pair of electrons.

Acid Strength and Strong Acids

The strength of an acid refers to how readily an acid will lose or donate a proton, oftentimes in solution. A stronger acid more readily ionizes, or dissociates, in a solution than a weaker acid. The six common strong acids are:

• hydrochloric acid (HCl)
• hydrobromic acid (HBr)
• hydroiodic acid (HI)
• sulfuric acid (H₂SO₄; only the first proton is considered strongly acidic)
• nitric acid (HNO₃)
• perchloric acid (HClO₄)

Each of these acids ionize essentially 100% in solution. By definition, a strong acid is one that completely dissociates in water; in other words, one mole of the generic strong acid, HA, will yield one mole of H⁺, one mole of the conjugate base, A⁻, with none of the unprotonated acid HA remaining in solution. By contrast, however, a weak acid, being less willing to donate its proton, will only partially dissociate in solution. At equilibrium, both the acid and the conjugate base will be present, along with a significant amount of the undissociated species, HA.

Factors Affecting Acid Strength

Two key factors contribute to overall strength of an acid:

• polarity of the molecule
• strength of the H-A bond

These two factors are actually related. The more polar the molecule, the more the electron density within the molecule will be drawn away from the proton. The greater the partial positive charge on the proton, the weaker the H-A bond will be, and the more readily the proton will dissociate in solution.

Acid strengths are also often discussed in terms of the stability of the conjugate base. Stronger acids have a larger K_a and a more negative pK_a than weaker acids.

Bases

There are three common definitions of bases:

• Arrhenius base: any compound that donates an hydroxide ion (OH^–) in solution.
• Brønsted-Lowry base: any compound capable of accepting a proton.
• Lewis base: any compound capable of donating an electron pair.

In water, basic solutions will have a pH between 7-14.

Base Strength and Strong Bases

A strong base is the converse of a strong acid; whereas an acid is considered strong if it can readily donate protons, a base is considered strong if it can readily deprotonate (i.e, remove an H⁺ ion) from other compounds. As with acids, we often talk of basic aqueous solutions in water, and the species being deprotonated is often water itself. The general reaction looks like:

[latex]\text{A}^-(\text{aq})+\text{H}_2\text{O}(\text{aq})\rightarrow \text{AH}(\text{aq})+\text{OH}^-(\text{aq})[/latex]

Thus, deprotonated water yields hydroxide ions, which is no surprise. The concentration of hydroxide ions increases as pH increases.

Most alkali metal and some alkaline earth metal hydroxides are strong bases in solution. These include:

• sodium hydroxide (NaOH)
• potassium hydroxide (KOH)
• lithium hydroxide (LiOH)
• rubidium hydroxide (RbOH)
• cesium hydroxide (CsOH)
• calcium hydroxide (Ca(OH)₂)
• barium hydroxide (Ba(OH)₂)
• strontium hydroxide (Sr(OH)₂)

The alkali metal hydroxides dissociate completely in solution. The alkaline earth metal hydroxides are less soluble but are still considered to be strong bases.

Acid/Base Neutralization

Acids and bases react with one another to yield water and a salt. For instance:

[latex]\text{HCl}(\text{aq})+\text{NaOH}(\text{aq})\rightarrow \text{H}_2\text{O}(\text{l})+\text{NaCl}(\text{aq})[/latex]

This reaction is called a neutralization reaction.

The Arrhenius Definition

An Arrhenius acid dissociates in water to form hydrogen ions, while an Arrhenius base dissociates in water to form hydroxide ions.

The Arrhenius Definition

An acid-base reaction is a chemical reaction that occurs between an acid and a base. Several concepts exist that provide alternative definitions for the reaction mechanisms involved and their application in solving related problems. Despite several differences in definitions, their importance as different methods of analysis becomes apparent when they are applied to acid-base reactions for gaseous or liquid species, or when acid or base character may be somewhat less apparent.

