AP Chemistry 8.4-8.8: Acid-Base Reactions and Buffer Properties

Salt hydrolysis

Salt hydrolysis is the reaction of a salt ion with water as an acid or base. Hydrolysis can produce $H_3O^+$, produce $OH^-$, or be negligible, determining whether the salt solution is acidic, basic, or neutral.

How can the acid-base character of an aqueous salt solution be predicted?

Identify whether each ion is an appreciable acid or base. A weak-acid cation makes the solution acidic, a weak-base anion makes it basic, and ions that are conjugates of strong acids or bases are usually spectators; if both ions react, compare their $K_a$ and $K_b$ values.

What hydrolysis reaction occurs when ammonium chloride dissolves in water?

The salt dissociates as $NH_4Cl(s)\rightarrow NH_4^+(aq)+Cl^-(aq)$. Ammonium hydrolyzes according to $NH_4^++H_2O\rightleftharpoons H_3O^++NH_3$, while $Cl^-$ is essentially inert, so the solution is acidic.

How is the acid ionization constant of a weak conjugate acid related to the base ionization constant of its conjugate base?

$K_aK_b=K_w$, so $K_a=\dfrac{K_w}{K_b}$. At $25\,^\circ\mathrm{C}$, $K_w=1.0\times10^{-14}$.

Why does chloride ion have negligible basicity in water?

Chloride is the conjugate base of the strong acid HCl. Because HCl ionizes essentially completely, the reverse reaction $Cl^-+H_2O\rightleftharpoons HCl+OH^-$ has a negligible $K_b$.

How can the hydronium concentration be estimated for a salt containing a weak-acid cation?

For a weak-acid cation with initial concentration $C$ and ionization constant $K_a$, write an ICE table and use $K_a=\dfrac{x^2}{C-x}$. If $x\ll C$, use $[H_3O^+]=x\approx\sqrt{K_aC}$, then calculate $pH=-\log[H_3O^+]$.

A 0.100 M solution of $NH_4NO_3$ has $K_a(NH_4^+)=5.6\times10^{-10}$. What is its approximate hydronium concentration?

Nitrate is inert, so $[H_3O^+]\approx\sqrt{(5.6\times10^{-10})(0.100)}=7.5\times10^{-6}\,\mathrm{M}$.

What hydrolysis reaction makes a sodium acetate solution basic?

Sodium ion is essentially inert, but acetate hydrolyzes: $CH_3CO_2^-+H_2O\rightleftharpoons CH_3CO_2H+OH^-$. Since acetate is the conjugate base of the weak acid acetic acid, $K_b=K_w/K_a$ is appreciable and the solution is basic.

How is the equilibrium concentration of a weak acid produced by an anion's hydrolysis calculated?

Use the base-ionization expression $K_b=\dfrac{[HA][OH^-]}{[A^-]}$. If the equilibrium concentrations of $OH^-$ and $A^-$ are known, solve for $[HA]=K_b[A^-]/[OH^-]$.

What is the approximate pH of a 0.083 M solution of NaCN?

Using $K_a(HCN)\approx4.9\times10^{-10}$, $K_b(CN^-)=K_w/K_a\approx2.0\times10^{-5}$. Thus $[OH^-]\approx\sqrt{(2.0\times10^{-5})(0.083)}$, and $pH=14.00-pOH\approx11.11$.

What is an inert or spectator ion in the context of salt hydrolysis?

It is an ion whose reaction with water is negligible and therefore does not significantly affect pH. Examples include $Na^+$, $K^+$, and the conjugate bases of strong acids such as $Cl^-$ and $NO_3^-$.

How should a salt containing both an acidic ion and a basic ion be classified?

Compare the acid ionization constant of the acidic ion with the base ionization constant of the basic ion. If $K_a>K_b$, the solution is acidic; if $K_b>K_a$, it is basic; if they are comparable, the solution is approximately neutral.

How is an amphiprotic ion's effect on pH determined?

An amphiprotic ion can both donate and accept a proton. Compare its $K_a$ for acid behavior with its $K_b$ for base behavior: the larger constant indicates the dominant behavior.

Why is aqueous $NaHCO_3$ basic?

$HCO_3^-$ is amphiprotic. Its base constant, $K_b=K_w/K_a(H_2CO_3)$, is greater than its acid constant for donating a proton, so bicarbonate produces more $OH^-$ than $H_3O^+$.

Classify aqueous solutions of $KBr$, $NaHCO_3$, $Na_2HPO_4$, and $NH_4F$ as acidic, basic, or neutral.

$KBr$ is approximately neutral. $NaHCO_3$ and $Na_2HPO_4$ are basic because their amphiprotic anions have stronger base than acid behavior. $NH_4F$ is acidic because $K_a(NH_4^+)=5.6\times10^{-10}$ is greater than $K_b(F^-)=1.6\times10^{-11}$.

Why can some dissolved metal ions act as acids even though their formulas contain no acidic hydrogen?

Many metal ions form hydrated complex ions in water, such as $[Al(H_2O)_6]^{3+}$. The positive metal center withdraws electron density from O-H bonds in coordinated water molecules, making proton donation to water favorable.

What is the first acid-ionization reaction of the hexaaquaaluminum(III) ion?

$[Al(H_2O)_6]^{3+}+H_2O\rightleftharpoons H_3O^++[Al(H_2O)_5(OH)]^{2+}$. For this reaction, $K_a=1.4\times10^{-5}$.

Why can hydrated metal ions undergo successive acid ionizations?

After one coordinated water molecule loses a proton, other coordinated water molecules can ionize in later steps. Thus, hydrated metal complexes can behave as polyprotic acids, although successive ionizations generally become weaker.

