16.5: Strong Acids and Bases (2023)

Solutions of strong acids and bases: the leveling effect

You will notice in table \(\PageIndex{1}\) that acids like \(H_2SO_4\) and \(HNO_3\) lie above the hydronium ion, which means they have \(pK_a\) values ​​less than zero and they are stronger acids than the ion \(H_3O^+\). Recall from Chapter 4 that in virtually all oxoacids the acidic proton is attached to one of the oxygen atoms in the oxoanion. Therefore, nitric acid must be correctly written as \(HONO_2\). Unfortunately, however, formulas for oxo acids are almost always written with hydrogen on the left and oxygen on the right, resulting in \(HNO_3\). In fact, the six common strong acids we first encountered in Chapter 4 have \(pK_a\) values ​​less than zero, meaning they have a greater tendency to lose a proton than \(H_3O^+ \ ). On the other hand, the conjugate bases of these strong acids are weaker bases than water. Consequently, the proton transfer equilibria for these strong acids are far to the right, and the addition of any of the common strong acids to water results in an essentially stoichiometric reaction of the acid with water to form a solution of \(H_3O ^+\ ) and the conjugate base of the acid .

Although \(K_a\) to \(HI\) is approximately 108 times greater than \(K_a\) to \(HNO_3\), the reaction of \(HI\) or \(HNO_3\) with water essentially yields a result stoichiometric solution of \(H_3O^+\) and I− or \(NO_3^−\). In fact, a 0.1 M aqueous solution of any strong acid actually contains 0.1 M \(H_3O^+\), regardless of the identity of the strong acid. This phenomenon is called the leveling effect: any species that is an acid stronger than the conjugate acid of water (\(H_3O^+\)) ​​levels off in aqueous solution to the strength of \(H_3O^+\ ) a because \(H_3O ^+\) is the strongest acid that can exist in equilibrium with water. Consequently, it is impossible to distinguish between the forces of acids such as e.gEYand HNO3 in aqueous solution, and an alternative approach must be used to determine their relative acidity.

One method is to use a solvent such as anhydrous acetic acid. Because acetic acid is a stronger acid than water, it must also be a weaker base, less likely to accept a proton than \(H_2O\). Conductivity measurements of 0.1 M solutions of HI and \(HNO_3\) in acetic acid show that HI is fully dissociated, but \(HNO_3\) is only partially dissociated and behaves like a weak acid in this solvent. This result tells us unequivocally that HI is a stronger acid than \(HNO_3\). The relative order of the strengths of the acids and the approximate values ​​of \(K_a\) and \(pK_a\) for the strong acids at the beginning of the \(\PageIndex{1}\) table were determined by measurements such as this and various non-aqueous solvents .

emaqueous solutions, \(H_3O^+\) is the strongest acid and \(OH^−\) is the strongest base that can exist in equilibrium with \(H_2O\).

The leveling effect also applies to solutions of strong bases: in aqueous solution, any base stronger than OH- will be balanced by the strength of OH-, since OH- is the strongest base that can exist in equilibrium with water. Salts such as \(K_2O\), \(NaOCH_3\) (sodium methoxide), and \(NaNH_2\) (sodium amide or sodium amide), whose anions are the conjugate bases of species listed in Table \( \PageIndex { 2}\), are all strong bases that essentially completely (and often violently) react with water by accepting a proton to give a solution of \(OH^−\) and the corresponding cation:

\[K_2O_{(s)}+H_2O_{(l)} \rightarrow 2OH^−_{(aq)}+2K^+_{(aq)} \label{16.5.18} \]

\[NaOCH_{3(s)}+H_2O_{(l)} \rightarrow OH^−_{(aq)}+Na^+_{(aq)}+CH_3OH_{(aq)} \label{16.5.19 } \]

\[NaNH_{2(s)}+H_2O_{(l)} \rightarrow OH^−_{(aq)}+Na^+_{(aq)}+NH_{3(aq)} \label{1} \]

Other examples you might come across are potassium hydride (\(KH\)) and organometallic compounds such as methyllithium (\(CH_3Li\)).