The Arrhenius definition of acid-base reactions, which was devised by Svante Arrhenius, is a development of the hydrogen theory of acids. It was used to provide a modern definition of acids and bases, and followed from Arrhenius’s work with Friedrich Wilhelm Ostwald in establishing the presence of ions in aqueous solution in 1884. This led to Arrhenius receiving the Nobel Prize in Chemistry in 1903.

As defined by Arrhenius:

• An Arrhenius acid is a substance that dissociates in water to form hydrogen ions (H⁺). In other words, an acid increases the concentration of H⁺ ions in an aqueous solution. This protonation of water yields the hydronium ion (H₃O⁺); in modern times, H⁺ is used as a shorthand for H₃O⁺ because it is now known that a bare proton (H⁺) does not exist as a free species in aqueous solution.
• An Arrhenius base is a substance that dissociates in water to form hydroxide (OH^–) ions. In other words, a base increases the concentration of OH^– ions in an aqueous solution.

Limitations of the Arrhenius Definition

The Arrhenius definitions of acidity and alkalinity are restricted to aqueous solutions and refer to the concentration of the solvated ions. Under this definition, pure H₂SO₄ or HCl dissolved in toluene are not acidic, despite the fact that both of these acids will donate a proton to toluene. In addition, under the Arrhenius definition, a solution of sodium amide (NaNH₂) in liquid ammonia is not alkaline, despite the fact that the amide ion ([latex]\text{NH}_2^-[/latex]) will readily deprotonate ammonia. Thus, the Arrhenius definition can only describe acids and bases in an aqueous environment.

Arrhenius Acid-Base Reaction

An Arrhenius acid-base reaction is defined as the reaction of a proton and an hydroxide ion to form water:

[latex]\text{H}^++\text{OH}^-\rightarrow \text{H}_2\text{O}[/latex]

Thus, an Arrhenius acid base reaction is simply a neutralization reaction.

The Brønsted-Lowry Definition of Acids and Bases

A Brønsted-Lowry acid is any species capable of donating a proton; a Brønsted-Lowry base is any species capable of accepting a proton.

Originally, acids and bases were defined by Svante Arrhenius. His original definition stated that acids were compounds that increased the concentration of hydrogen ions (H⁺) in solution, whereas bases were compounds that increased the concentration of hydroxide ions (OH^–) in solutions. Problems arise with this conceptualization because Arrhenius’s definition is limited to aqueous solutions, referring to the solvation of aqueous ions, and is therefore not inclusive of acids dissolved in organic solvents. To solve this problem, Johannes Nicolaus Brønsted and Thomas Martin Lowry, in 1923, both independently proposed an alternative definition of acids and bases. In this newer system, Brønsted-Lowry acids were defined as any molecule or ion that is capable of donating a hydrogen cation (proton, H⁺), whereas a Brønsted-Lowry base is a species with the ability to gain, or accept, a hydrogen cation. A wide range of compounds can be classified in the Brønsted-Lowry framework: mineral acids and derivatives such as sulfonates, carboxylic acids, amines, carbon acids, and many more.

Brønsted-Lowry Acid/Base Reaction

Keep in mind that acids and bases must always react in pairs. This is because if a compound is to behave as an acid, donating its proton, then there must necessarily be a base present to accept that proton. The general scheme for a Brønsted-Lowry acid/base reaction can be visualized in the form:

acid + base [latex]\rightleftharpoons[/latex] conjugate base + conjugate acid

Here, a conjugate base is the species that is left over after the Brønsted acid donates its proton. The conjugate acid is the species that is formed when the Brønsted base accepts a proton from the Brønsted acid. Therefore, according to the Brønsted-Lowry definition, an acid-base reaction is one in which a conjugate base and a conjugate acid are formed (note how this is different from the Arrhenius definition of an acid-base reaction, which is limited to the reaction of H⁺ with OH^– to produce water). Lastly, note that the reaction can proceed in either the forward or the backward direction; in each case, the acid donates a proton to the base.

