Acid-Base Equilibria: Definitions, Properties, and Applications

Acid-Base Equilibria

Overview

This chapter explores the fundamental concepts of acid-base equilibria, including definitions, conjugate pairs, autoionization of water, pH calculations, strengths of acids and bases, properties of dissolved salts, and the influence of chemical structure on acid-base behavior.

Acid and Base Definitions

Arrhenius Definition

The Arrhenius definition classifies acids and bases based on their behavior in water:

• Acid: Increases H+ concentration when dissolved in water. e.g., hydrogen chloride: $\mathrm{HCl}(g) \xrightarrow{H_2O} \mathrm{H^+}(aq) + \mathrm{Cl^-}(aq)$

• Base: Increases OH- concentration when dissolved in water. e.g., sodium hydroxide: $\mathrm{NaOH}(s) \xrightarrow{H_2O} \mathrm{Na^+}(aq) + \mathrm{OH^-}(aq)$

Brønsted-Lowry Definition

The Brønsted-Lowry definition broadens the concept:

• Acid: Donates a proton (H+) to another substance.

• Base: Accepts a proton from another substance.

Example reaction: $\mathrm{HCl}(g) + \mathrm{H_2O}(\ell) \rightarrow \mathrm{Cl^-}(aq) + \mathrm{H_3O^+}(aq)$

Note: Bare protons do not exist in solution; they coordinate to water molecules to form hydronium ions (H3O+).

Brønsted-Lowry Advantage

• Applies to non-aqueous systems (Arrhenius requires H2O).

• Example: $\mathrm{HCl}(g) + \mathrm{NH_3}(g) \rightarrow \mathrm{NH_4Cl}(s)$

Water is Amphiprotic

Water can act as both a Brønsted-Lowry acid and base:

• As a base: $\mathrm{HCl}(g) + \mathrm{H_2O}(\ell) \rightarrow \mathrm{Cl^-}(aq) + \mathrm{H_3O^+}(aq)$

• As an acid: $\mathrm{H_2O}(\ell) + \mathrm{NH_3}(aq) \rightarrow \mathrm{OH^-}(aq) + \mathrm{NH_4^+}(aq)$

A Brønsted-Lowry acid must be paired with a Brønsted-Lowry base.

Lewis Definition

• Acid: Electron-pair acceptor

• Base: Electron-pair donor

Example: $\mathrm{H^+} + \mathrm{NH_3} \rightarrow [\mathrm{H-NH_3}]^+$

All Brønsted-Lowry acids and bases are also Lewis acids and bases.

Lewis Advantage

• Not every reaction includes a proton transfer.

• All reactions involve electrons.

• Lewis definition accounts for acids and bases without free H+.

• Encompasses all Arrhenius and Brønsted-Lowry species.

Example: $\mathrm{NH_3}(g) + \mathrm{BF_3}(g) \rightarrow \mathrm{H_3NBF_3}(g)$

Conjugate Acid-Base Pairs

Brønsted-Lowry Conjugates

Acid-base pairs exchange a proton and reactions are reversible:

• Acid in forward reaction becomes conjugate base in reverse.

• Base in forward reaction becomes conjugate acid in reverse.

Example: $\mathrm{HNO_3}(aq) + \mathrm{H_2O}(\ell) \rightleftharpoons \mathrm{NO_2^-}(aq) + \mathrm{H_3O^+}(aq)$

Acid and Base Strength

Strengths and Dissociation

• Strong acids fully dissociate in water. $\mathrm{HCl}(g) \xrightarrow{H_2O} \mathrm{H^+}(aq) + \mathrm{Cl^-}(aq)$

• Weak acids partially dissociate. $\mathrm{HF}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{F^-}(aq)$

• The stronger the acid, the weaker its conjugate base (and vice versa).

Conjugate Strengths

Relative strengths of acids and bases can be compared using tables:

Acid	Conjugate Base
Strong acids (e.g., HCl, HNO3)	Negligible basicity (e.g., Cl-, NO3-)
Weak acids (e.g., CH3COOH)	Weak bases (e.g., CH3COO-)
Negligible acidity (e.g., CH4)	Strong bases (e.g., CH3-)

Relative Strengths and Equilibrium

For reactions such as $\mathrm{HSO_4^-}(aq) + \mathrm{CO_3^{2-}}(aq) \rightleftharpoons \mathrm{SO_4^{2-}}(aq) + \mathrm{HCO_3^-}(aq)$, compare acid and base strengths to predict equilibrium direction:

• If $K_c > 1$, equilibrium favors products.

• If $K_c < 1$, equilibrium favors reactants.

