Ionic Equilibria PHM 312

What are the learning objectives regarding electrolytes and ions?

Define a strong electrolyte, a weak electrolyte, and a nonelectrolyte; and differentiate between a cation and an anion.

What are the learning objectives regarding acids and bases?

Define an acid, a base, and the different types of salts; describe the ionization equilibria of strong and weak electrolytes; and calculate and interpret ionization constants (Ka, Kb, pKa, pKb).

What are the learning objectives regarding pH and drug absorption?

Calculate pH, pOH, and the concentrations of components in aqueous solutions of weak electrolytes; calculate percent ionization as a function of pH; and describe the physiologic implications of ionization (pH partition hypothesis) in drug absorption, transport, and excretion.

What is the hydronium ion (H₃O⁺)?

The ion produced from water's self-ionization. Its concentration in pure water is 10⁻⁷ M at 25°C.

What is the equation for the ionization of water?

H₂O + H₂O ⇌ H₃O⁺ + OH⁻.

What is the equilibrium constant (K) expression for the ionization of water?

K = (H₃O⁺)(OH⁻) / (H₂O)(H₂O).

Why can we assume (H₂O) is constant in the water ionization equilibrium?

Because (H₃O⁺) <<< (H₂O).

What is the ion product of water (Kw)?

Kw = K(H₂O)² = (H₃O⁺)(OH⁻) = 1 × 10⁻¹⁴.

What is the formula for pH?

pH = -log[H₃O⁺].

What is the formula for pOH?

pOH = -log[OH⁻].

What is the relationship between pH and pOH?

pH + pOH = 14.

Calculate the pH of a 0.05M HCl solution in water (assume 100% ionization).

HCl is a strong acid, so [H₃O⁺] = 0.05. pH = -log(0.05) = 1.3.

What is the Bronsted-Lowry Acid-Base Theory?

An acid donates a proton in solution, and a base accepts a proton in solution, resulting in conjugate acid-base pairs.

What is the Bronsted-Lowry equation for acetic acid in water?

CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO⁻.

What is the Bronsted-Lowry equation for ammonia in water?

NH₃ + H₂O ⇌ NH₄⁺ + OH⁻.

In the reaction HA + H₂O ⇌ A⁻ + H₃O⁺, what is A⁻ and what is H₃O⁺?

A⁻ (anion) is the conjugate base of HA, and H₃O⁺ (hydronium ion) is the conjugate acid of H₂O.

What are hydronium ions?

Hydrated protons. The terms "hydronium ion" and "proton" are sometimes used interchangeably.

What is the equilibrium constant expression for a weak acid (HA)?

K = (A⁻)(H₃O⁺) / (HA)(H₂O).

What is the Ka expression for a weak acid?

Ka = K(H₂O) = (A⁻)(H₃O⁺) / (HA).

What is the Henderson-Hasselbalch equation for a weak acid?

pH = pKa + log([A⁻]/[HA]).

What is the equation for the ionization of a weak base (B)?

B + H₂O ⇌ BH⁺ + OH⁻.

In the weak base reaction, what is BH⁺ and what is OH⁻?

BH⁺ (cation) is the conjugate acid of B. OH⁻ (hydroxide ion) is the conjugate base of water (since water donated a proton).

What is the Kb expression for a weak base?

Kb = K(H₂O) = (BH⁺)(OH⁻) / (B).

What is the relationship between Ka, Kb, and Kw?

Kw = Ka × Kb. Also, Ka = Kw / Kb.

What is the Henderson-Hasselbalch equation for a weak base?

pH = pKa + log([B]/[BH⁺]).

At 25°C, what is the value of Kw and what does it mean for a neutral solution?

Kw = [OH⁻][H₃O⁺] = 10⁻¹⁴. For a neutral solution, [OH⁻] = [H₃O⁺] = 10⁻⁷ M.

For an acidic solution, what is the relationship between [OH⁻] and [H₃O⁺]?