Consider the reaction between acetic acid and water:

[latex]\text{H}_3\text{CCOOH}(\text{aq})+\text{H}_2\text{O}(\text{l})\rightleftharpoons \text{H}_3\text{CCOO}^-(\text{aq})+\text{H}_3\text{O}^+(\text{aq})[/latex]

Here, acetic acid acts as a Brønsted-Lowry acid, donating a proton to water, which acts as the Brønsted-Lowry base. The products include the acetate ion, which is the conjugate base formed in the reaction, as well as hydronium ion, which is the conjugate acid formed.

Note that water is amphoteric; depending on the circumstances, it can act as either an acid or a base, either donating or accepting a proton. For instance, in the presence of ammonia, water will donate a proton and act as a Brønsted-Lowry acid:

[latex]\text{NH}_3(\text{aq})+\text{H}_2\text{O}(\text{l})\rightleftharpoons \text{NH}_4^+(\text{aq})+\text{OH}^-(\text{aq})[/latex]

Here, ammonia is the Brønsted-Lowry base. The conjugate acid formed in the reaction is the ammonium ion, and the conjugate base formed is hydroxide.

Acid-Base Properties of Water

Water is capable of acting as either an acid or a base and can undergo self-ionization.

Under standard conditions, water will self-ionize to a very small extent. The self-ionization of water refers to the reaction in which a water molecule donates one of its protons to a neighboring water molecule, either in pure water or in aqueous solution. The result is the formation of a hydroxide ion (OH^–) and a hydronium ion (H₃O⁺). The reaction can be written as follows:

[latex]{\text{H}}_{2}\text{O} + {\text{H}}_{2}\text{O} \rightleftharpoons {\text{H}}_{3}{\text{O}}^{+} + \text{O}{\text{H}}^{-}[/latex]

This is an example of autoprotolysis (meaning “self-protonating”) and it exemplifies the amphoteric nature of water (ability to act as both an acid and a base ).

The Water Ionization Constant, K_W

Note that the self-ionization of water is an equilibrium reaction:

[latex]{\text{H}}_{2}\text{O} + {\text{H}}_{2}\text{O} \rightleftharpoons {\text{H}}_{3}{\text{O}}^{+} + \text{O}{\text{H}}^{-}\quad\quad\quad \text{K}_\text{W}=1.0\times10^{-14}[/latex]

Like all equilibrium reactions, this reaction has an equilibrium constant. Because this is a special equilibrium constant, specific to the self-ionization of water, it is denoted K_W; it has a value of 1.0 x 10⁻¹⁴. If we write out the actual equilibrium expression for K_W, we get the following:

[latex]\text{K}_\text{W}=[\text{H}^+][\text{OH}^-]=1.0\times 10^{-14}[/latex]

However, because H⁺ and OH^– are formed in a 1:1 molar ratio, we have:

[latex][\text{H}^+]=[\text{OH}^-]=\sqrt{1.0\times 10^{-14}}=1.0\times 10^{-7}\;\text{M}[/latex]

Now, note the definition of pH and pOH:

[latex]\text{pH}=-\text{log}[\text{H}^+][/latex]

[latex]\text{pOH}=-\text{log}[\text{OH}^-][/latex]

If we plug in the above value into our equation for pH, we find that:

[latex]\text{pH}=-\text{log}(1.0\times 10^{-7})=7.0[/latex]

[latex]\text{pOH}=-\text{log}(1.0\times 10^{-7})=7.0[/latex]

Here we have the reason why neutral water has a pH of 7.0; it represents the condition at which the concentrations of H⁺ and OH^– are exactly equal in solution.

pH, pOH, and pK_W

We have already established that the equilibrium constant K_W can be expressed as:

[latex]\text{K}_\text{W}=[\text{H}^+][\text{OH}^-][/latex]

If we take the negative logarithm of both sides of this equation, we get the following:

[latex]-\text{log}(\text{K}_\text{W})=-\text{log}([\text{H}^+][\text{OH}^-])[/latex]

[latex]-\text{log}(\text{K}_\text{W})=-\text{log}[\text{H}^+]+-\text{log}[\text{OH}^-][/latex]

[latex]\text{pK}_\text{W}=\text{pH}+\text{pOH}[/latex]

However, because we know that pK_W = 14, we can establish the following relationship:

[latex]\text{pH}+\text{pOH}=14[/latex]

This relationship always holds true for any aqueous solution, regardless of its level of acidity or alkalinity. Utilizing this equation is a convenient way to quickly determine pOH from pH and vice versa, as well as to determine hydroxide concentration given hydrogen concentration, or vice versa.