Autoionization of Water

Process and Equilibrium

Water self-ionizes because it is amphiprotic:

• $2\mathrm{H_2O}(\ell) \rightleftharpoons \mathrm{OH^-}(aq) + \mathrm{H_3O^+}(aq)$

• This process is called autoionization.

Neutral Solutions

• At 25°C: $K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}$

• In neutral solutions: $[\mathrm{H^+}] = [\mathrm{OH^-}]$

Acidic and Basic Solutions

• Acidic: $[\mathrm{H^+}] > [\mathrm{OH^-}]$

• Basic: $[\mathrm{OH^-}] > [\mathrm{H^+}]$

• Neutral: $[\mathrm{H^+}] = [\mathrm{OH^-}]$

Temperature Dependence of $K_w$

$K_w$ varies with temperature:

Temp (°C)	$K_w$ (x 10-14)
0	0.12
25	1.0
50	5.3
100	54

pH and Related Calculations

pH Scale

• pH is defined as $\mathrm{pH} = -\log[\mathrm{H^+}]$

• Each pH unit change corresponds to a tenfold change in $[\mathrm{H^+}]$

• At 25°C, neutral solution: $[\mathrm{H^+}] = 1.0 \times 10^{-7}$ M, so pH = 7.00

Using p as a Function

• pOH = $-\log[\mathrm{OH^-}]$

• p$K_w$ = $-\log K_w = 14.00$ at 25°C

• pH + pOH = 14.00 (memorize this!)

Concentration Ranges

• For solutions at 25°C: $K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}$

• $[\mathrm{H^+}]$ and $[\mathrm{OH^-}]$ can range from $8.3 \times 10^{-16}$ M to 12 M

• When one increases, the other decreases

Solutions at 25°C

Solution	pH	pOH
Stomach acid	1.0	13.0
Water	7.0	7.0
Household ammonia	11.0	3.0

Measuring pH

• pH meters: Precise and accurate, measure voltage between electrodes

• Chemical indicators: Easy to use, change color over a pH range, less precise

• Indicators can be combined and soaked into paper to make pH strips

Strong and Weak Acids and Bases

Strong Acids and Bases

• Strong acids fully dissociate: $[\mathrm{H^+}] = [\text{acid}]$

• Strong bases fully dissociate: $[\mathrm{OH^-}] = [\text{base}] \times$ (number of OH- per formula unit)

• At 25°C: $[\mathrm{H^+}] = \frac{1.0 \times 10^{-14}}{[\mathrm{OH^-}]}$ or pH = 14.00 - pOH

Weak Acids

• Weak acids (HA) do not fully dissociate: $\mathrm{HA}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{A^-}(aq)$

• Equilibrium constant: $K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

• $K_a$ varies with acid identity and temperature

Strong vs. Weak Acids

• Strong acids: $K_a$ is very large, complete dissociation

• Weak acids: $K_a$ is small, partial dissociation

Selected Weak Acids at 25°C

Acid	Conjugate Base	$K_a$
Acetic acid (CH3COOH)	CH3COO-	$1.8 \times 10^{-5}$
Formic acid (HCOOH)	HCOO-	$1.8 \times 10^{-4}$
Benzoic acid (C6H5COOH)	C6H5COO-	$6.3 \times 10^{-5}$

Calculating $K_a$ from pH

• Use ICE tables to determine equilibrium concentrations

• Example: For formic acid, $\mathrm{CHOOH}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{CHOO^-}(aq)$, pH = 2.38 for 0.10 M solution

Calculating pH from $K_a$

• Example: For acetic acid, $\mathrm{CH_3COOH}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{CH_3COO^-}(aq)$, $K_a = 1.8 \times 10^{-5}$

• Use ICE table to solve for [H+] and calculate pH

Weak Acid Percent Dissociation

• Percent ionization = $\frac{[\mathrm{H^+}]_{\text{equilibrium}}}{[\mathrm{HA}]_{\text{initial}}} \times 100$

• Strong acids have nearly 100% ionization

Kinetic Effects of Acid Strength

• Strong acids react more rapidly, but both strong and weak acids reach the same equilibrium

Polyprotic Acids

Definition and Properties

• Polyprotic acids can donate more than one proton (H+)

• Each proton has a different $K_a$ value: $K_{a1}$, $K_{a2}$, etc.

• Each successive proton is harder to remove

Example: Sulfurous acid $\mathrm{H_2SO_3}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{HSO_3^-}(aq)$, $K_{a1} = 1.7 \times 10^{-2}$ $\mathrm{HSO_3^-}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{SO_3^{2-}}(aq)$, $K_{a2} = 6.4 \times 10^{-8}$

Which Protons Are Acidic?