[OH⁻] < [H₃O⁺].

For a basic solution, what is the relationship between [OH⁻] and [H₃O⁺]?

[OH⁻] > [H₃O⁺].

How do Ka and pKa relate to acid strength?

The larger the value of Ka, the stronger the acid. The smaller the pKa, the stronger the acid.

Given the Ka and pKa values, which is the strongest and weakest acid: Penicillin G (Ka = 1.7 x 10⁻³; pKa = 2.8), Aspirin (Ka = 3.3 x 10⁻⁴; pKa = 3.5), Phenobarbital (Ka = 3.9 x 10⁻⁸; pKa = 7.4), Sulfapyridine (Ka = 3.6 x 10⁻⁹; pKa = 8.4)?

Penicillin G is the strongest acid (largest Ka, smallest pKa). Sulfapyridine is the weakest acid (smallest Ka, largest pKa).

What is the molecular weight, Ka, and pKa of Acetaminophen?

MW: 151.16; Ka: 3 × 10⁻¹⁰; pKa: 9.5.

What is the molecular weight, Ka, and pKa of Acetic acid?

MW: 60.05; Ka: 1.75 × 10⁻⁵; pKa: 4.76.

What is the molecular weight, Ka, and pKa of Acetylsalicylic acid (Aspirin)?

MW: 180.15; Ka: 3.27 × 10⁻⁴; pKa: 3.49.

What is the molecular weight, Ka, and pKa of Ampicillin (K1 and K2)?

MW: 349.42; K1: 3 × 10⁻³ (pKa 2.65); K2: 5.6 × 10⁻⁸ (pKa 7.2).

How do Kb and pKb relate to base strength?

The larger the value of Kb, the stronger the base. The smaller the pKb, the stronger the base.

Given the Kb and pKb values, which is the strongest and weakest base: Ephedrine (Kb = 2.3 x 10⁻⁵; pKb = 4.6), Tetracycline (Kb = 2.0 x 10⁻⁶; pKb = 5.7), Codeine (Kb = 9.0 x 10⁻⁷; pKb = 6.1), Theophylline (Kb = 5.0 x 10⁻¹⁴; pKb = 13.3)?

Ephedrine is the strongest base (largest Kb, smallest pKb). Theophylline is the weakest base (smallest Kb, largest pKb).

What is the molecular weight, Kb, pKb, and pKa of Acetanilide?

MW: 135.6 (at 40°); Kb: 4.1 × 10⁻¹⁴; pKb: 13.39; pKa: 0.3.

What is the molecular weight, Kb, pKb, and pKa of Ammonia?

MW: 35.05; Kb: 1.74 × 10⁻⁵; pKb: 4.76; pKa: 9.24.

What is the molecular weight, Kb, pKb, and pKa of Apomorphine?

MW: 267.31; Kb: 1.0 × 10⁻⁷; pKb: 7.00; pKa: 7.00.

What is the molecular weight, Kb, pKb, and pKa of Atropine?

MW: 289.4; Kb: 4.5 × 10⁻⁵; pKb: 4.35; pKa: 9.65.

What is the molecular weight, Kb, pKb, and pKa of Benzocaine?

MW: 165.19; Kb: 6.0 × 10⁻¹²; pKb: 11.22; pKa: 2.78.

How do you calculate the hydronium ion concentration [H₃O⁺] for a weak acid solution?

[H₃O⁺] = (Ka × Ca)^(1/2), where Ca is the concentration of the acid.

How do you calculate the hydroxide ion concentration [OH⁻] for a weak base solution?

[OH⁻] = (Kb × Cb)^(1/2), where Cb is the concentration of the base.

Calculate the pH of a 0.01M solution of acetic acid (Ka = 1.75 x 10⁻⁵).

[H₃O⁺] = √(1.75 × 10⁻⁵ × 0.01) = 0.000418. pH = -log(0.000418) = 3.38.

