Acid-Base Equilibria and Additional Aspects of Aqueous Equilibria: Study Notes

Acid-Base Equilibria

Brønsted-Lowry Acid and Base Theory

The Brønsted-Lowry theory defines acids as proton donors and bases as proton acceptors. This concept is fundamental to understanding acid-base reactions in aqueous solutions.

• Acid: Substance that donates a proton (H+).

• Base: Substance that accepts a proton (H+).

• Example: In the reaction between hydrochloric acid (HCl) and ammonia (NH3), HCl acts as an acid and NH3 as a base.

Conjugate Acid-Base Pairs

Every acid-base reaction involves a pair of conjugate acids and bases. The acid forms its conjugate base after donating a proton, and the base forms its conjugate acid after accepting a proton.

• Conjugate acid: Species formed when a base gains a proton.

• Conjugate base: Species formed when an acid loses a proton.

• Example: NH4+ is the conjugate acid of NH3; Cl- is the conjugate base of HCl.

pH and pOH Calculations

pH and pOH are measures of the acidity and basicity of a solution, respectively. They are related to the concentrations of hydrogen ions and hydroxide ions.

• pH: $pH = -\log[H^+]$

• pOH: $pOH = -\log[OH^-]$

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

• Example: If $[H^+] = 1 \times 10^{-3}$ M, then $pH = 3$.

Strong vs. Weak Acids and Bases

Strong acids and bases dissociate completely in water, while weak acids and bases only partially dissociate.

• Strong acid/base: Complete ionization in solution (e.g., HCl, NaOH).

• Weak acid/base: Partial ionization (e.g., CH3COOH, NH3).

• Example: HCl is a strong acid; acetic acid (CH3COOH) is a weak acid.

Calculating pH of Strong and Weak Acids/Bases

The method for calculating pH depends on whether the acid/base is strong or weak.

• Strong acid/base: Use direct concentration for $[H^+]$ or $[OH^-]$.

• Weak acid/base: Use equilibrium calculations involving $K_a$ or $K_b$.

• Example: For 0.1 M HCl, $pH = 1$; for 0.1 M acetic acid, use $K_a$ to find $[H^+]$.

Acid and Base Strength (Ka and Kb)

The strength of an acid or base is quantified by its dissociation constant: $K_a$ for acids and $K_b$ for bases.

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

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

• Relationship: $K_a \times K_b = K_w = 1 \times 10^{-14}$ (at 25°C)

Classification of Substances as Acidic, Basic, or Neutral

Substances can be classified based on their behavior in water.

• Acidic: $pH < 7$

• Basic: $pH > 7$

• Neutral: $pH = 7$

• Example: Pure water is neutral; lemon juice is acidic; soap solution is basic.

Relative Strengths of Acids and Bases

The strength of acids and bases is compared using their $K_a$ and $K_b$ values.

• Higher $K_a$: Stronger acid

• Lower $K_a$: Weaker acid

• Example: HCl ($K_a$ very large) vs. acetic acid ($K_a = 1.8 \times 10^{-5}$)

Ranking Acids and Bases by Strength

Acids and bases can be ranked from strongest to weakest based on their dissociation constants.

• Strongest acid: Highest $K_a$

• Weakest acid: Lowest $K_a$

• Example: List: HCl > HNO3 > CH3COOH

Additional Aspects of Aqueous Equilibria

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, or a weak base and its conjugate acid.

• Preparation: Mix a weak acid with its salt (e.g., acetic acid and sodium acetate).

• Function: Maintains pH stability in biological and chemical systems.

• Example: Blood contains a bicarbonate buffer system.

Buffer Calculations and the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the pH of buffer solutions.

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

• Application: Used to design buffers with specific pH values.

• Example: For a buffer with $[A^-] = 0.1$ M and $[HA] = 0.1$ M, $pH = pK_a$.

Titration of Acids and Bases

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

• Strong acid/strong base titration: Sharp pH change at equivalence point.

• Weak acid/strong base titration: Buffer region before equivalence point.

• Example: Titrating acetic acid with NaOH.

pH at Equivalence Point

The pH at the equivalence point depends on the strength of the acid and base involved in the titration.

• Strong acid/strong base: $pH = 7$ at equivalence.

• Weak acid/strong base: $pH > 7$ at equivalence.

• Weak base/strong acid: $pH < 7$ at equivalence.

Effect of Dilution on Buffer pH

When a buffer solution is diluted, the ratio of acid to base remains the same, so the pH does not change significantly.

• Key point: Buffer capacity decreases with dilution, but pH remains nearly constant.

Effect of Acid/Base Strength on pH

The strength of the acid or base affects the resulting pH of a solution.

• Stronger acid: Lower pH

• Stronger base: Higher pH

• Example: 0.1 M HCl (strong acid) has lower pH than 0.1 M acetic acid (weak acid).

Relationship Between Ka, Kb, and Kw

The acid dissociation constant ($K_a$) and base dissociation constant ($K_b$) are related to the ion product of water ($K_w$).

• Equation: $K_a \times K_b = K_w$

• At 25°C: $K_w = 1 \times 10^{-14}$

• Application: If $K_a$ is known, $K_b$ can be calculated, and vice versa.

Short Answer Topics

pH of Weak and Strong Acids/Bases

Calculating the pH of weak and strong acids/bases requires different approaches.

• Strong acid/base: Use direct concentration for $[H^+]$ or $[OH^-]$.

• Weak acid/base: Use $K_a$ or $K_b$ and equilibrium calculations.

Buffer pH After Addition of Strong Acid/Base

Adding a strong acid or base to a buffer changes the ratio of acid to base, but the buffer resists drastic pH changes.

• Calculation: Use the Henderson-Hasselbalch equation after adjusting concentrations.

Buffer pH After Dilution

When a buffer is diluted, the concentrations of acid and base decrease, but their ratio remains the same, so pH is largely unchanged.

Buffer pH After Addition of Strong Base

Adding a strong base to a buffer increases the concentration of the conjugate base and decreases the concentration of the acid.

• Calculation: Adjust concentrations and use the Henderson-Hasselbalch equation.

Converting Between Ka and Kb

Ka and Kb are related through the ion product of water, $K_w$.

• Equation: $K_a \times K_b = K_w$

• To find $K_b$: $K_b = \frac{K_w}{K_a}$

• To find $K_a$: $K_a = \frac{K_w}{K_b}$