Ka and Kb

Weak Acids and Bases: Ka and Kb

Introduction

• Strong acids and bases:
  • Typically inorganic (e.g., hydrochloric acid, sulfuric acid, sodium hydroxide).
  • Dissociate or react nearly 100% in the forward direction (Arrhenius and Bronsted theories).
  • Example: $"HCl(aq) \rightarrow H^+(aq) + Cl^-(aq)"$ (one-way arrow indicates complete dissociation).
  • Example: Sodium hydroxide (NaOH) as a strong base.
• Weak acids and bases:
  • Most organic or biochemical acids are carboxylic acids.
  • Organic/biochemical bases are amines.
  • Do not react 100% in the forward direction; exist in equilibrium.

Carboxylic Acids

• Functional group: Carboxyl group (-COOH) at the end of a carbon chain.
• Structure: C double bond O (carbonyl group), with an -OH group attached.
• Acidic hydrogen: Hydrogen atom bonded to the oxygen of the carboxyl group is acidic.
• General formula: R-COOH, where R represents the rest of the molecule.

Amines

• Similar to ammonia (NH3).
• Lone pair on the nitrogen atom attracts H+.
• Basicity illustrated using the Bronsted definition.
• Formed by replacing one or more hydrogens in ammonia with carbon groups.
• Primary, secondary, and tertiary amines are based on the number of carbon atoms bonded to the nitrogen.

Weak Acids and Bases

• Exist in equilibrium between molecular (undissociated) and ionized (acid and base) forms.
• Molecular form: Reactant side of the equilibrium.
• Acid or base forms: Ionized or product side of the equilibrium expression.
• Do not dissociate 100% (Arrhenius definition).

Acetic Acid Example

• Acetic acid (CH3COOH) is the acid found in vinegar.
• Has a C double bond O with an -OH group, making the hydrogen acidic.
• Other hydrogens (e.g., in CH3) are not acidic.
• Alcohols (H attached to O, but not C double bond O) are generally not acidic (except for phenol).
• Bronsted dissociation: $"CH<em>3COOH(aq) + H</em>2O(l) \rightleftharpoons CH<em>3COO^-(aq) + H</em>3O^+(aq)"$
• Representations of acetic acid:
  • Structural formula: Shows the connection of all atoms.
  • Molecular formula: Written as HC2H3O2 (acidic hydrogen written first).
  • Condensed structural formula: CH3COOH (COOH at the end indicates C double bond OOH, which is acidic).

Equilibrium Constant Expressions

• Weak acids and bases exist in equilibrium.
• Ka: Acid ionization constant.
• Kb: Base ionization constant.
• Water (a pure liquid) is not included in the equilibrium constant expression.
• Kc, Ka, and Kb are experimentally determined.
• For weak acids and bases, K is less than one (usually much less).

Examples of Ka and Kb

• Hydrocyanic acid (HCN) as a weak acid:
  • Dissolves in water to form hydronium (H3O+) and cyanide (CN-).
  • Reaction: $"HCN(aq) + H<em>2O(l) \rightleftharpoons H</em>3O^+(aq) + CN^-(aq)"$
  • $K<em>a = \frac{[H</em>3O^+][CN^-]}{[HCN]}$
  • Ka value is experimentally determined (e.g., $4.9 \times 10^{-10}$).
  • Can also be written as Arrhenius expression: $"HCN \rightleftharpoons H^+ + CN^-"$
• Methylamine as a weak base:
  • Breaks water into H-OH, takes H+ to form methylammonium cation and OH-.
  • $K<em>b = \frac{[CH</em>3NH<em>3^+][OH^-]}{[CH</em>3NH_2]}$

Ka and Acidity/Basicity

• As Ka increases, acid strength increases.
• As Kb increases, base strength increases.
• No Ka for strong acids or strong bases because the denominator in the Ka expression approaches zero.
• Ka and Kb apply only to weak acids and bases.