Calculate the pH of a 0.05M solution of boric acid (Ka = 5.8 x 10⁻¹⁰). (Try this one)

[H₃O⁺] = √(5.8 × 10⁻¹⁰ × 0.05) = 5.39 × 10⁻⁶. pH = -log(5.39 × 10⁻⁶) = 5.27.

Calculate the pH of a 0.01M solution of procaine (Kb = 7 x 10⁻⁶).

[OH⁻] = √(7 × 10⁻⁶ × 0.01) = 0.000264. pOH = -log(0.000264) = 3.58. pH = 14 - 3.58 = 10.4.

Calculate the pH of a 0.05M solution of ammonia (NH₃, Ka = 1.74 x 10⁻⁵). (Try this one)

First, find Kb using Kw/Ka: Kb = 1 × 10⁻¹⁴ / 1.74 × 10⁻⁵ = 5.75 × 10⁻¹⁰. [OH⁻] = √(5.75 × 10⁻¹⁰ × 0.05) = 5.36 × 10⁻⁶. pOH = 5.27. pH = 14 - 5.27 = 8.73.

What is the rule for the pH of a salt solution?

The salt of a strong base + weak acid = weak base. The salt of a strong acid + weak base = weak acid.

Calculate the pH of a 0.01M sodium acetate solution (Ka = 1.75 x 10⁻⁵).

Sodium acetate is a weak base. Kb = Kw/Ka = 1 × 10⁻¹⁴ / 1.75 × 10⁻⁵ = 5.7 × 10⁻¹⁰. [OH⁻] = √(5.7 × 10⁻¹⁰ × 0.01) = 2.39 × 10⁻⁶ M. [H₃O⁺] = 1 × 10⁻¹⁴ / 2.39 × 10⁻⁶ = 4.184 × 10⁻⁹. pH = 8.4.

Calculate the pH of a 0.01M procaine HCl solution (Kb = 7 x 10⁻⁶).

Procaine HCl is a weak acid. Ka = Kw/Kb = 1 × 10⁻¹⁴ / 7 × 10⁻⁶ = 1.43 × 10⁻⁹. [H₃O⁺] = √(1.43 × 10⁻⁹ × 0.01) = 3.78 × 10⁻⁶ M. pH = 5.4.

What are buffers used for?

To prevent drastic changes in the pH of a solution.

What is another name for the Henderson-Hasselbalch equation?

The buffer equation.

Why are buffers significant in pharmacy?

pH can affect many aspects of drug therapy. Buffers help predict the pH of a physiological or pharmacological environment and control/maintain pH at a desirable value.

What is a buffered solution?

A solution for which the pH is approximately constant and will remain so even when challenged by a small amount of strong acid or base.

What are buffers generally composed of?

Solutions of a weak acid and a salt of that acid in practically equal amounts (same order of magnitude). Alternatively, a weak base and a salt of that base in relatively equal quantities.

Calculate the pH of a buffer solution containing 0.04 M sodium acetate and 0.01 M acetic acid (pKa = 4.76).

pH = pKa + log([A⁻]/[HA]) = 4.76 + log(0.04/0.01) = 4.76 + 0.601 = 5.36.

What happens to the pH if 0.001M HCl is added to the buffer solution (0.04 M sodium acetate and 0.01 M acetic acid)?

The hydronium ion from HCl reacts with 0.001 moles/liter of A⁻ (from NaA). This adds 0.001 moles/l of HA to the solution and uses up 0.001 moles/l of A⁻. New [A⁻] = 0.039, new [HA] = 0.011. pH = 4.76 + log(0.039/0.011) = 4.76 + 0.55 = 5.31.

What is buffer capacity (β) or buffer strength?

The measure of the change in pH by added base, determined by the change in [HA] and [A⁻] in a buffer system.

What is the formula for buffer capacity (β)?

β = 2.303 × Ct × (Ka[H₃O⁺]) / (Ka + [H₃O⁺])².

