Acids, Bases, and Equilibrium: General Chemistry Study Notes

Acids and Bases

Acid Strength and Dissociation Constants

Acids are substances that donate protons (H+) in aqueous solution, while bases accept protons. The strength of an acid is determined by its ability to dissociate in water, which is quantified by the acid dissociation constant, Ka.

• Strong acids dissociate completely in water; weak acids only partially dissociate.

• Ka values indicate acid strength: higher Ka means a stronger acid.

• Example table of acid strengths:

Acid	Ka
HNO3	4.5 × 10–1
HClO4	1.0 × 10–2
HNO2	4.5 × 10–4
HCN	4.9 × 10–10

• Strongest acid: HNO3 (highest Ka)

• Weakest acid: HCN (lowest Ka)

Formula:

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

pH and pOH Calculations

The pH of a solution measures its acidity, defined as the negative logarithm of the hydrogen ion concentration.

• pH formula: $pH = -\log[H^+]$

• pOH formula: $pOH = -\log[OH^-]$

• Relationship: $pH + pOH = 14$ (at 25°C)

• For strong acids, $[H^+]$ equals the acid concentration.

• For weak acids, use the $K_a$ expression to solve for $[H^+]$.

Example: For a 0.01 M HCl solution (strong acid):

$[H^+] = 0.01$

$pH = -\log(0.01) = 2$

Equilibrium and Acid-Base Reactions

Equilibrium Constants

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal. The equilibrium constant, K, quantifies the ratio of product to reactant concentrations at equilibrium.

• Ka: Acid dissociation constant

• Kb: Base dissociation constant

• Kw: Water dissociation constant ($K_w = 1.0 \times 10^{-14}$ at 25°C)

• Relationship: $K_a \times K_b = K_w$

Example: For NH3 (ammonia), a weak base:

$K_b = \frac{[NH_4^+][OH^-]}{[NH_3]}$

Buffer Solutions

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They are typically made from a weak acid and its conjugate base.

• Henderson-Hasselbalch equation:

$pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Effective buffers have $pH$ within 1 unit of the $pK_a$ of the acid.

• Example: To prepare a buffer with $pH = 9.65$, choose an acid with $pK_a$ close to 9.65.

Solubility and Precipitation

Solubility Product Constant (Ksp)

The solubility product constant, Ksp, describes the equilibrium between a solid and its ions in solution.

• Formula: For $AB_2$ dissolving: $K_{sp} = [A^{2+}][B^-]^2$

• To find solubility ($s$): Set up the equilibrium expression and solve for $s$.

Example: For PbI2:

$K_{sp} = [Pb^{2+}][I^-]^2$

If $K_{sp} = 1.4 \times 10^{-8}$, then:

$[Pb^{2+}] = s$

$[I^-] = 2s$

$K_{sp} = s \times (2s)^2 = 4s^3$

Solve for $s$:

$s = \sqrt[3]{\frac{K_{sp}}{4}}$

Titrations and pH at Equivalence Point

Acid-Base Titrations

Titration is a technique to determine the concentration of an acid or base by reacting it with a solution of known concentration.

• At the equivalence point, moles of acid equal moles of base.

• For strong acid-strong base titrations, the pH at equivalence is 7.

• For weak acid-strong base titrations, the pH at equivalence is greater than 7.

Example: Titrating 0.100 M acetic acid with 0.100 M NaOH:

• At equivalence, all acetic acid is converted to acetate ion.

• Calculate pH using the hydrolysis of acetate:

$CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$

Use $K_b$ for acetate to find $[OH^-]$, then calculate pOH and pH.

Summary Table: Key Constants and Relationships

Constant	Definition	Formula
Ka	Acid dissociation	$K_a = \frac{[H^+][A^-]}{[HA]}$
Kb	Base dissociation	$K_b = \frac{[BH^+][OH^-]}{[B]}$
Kw	Water dissociation	$K_w = [H^+][OH^-]$
Ksp	Solubility product	$K_{sp} = [M^{n+}]^x [A^{m-}]^y$

Additional info:

• Some questions and handwritten notes were skipped or marked as not relevant; only core General Chemistry concepts were included.

• All equations are provided in LaTeX format for clarity.

• Examples and tables are reconstructed based on standard textbook knowledge.