Weak Acids and Percent Ionization

• Initial concentration: Pre-dissociation concentration of the acid.
• Most acids in labs are already in solution.
• Thought experiment: Imagine dissolving a pure acid in water.
• Percent ionization: Percentage of the initial acid that converts to the ionized form at equilibrium.
  • $\% \text{ ionization} = \frac{[H^+]<em>{\text{equilibrium}}}{[HA]</em>{\text{initial}}} \times 100\%$
  • Lower Ka has the lowest percent ionization.
  • As Ka increases, percent ionization increases.

Multiple Equilibria

• Diprotic and triprotic acids do not dissociate to yield all hydrogens in one step.
• Each step has a different Ka value (Ka1 > Ka2 > Ka3).
• Example: Carbonic acid (H2CO3) dissociates in two steps.
• Example: Phosphoric acid (H3PO4) dissociates in three steps.

Strength vs. Concentration

• Strength: Percent ionization.
• Concentration: Molar concentration written on the bottle (initial concentration).
• pH depends on both strength and concentration.

Comparing pH of Acids

• Example: Comparing 1 M nitrous acid (HNO2) and 1 M hydrochloric acid (HCl).
• HCl is a strong acid, so 100% dissociates.
• HNO2 is a weak acid, with only 2.1% dissociation.
• pH = -log[H+], where [H+] is the ionized hydrogen concentration.
• For HCl, pH = -log(1) = 0.
• For HNO2, pH = -log(0.021 * 1) = 1.7.
• pH depends on both strength and concentration.

Calculating Equilibrium Concentrations

• Using the Ka value and initial concentration to find equilibrium concentrations.
• Example: Calculating pH of a 0.1 M vinegar solution (acetic acid).
• Reaction: $"CH<em>3COOH \rightleftharpoons H^+ + CH</em>3COO^-"$
• Ka = [H+][CH3COO-]/[CH3COOH].

ICE Table

• Initial concentration (I).
• Change in concentration (C).
• Equilibrium concentration (E).
• Pretend all acetic acid is in the molecular form initially.
• Let x equal the change in hydrogen ion concentration.
• Equilibrium concentrations: initial - x, +x, +x.
• Ka = x * x / (0.1 - x) = x^2 / (0.1 - x).

Approximation

• If Ka is small, assume initial concentration - x ≈ initial concentration.
• x is the fly on the hippo's back.
• Then, Ka = x^2 / 0.1, so x = √(Ka * 0.1).
• With this approximation, x = 0.0013 M.

Percent Ionization and pH

• Percent ionization = (equilibrium concentration of H+ / initial concentration) * 100%.
• pH = -log[H+] = -log(0.0013) = 2.9.
• Rule of thumb: If percent ionization is less than 5%, or Ka is less than 10^-4, the approximation is valid.
• Double check percent ionization to confirm validity.

Additional Examples and Considerations

• Example: Calculating [H+], [CH3COO-], and [CH3COOH] in a 0.5 M acetic acid solution.
• Reiterate that pH depends on both strength and concentration of the acid.
• As concentrations get smaller, the amount that dissociates, as a percentage, gets bigger and bigger.
• For the four serial dilutions you'll do of acetic acid in the lab, the approximation may not work for all of them.
• Ka is experimentally measured using pH measurements and working backwards.
• Measuring pHs of different acetic acid concentrations, then compare calculated Ka with known Ka for acetic acid (1.8 × 10^-5).

Weak Base Calculations

• What is the pH of a two molar aniline aqueous solution? Aniline has a Kb of 3.8 * 10^-10.
• Solve for x.
• The x that you solve for is OH-.

Methylamine

• Equation to use: pH = 14 - pOH
• Have to write the equation and the K expression.
• Aniline + water -> C6H5NH3+ + OH-
• Kb = [anilinium cation][hydroxide] / [aniline]
• Much of the same K is so small.
• Assume two minus x Equals two
• Calculate it out 9.4 is roughly pH

Practice Problems

• Have fun working problems well see in lab soon.
• Some additional questions I'd asked (see them here).\
• Calculate H+ and para aminobenzoate ion in a solution.
• Set c6h5nh2coo Equals one can you just the generic form
• Set solve percent ionization comes out to be lower.
• Hydrochloric and hydronic are weak electrolytes what it's the initial.
• I tried to with information If is greater than the not right
• Get a with the quadratic of course.
• If are given three so pigs.
• Now let's get and the the equation expression and and start.