Acid Dissociation Constant (Ka)

The acid dissociation constant (K_a) is the measure of the strength of an acid in solution.

The acid dissociation constant (K_a) is a quantitative measure of the strength of an acid in solution. K_a is the equilibrium constant for the following dissociation reaction of an acid in aqueous solution:

[latex]\text{HA}(\text{aq}) \rightleftharpoons \text{H}^+(\text{aq}) + \text{A}^-(\text{aq})[/latex]

In the above reaction, HA (the generic acid), A^– (the conjugate base of the acid), and H⁺ (the hydrogen ion or proton) are said to be in equilibrium when their concentrations do not change over time. As with all equilibrium constants, the value of K_a is determined by the concentrations (in mol/L) of each aqueous species at equilibrium. The K_a expression is as follows:

[latex]\text{K}_\text{a}=\frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}[/latex]

Acid dissociation constants are most often associated with weak acids, or acids that do not completely dissociate in solution. This is because strong acids are presumed to ionize completely in solution and therefore their K_a values are exceedingly large.

K_a and pK_a

Due to the many orders of magnitude spanned by K_a values, a logarithmic measure of the acid dissociation constant is more commonly used in practice. The logarithmic constant (pK_a) is equal to -log₁₀(K_a).

The larger the value of pK_a, the smaller the extent of dissociation. A weak acid has a pK_a value in the approximate range of -2 to 12 in water. Acids with a pK_a value of less than about -2 are said to be strong acids. A strong acid is almost completely dissociated in aqueous solution; it is dissociated to the extent that the concentration of the undissociated acid becomes undetectable. pK_a values for strong acids can be estimated by theoretical means or by extrapolating from measurements in non-aqueous solvents with a smaller dissociation constant, such as acetonitrile and dimethylsulfoxide.

pOH and Other p Scales

A p-scale is a negative logarithmic scale.

pH and pOH

Recall the reaction for the autoionization of water:

[latex]\text{H}_2\text{O}\rightleftharpoons \text{H}^+(\text{aq})+\text{OH}^-(\text{aq})[/latex]

This reaction has a special equilibrium constant denoted K_W, and it can be written as follows:

[latex]\text{K}_\text{W}=[\text{H}^+][\text{OH}^-]=1.0\times 10^{-14}[/latex]

Because H+ and OH- dissociate in a one-to-one molar ratio,

[latex][\text{H}^+]=[\text{OH}^-]=\sqrt{1.0\times 10^{-14}}=1.0\times 10^{-7}[/latex]

If we take the negative logarithm of each concentration, we get:

[latex]\text{pH}=-\text{log}[\text{H}^+]=-\text{log}(1.0\times 10^{-7})=7.0[/latex]

[latex]\text{pOH}=-\text{log}[\text{OH}^-]=-\text{log}(1.0\times 10^{-7})=7.0[/latex]

Here we have the reason that neutral water has a pH of 7.0 -; this is the pH at which the concentrations of H⁺ and OH^– are exactly equal.

Lastly, we should take note of the following relationship:

[latex]\text{pH}+\text{pOH}=14[/latex]

This relationship will always apply to aqueous solutions. It is a quick and convenient way to find pH from pOH, hydrogen ion concentration from hydroxide ion concentration, and more.

pK_a and pK_b

Generically, this p-notation can be used for other scales. In acid -base chemistry, the amount by which an acid or base dissociates to form H⁺ or OH^– ions in solution is often given in terms of their dissociation constants (K_a or K_b). However, because these values are often very small for weak acids and weak bases, the p-scale is used to simplify these numbers and make them more convenient to work with. Quite often we will see the notation pK_a or pK_b, which refers to the negative logarithms of K_a or K_b, respectively.