What is Ct in the buffer capacity equation?

Ct is the sum of the acid concentration and the anion concentration: Ct = [HA] + [A⁻].

By definition, when is buffering capacity the greatest?

When [HA] = [A⁻]. At this point, pH = pKa and [H₃O⁺] = Ka.

What is the formula for maximum buffer capacity (βmax)?

βmax = 0.575 × Ct.

If [HA] = [A⁻] = 0.1 M, what is Ct and βmax?

Ct = 0.2. βmax = 0.575 × 0.2 = 0.115.

If [HA] = [A⁻] = 1 M, what is Ct and βmax?

Ct = 2. βmax = 0.575 × 2 = 1.15 (which is ten times the value when [HA] = [A⁻] = 0.1 M).

How does the concentration of [HA] and [A⁻] affect buffer capacity?

The more [HA] or [A⁻], the greater the reservoir to resist pH changes when a small amount of strong acid or base is added. Therefore, a higher Ct means a greater buffer capacity.

What is the buffer zone?

± 1.5 pH units near the pKa. The effects of added acid (or base) are suppressed within this range.

What are common buffer systems used in pharmaceuticals?

Acetic acid – acetate; Boric acid – borate; Citric acid – citrate; Monobasic phosphate – dibasic phosphate.

In the buffer capacity graph, what does comparing A vs. B show?

The pH where you see the greatest buffer capacity depends on the pKa.

In the buffer capacity graph, what does comparing B vs. C show?

Buffer capacity increases with concentration.

What is the arterial blood pH?

7.45.

What is the venous blood pH?

7.35.

What is the pH range of urine?

4.5 – 7.8.

What is the pH of lacrimal fluid and its isotonicity?

pH = 7.4; similar isotonicity to plasma.

What is the median fasted pH and fed pH of gastrointestinal fluids?

Fasted: 1.7; Fed: 6.4.

What is the hemoglobin-bicarbonate buffer system in blood?

A physiological buffer system where CO₂ and H₂O are converted to H⁺ and HCO₃⁻ (catalyzed by carbonic anhydrase) to help maintain blood pH.

Why is drug ionization important?

The degree of ionization of a medication can impact drug activity. Most medications are weak electrolytes, so ionization depends on pH.

What is the pH partition hypothesis regarding membranes?

Only the unionized form of a drug can cross biological membranes.

What is the relationship between drug solubility and ionization?

The ionized form of a medication is more soluble.

How is the percentage of drug ionized (%I) at any given pH estimated using the H-H equation for a weak acid?

%I = [A⁻] / ([A⁻] + [HA]) × 100 = 10^(pH - pKa) / (1 + 10^(pH - pKa)) × 100.

How is the percentage of drug ionized (%I) at any given pH estimated using the H-H equation for a weak base?

%I = [BH⁺] / ([B] + [BH⁺]) × 100 = 10^(pKa - pH) / (1 + 10^(pKa - pH)) × 100.

For a weak acid with pKa = 5, what is the % ionization at pH 3, 4, 5, 6, and 7?

pH 3: 1%; pH 4: 10%; pH 5: 50%; pH 6: 90%; pH 7: 99%.

For a weak base with pKa = 9, what is the % ionization at pH 7, 8, 9, 10, and 11?

pH 7: 99%; pH 8: 90%; pH 9: 50%; pH 10: 10%; pH 11: 1%.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 1.2?

% Ionized: 0.50; % Unionized: 99.5.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 2.0?

% Ionized: 3.10; % Unionized: 96.9.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 3.5?

% Ionized: 50.0; % Unionized: 50.0.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 5.0?

% Ionized: 96.9; % Unionized: 3.1.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 6.5?

% Ionized: 99.9; % Unionized: 0.1.

For Aspirin (pKa = 3.5), what is the % ionized and % unionized at pH 7.4?

% Ionized: 99.98; % Unionized: 0.02.