Ionic Equilibrium

6.52

Step 1: In a neutral solution, [H₃O⁺] = [OH⁻]. Using Kw = [H₃O⁺][OH⁻] = 9 × 10⁻¹⁴. Step 2: [H₃O⁺]² = 9 × 10⁻¹⁴, so [H₃O⁺] = 3 × 10⁻⁷ M. Step 3: pH = -log(3 × 10⁻⁷) = 7 - log 3 = 7 - 0.477 = 6.52. Step 4: pH = 7 is only neutral at 25°C where Kw = 10⁻¹⁴. At higher temperatures, Kw increases (endothermic dissociation), so neutral pH < 7 but the solution is still neutral (not acidic) because [H₃O⁺] = [OH⁻]. Option C (7.48) confuses this with lower temperature.

1.35 × 10⁻¹¹

Step 1: Ag₂CrO₄(s) ⇌ 2Ag⁺(aq) + CrO₄²⁻(aq). For every mole of Ag₂CrO₄ that dissolves, 2 moles of Ag⁺ and 1 mole of CrO₄²⁻ are produced. Step 2: If s = 1.5 × 10⁻⁴ M, then [Ag⁺] = 2s = 3.0 × 10⁻⁴ M and [CrO₄²⁻] = s = 1.5 × 10⁻⁴ M. Step 3: Ksp = [Ag⁺]²[CrO₄²⁻] = (3.0 × 10⁻⁴)² × (1.5 × 10⁻⁴) = 9 × 10⁻⁸ × 1.5 × 10⁻⁴ = 1.35 × 10⁻¹¹. Step 4: Option A (2.25 × 10⁻⁸) uses Ksp = s² incorrectly. Option C ignores the coefficient 2 for Ag⁺. Option D is a common arithmetic error.

5.13

Step 1: NH₄Cl is a salt of strong acid (HCl) and weak base (NH₄OH). The NH₄⁺ undergoes cationic hydrolysis making the solution acidic. Step 2: For salt of strong acid and weak base: pH = 7 - ½pKb - ½logC. Step 3: pKb = -log(1.8 × 10⁻⁵) = 5 - log 1.8 = 4.74. Step 4: pH = 7 - (4.74/2) - (log 0.1/2) = 7 - 2.37 - (-0.5) = 7 - 2.37 + 0.5 = 5.13. Step 5: Option A (9.13) is wrong — that would be a basic solution. NH₄Cl is acidic. Option D (8.87) would be for a salt of weak acid + strong base. Option C (4.87) has a sign error in the formula.

Strong acids dissociate completely, meaning their conjugate bases have negligible tendency to accept a proton.

Step 1: A strong acid like HCl dissociates almost 100% in water: HCl + H₂O → H₃O⁺ + Cl⁻. Step 2: The equilibrium lies far to the right, meaning the reverse reaction (Cl⁻ accepting a proton from H₃O⁺) is negligible. Step 3: This means Cl⁻ has virtually no tendency to act as a proton acceptor — making it a very weak base. Step 4: The relationship: stronger the acid → greater dissociation → weaker the conjugate base. This is a fundamental principle of Bronsted-Lowry theory. Options A, C, D all contain incorrect reasoning — molecular weight, neutrality, and OH⁻ production are irrelevant to conjuga