Acids and bases

Here is an explanation of the core concepts covered in your notes:

1. Fundamental Theories of Acids and Bases

• Arrhenius Theory: Focuses on aqueous solutions. An acid increases $H^+<em>{(aq)}$ concentration, while a base increases $OH^-</em>{(aq)}$ concentration. Its limitation is that it only applies to water solutions and fails to explain substances like $NH_3$ that act as bases without containing hydroxide ions.

• Brønsted-Lowry Theory: Expands acid-base reactions to proton transfer. An acid is a proton ($H^+$) donor, and a base is a proton acceptor. When an acid loses a proton, it forms its conjugate base; when a base gains a proton, it forms its conjugate acid. Substances that can either donate or accept a proton (such as $H<em>2O$ and $HCO</em>3^-$) are called amphiprotic.

• Lewis Theory: Focuses on electron pairs. A Lewis acid accepts an electron pair into an empty orbital (e.g., $BF<em>3$), while a Lewis base donates a lone pair (e.g., $NH</em>3$). Their reaction forms a coordinate covalent bond.

2. Autoionization of Water and the pH Scale

• Water naturally self-ionizes in an endothermic reaction: $2H<em>2O</em>{(l)} <br>ightleftharpoons H<em>3O^+</em>{(aq)} + OH^-_{(aq)}$.

• The ion product constant of water at $298\,K$ is $K<em>w = [H^+][OH^-] = 1.00 \times 10^{-14}\,mol^2\,dm^{-6}$. Because the process is endothermic, increasing the temperature increases $K</em>w$, shifting the neutral $pH$ below $7$.

• The $pH$ and $pOH$ scales quantify acidity and basicity logarithmically: $pH = -\log<em>{10}([H^+])$ and $pOH = -\log</em>{10}([OH^-])$. At $298\,K$, they relate by $pH + pOH = 14.00$.

3. Strong vs. Weak Acids and Bases

• Strong Acids and Bases: Completely dissociate in water ($\alpha \approx 100\%$), meaning $[H^+]$ or $[OH^-]$ is directly determined from the initial concentration.

• Weak Acids and Bases: Only partially dissociate and reach dynamic equilibrium. Their strengths are measured by dissociation constants ($K<em>a$ and $K</em>b$) and their logarithmic values ($pK<em>a$ and $pK</em>b$). Lower values of $pK<em>a$ or $pK</em>b$ signify stronger acids or bases. For a conjugate pair, $K<em>a \times K</em>b = K<em>w$ and $pK</em>a + pK_b = 14.00$ at $298\,K$.

4. Neutralization Reactions and Titrations

• When acids and bases neutralize each other, the equivalence point $pH$ depends on their relative strengths:

  • Strong acid + strong base yields a neutral solution ($pH = 7.00$ at $298\,K$).

  • Weak acid + strong base results in an equivalence point with $pH > 7$ due to conjugate base hydrolysis.

  • Strong acid + weak base results in an equivalence point with $pH < 7$ due to conjugate acid hydrolysis.

5. Buffer Solutions

• Buffers resist changes in $pH$ when small amounts of acid or base are added. An acidic buffer consists of a weak acid and its conjugate base salt (such as $CH<em>3COOH$ and $$CH3