Polyprotic acids and bases

As you learned, polyprotic acids like \(H_2SO_4\), \(H_3PO_4\), and \(H_2CO_3\) contain more than one ionizable proton, and the protons are gradually lost. The fully protonated species is always the strongest acid because it is easier to remove a proton from a neutral molecule than from a negatively charged ion. Therefore, the strength of the acid decreases with the subsequent loss of protons and consequently \(pK_a\) increases. For example, consider \(H_2SO_4\):

\[HSO^−_{4(aq)} \ce{ <=>>} SO^{2−}_{4(aq)}+H^+_{(aq)} \;\;\; pK_a=-2 \unnumbered\]

The equilibrium in the first reaction is far to the right, consistent with \(H_2SO_4\) being a strong acid. In contrast, in the second reaction, significant amounts of \(HSO_4^−\) and \(SO_4^{2−}\) are present in equilibrium.

For a polyprotic acid, the strength of the acid decreases and \(pK_a\) increases with the sequential loss of each proton.

The hydrogen sulfate ion (\(HSO_4^−\)) is the conjugate base of \(H_2SO_4\) and the conjugate acid of \(SO_4^{2−}\). Like water, HSO4- can act as either an acid or a base depending on whether the other reactant is a stronger acid or a stronger base. On the other hand, the sulfate ion (\(SO_4^{2−}\)) is a polyprotic base capable of gradually accepting two protons:

\[SO^{2−}_{4(aq)} + H_2O_{(aq)} \ce{ <=>>} HSO^{−}_{4(aq)}+OH_{(aq)}^ - \Anzahl von nenhum\]

\[HSO^{−}_{4(aq)} + H_2O_{(aq)} \ce{ <=>>} H_2SO_{4(aq)}+OH_{(aq)}^- \label{16.6} \]

As with any other conjugate acid-base pair, the strengths of conjugate acids and bases are related as \(pK_a\) + \(pK_b\) = pKw. For example, consider the conjugate acid-base pair \(HSO_4^−/ SO_4^{2−}\). From the table \(\PageIndex{1}\) we see that \(pK_a\) of \(HSO_4^−\) is 1.99. So \(pK_b\) of \(SO_4^{2−}\) is 14.00 − 1.99 = 12.01. Hence, sulfate is a fairly weak base while \(OH^−\) is a strong base, so the equilibrium shown in equation \(\ref{16.6}\) is on the left-hand side. The ion \(HSO_4^−\) is also a very weak base (\(pK_a\) of \(H_2SO_4\) = 2.0, \(pK_b\) of \(HSO_4^− = 14 − (−2, 0) = 16 \)), which agrees with what we expect for the conjugate base of a strong acid.

A video about polyprotic acids:polybasic acids[Youtube]

Summary

Acid-base reactions always involve two conjugate acid-base pairs. Every acid and every base has an associated ionization constant that corresponds to its acid or base strength. Two species that differ only by a proton form a conjugate acid-base pair. The magnitude of the equilibrium constant for an ionization reaction can be used to determine the relative strengths of acids and bases. For an aqueous solution of a weak acid, the dissociation constant is called the acid ionization constant (\(K_a\)). Likewise, the equilibrium constant for the reaction of a weak base with water is the ionization constant of the base (\(K_b\)). For each conjugate acid-base pair, \(K_aK_b = K_w\). Lower values ​​of \(pK_a\) correspond to higher acid ionization constants and therefore stronger acids. On the other hand, smaller values ​​of \(pK_b\) correspond to ionization constants of larger bases and thus stronger bases. At 25°C, \(pK_a + pK_b = 14.00\). Acid-base reactions always proceed in the direction in which the weaker acid-base pair is formed. No acid stronger than \(H_3O^+\) and no base stronger than \(OH^−\) can exist in aqueous solution, leading to the phenomenon known as the capping effect . Polyprotic acids (and bases) gradually lose (and gain) protons, with fully protonated species being the strongest acid and fully deprotonated species being the strongest base.

key equations

• Acid ionization constant: \[K_a=\dfrac{[H_3O^+][A^−]}{[HA]} \nonumber \]
• Basic ionization constant: \[K_b= \dfrac{[BH^+][OH^−]}{[B]} \nonumber \]
• Relation between \(K_a\) and \(K_b\) of a conjugate acid-base pair: \[K_aK_b = K_w \nonumber \]
• Definition von \(pK_a\): \[pKa = −\log_{10}K_a \nonumber\] \[K_a=10^{−pK_a}\nonumber\]
• Definition von \(pK_b\): \[pK_b = −\log_{10}K_b \nonumber \] \[K_b=10^{−pK_b} \nonumber \]
• Ratio between \(pK_a\) and \(pK_b\) of a conjugate acid-base pair: \[pK_a + pK_b = pK_w \nonumber \] \[pK_a + pK_b = 14.00 \; \text{at 25°C} \nonumber \]

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