What structural trends generally increase the acidity of hydrated metal ions?

Greater positive charge and smaller ionic radius generally increase acidity. These properties create a stronger electric field, polarize coordinated O-H bonds more strongly, and promote proton donation.

Which hydrated metal ion is expected to be the stronger acid: $[Fe(H_2O)_6]^{3+}$ or $[Cu(H_2O)_6]^{2+}$?

$[Fe(H_2O)_6]^{3+}$ is stronger because its higher charge produces greater polarization of the coordinated water molecules. Its $pK_a$ is about 2.74, compared with about 6.3 for the copper(II) complex.

How can the pH of a solution of a hydrated metal ion be estimated?

Treat the first proton transfer as a weak-acid equilibrium. For initial hydrated-ion concentration $C$, use $K_a\approx x^2/(C-x)$; if $x\ll C$, then $[H_3O^+]\approx\sqrt{K_aC}$ and $pH=-\log[H_3O^+]$.

What is the approximate pH of a 0.10 M solution of $AlCl_3$ given $K_a([Al(H_2O)_6]^{3+})=1.4\times10^{-5}$?

$[H_3O^+]\approx\sqrt{(1.4\times10^{-5})(0.10)}=1.2\times10^{-3}\,\mathrm{M}$. Therefore, $pH\approx2.92$.

What is the net ionic equation for neutralization of hydronium by hydroxide?

The neutralization reaction is $H_3O^+(aq)+OH^-(aq)\rightarrow2H_2O(l)$. Its stoichiometry is 1:1, so the limiting reactant is determined by comparing the moles of $H_3O^+$ and $OH^-$.

Buffer solution

A buffer contains appreciable amounts of a weak acid and its conjugate base, or a weak base and its conjugate acid. It resists large pH changes when relatively small amounts of strong acid or strong base are added.

What combinations of substances commonly form buffers?

A weak acid and a soluble salt containing its conjugate base form an acidic buffer, such as $CH_3COOH/CH_3COO^-$. A weak base and a soluble salt containing its conjugate acid form a basic buffer, such as $NH_3/NH_4^+$.

How does an acetate buffer respond to added strong acid?

Acetate consumes the added hydronium: $H_3O^++CH_3COO^-\rightarrow CH_3COOH+H_2O$. This converts strong acid into the weak acid component and shifts the weak-acid equilibrium toward $CH_3COOH$, limiting the pH change.

How does an acetate buffer respond to added strong base?

Acetic acid neutralizes the added hydroxide: $OH^-+CH_3COOH\rightarrow CH_3COO^-+H_2O$. This converts strong base into the weak conjugate base component and consumes some $CH_3COOH$.

What is the Henderson-Hasselbalch equation for a weak-acid/conjugate-base buffer?

$pH=pK_a+\log\left(\dfrac{[A^-]}{[HA]}\right)$. It is derived from $K_a=\dfrac{[H_3O^+][A^-]}{[HA]}$ and is most useful when both buffer components are present in substantial concentrations.

When is the Henderson-Hasselbalch equation especially convenient for buffer calculations?

It is convenient when the weak acid and conjugate base are both present and the change from their equilibrium ionization is small compared with their initial concentrations. For added strong acid or base, first use stoichiometry to update the moles of $HA$ and $A^-$, then apply the equation.

What is the pH of a buffer containing equal concentrations of acetic acid and acetate ion?

Because $[A^-]/[HA]=1$, $\log(1)=0$, so $pH=pK_a$. For acetic acid with $K_a=1.8\times10^{-5}$, $pK_a\approx4.74$.

How should added strong acid or base be handled before applying the Henderson-Hasselbalch equation?

Perform the limiting-reactant neutralization using moles first. Subtract moles of $OH^-$ from $HA$ and add the same amount to $A^-$, or subtract moles of $A^-$ when it reacts with added $H_3O^+$; then use the updated ratio, with concentrations or moles as long as both use the same total volume.

Why does a buffer undergo a much smaller pH change than an unbuffered solution after adding a small amount of strong base?

In a buffer, the added $OH^-$ reacts nearly completely with the weak acid, changing the $HA/A^-$ ratio only slightly. In an unbuffered solution, the same base can greatly exceed the initial hydronium amount, leaving excess $OH^-$ and causing a large pH increase.

Buffer capacity

Buffer capacity is the amount of strong acid or strong base that can be added to a given amount of buffer before the pH changes substantially, often defined as a change of about one pH unit. It increases with the total concentrations and amounts of both conjugate partners.

How do buffer composition and concentration affect buffer performance?

A buffer works best when $[HA]$ and $[A^-]$ are approximately equal, giving $pH\approx pK_a$. Greater total concentrations provide greater capacity, even if two buffers have the same pH; a buffer becomes much less effective when one component falls below roughly 10% of the other.

How should a buffer be selected for a target pH?

Choose a weak acid whose $pK_a$ is close to the desired pH, or a weak base whose conjugate-acid $pK_a$ is close to the desired pH. Weak-acid buffers are generally suited to pH values below 7, while weak-base buffers are generally suited to pH values above 7.

What reactions allow the carbonic acid-bicarbonate buffer in blood to resist pH changes?

Added acid is consumed by $H_3O^++HCO_3^-\rightarrow H_2CO_3+H_2O$. Added base is consumed by $OH^-+H_2CO_3\rightarrow HCO_3^-+H_2O$, keeping blood pH near 7.4.

Why does dilution have little effect on the pH of a buffer but reduce its capacity?

If both $HA$ and $A^-$ are diluted by the same factor, their concentration ratio remains nearly unchanged, so the Henderson-Hasselbalch pH remains similar. However, dilution reduces the total moles per volume available to neutralize added acid or base, lowering capacity.