• Hydrogen atoms bonded to carbon are usually NOT acidic

• Acidic hydrogens are often bonded to O, S, N, F, Cl, Br, I

Polyprotic Acid Example

When CO2 is dissolved in water: $\mathrm{CO_2}(aq) + \mathrm{H_2O}(\ell) \rightarrow \mathrm{H_2CO_3}(aq)$ $\mathrm{H_2CO_3}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{HCO_3^-}(aq)$, $K_{a1} = 4.3 \times 10^{-7}$ $\mathrm{HCO_3^-}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{CO_3^{2-}}(aq)$, $K_{a2} = 5.6 \times 10^{-11}$

Weak Bases

Definition and Equilibrium

• Weak bases (B) do not fully dissociate: $\mathrm{B}(aq) + \mathrm{H_2O}(\ell) \rightleftharpoons \mathrm{BH^+}(aq) + \mathrm{OH^-}(aq)$

• Equilibrium constant: $K_b = \frac{[\mathrm{BH^+}][\mathrm{OH^-}]}{[\mathrm{B}]}$

• $K_b$ varies with base identity and temperature

Weak Base Examples (Brønsted-Lowry)

Base	Structure	Conjugate Acid	$K_b$
Ammonia (NH3)	NH3	NH4+	$1.8 \times 10^{-5}$
Hydroxylamine (NH2OH)	NH2OH	NH3OH+	$9.1 \times 10^{-7}$
Hypochlorite ion (ClO-)	ClO-	HClO	$3.3 \times 10^{-7}$

Acid-Base Properties of Dissolved Salts

Acid-Base Salts

• Sodium chloride solution is neutral; sodium carbonate solution is basic

• Complete dissociation in water: NaCl → Na+ + Cl-; Na2CO3 → 2Na+ + CO32-

• NaOH is a strong base (Na+ negligible acidity); HCl is a strong acid (Cl- negligible basicity)

• CO32- is a weak base; HCO3- is a very weak acid

Cation Induced Hydrolysis

• Cations are Lewis acids (electron-pair acceptors)

• Water acts as a Lewis base (electron-pair donor)

• Water molecules coordinated to cations have increased tendency to dissociate (hydrolysis)

• Lewis acidity increases with cation charge

Cation	$K_a$
Fe3+	$6.3 \times 10^{-3}$
Cr3+	$1.6 \times 10^{-4}$
Al3+	$1.4 \times 10^{-5}$
Fe2+	$3.2 \times 10^{-10}$
Ni2+	$2.5 \times 10^{-11}$

Charge and Electronegativity

• Charge effect on acidity is minimal for Groups 1 and 2 cations

• Small charges cannot disrupt filled shells (except Mg2+ and Be2+)

• Lewis acidity increases with cation charge and electronegativity

Element	EN Value
Al	1.61
Cr	1.66
Fe	1.83
Ni	1.65

Chemical Structure Effects on Acid-Base Behavior

Factors Affecting Acid Strength

• Bond polarity: Higher electronegativity of A in HA increases acidity

• Bond strength: Stronger HA bonds make H less acidic

• Conjugate base stability: More stable conjugate base increases acidity

For binary acids (H-A), bond strength and polarity are key. For oxyacids (H-O-Y), electronegativity and number of oxygens affect strength.

Oxyacids

• Oxyacids have acidic H bonded to O, which is bonded to Y (often a nonmetal)

• More oxygen atoms increase acid strength due to electron withdrawal

Carboxylic Acids

• Contain a carboxyl group (-COOH)

• Acidity is enhanced by resonance stabilization and electron withdrawal

• Examples: Formic acid (Ka = $1.8 \times 10^{-4}$), Benzoic acid (Ka = $6.3 \times 10^{-5}$)

Summary Table: Acid-Base Definitions

Definition	Acid	Base
Arrhenius	Increases [H+]	Increases [OH-]
Brønsted-Lowry	Proton donor	Proton acceptor
Lewis	Electron-pair acceptor	Electron-pair donor

Key Equations

• $K_w = [\mathrm{H^+}][\mathrm{OH^-}]$

• $\mathrm{pH} = -\log[\mathrm{H^+}]$

• $\mathrm{pOH} = -\log[\mathrm{OH^-}]$

• $K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

• $K_b = \frac{[\mathrm{BH^+}][\mathrm{OH^-}]}{[\mathrm{B}]}$

• Percent ionization = $\frac{[\mathrm{H^+}]_{\text{eq}}}{[\mathrm{HA}]_{\text{initial}}} \times 100$

Applications

• pH measurement in laboratory and industry

• Understanding acid-base properties of household substances (e.g., vinegar, bleach)

• Predicting solution behavior based on salt composition

• Designing buffer solutions and controlling pH in chemical processes

Additional info: Some context and examples have been expanded for clarity and completeness, including tables and explanations of chemical structure effects.