Answer
Methylamine Equilibrium and pH Calculations
(a) Concentrations and pH from Percent Ionization
Given: 0.16 M CH₃NH₂, 4.7% ionized at 25°C
Reaction:
CH₃NH₂(aq) + H₂O(l) ⇌ CH₃NH₃⁺(aq) + OH⁻(aq)
Step 1: Find ionized concentration (4.7% of 0.16 M)
0.047 × 0.16 M = 0.00752 M (OH⁻ and CH₃NH₃⁺)
Step 2: Find [CH₃NH₂]
0.16 – 0.00752 = 0.15248 M
Step 3: Calculate pOH and then pH
pOH = -log(0.00752) ≈ 2.123
pH = 14 – 2.123 = 11.88
pH = 14 – 2.123 = 11.88
Final Answers:
- [OH⁻] = [CH₃NH₃⁺] = 0.00752 M
- [CH₃NH₂] = 0.15248 M
- pH = 11.88
(b) Calculate Kb for CH₃NH₂
Use expression for base dissociation constant:
Kb = [CH₃NH₃⁺][OH⁻] / [CH₃NH₂]
Kb = (0.00752)² / 0.15248 ≈ 3.71 × 10⁻⁴
(c) pH of CH₃NH₃Cl (acidic salt)
Step 1: Calculate moles
Molar mass CH₃NH₃Cl ≈ 65.5 g/mol
Moles = 6.9 g / 65.5 g/mol ≈ 0.1053 mol
Moles = 6.9 g / 65.5 g/mol ≈ 0.1053 mol
Step 2: Molarity in 500.0 mL
M = 0.1053 mol / 0.500 L = 0.2106 M
Step 3: CH₃NH₃⁺ is a weak acid. Use Ka = Kw/Kb
Ka = 1.0 × 10⁻¹⁴ / 3.71 × 10⁻⁴ = 2.694 × 10⁻¹¹
Step 4: ICE table and solve for [H₃O⁺]
CH₃NH₃⁺ ⇌ CH₃NH₂ + H₃O⁺
[H₃O⁺] = √(Ka × [acid]) = √(2.694 × 10⁻¹¹ × 0.2106) ≈ 7.52 × 10⁻⁶
pH = -log(7.52 × 10⁻⁶) ≈ 5.12
pH = -log(7.52 × 10⁻⁶) ≈ 5.12
(d) CH₃NH₂ as Brønsted-Lowry and Lewis Base
- Brønsted-Lowry base: CH₃NH₂ accepts a proton (H⁺) from water to form CH₃NH₃⁺.
- Lewis base: It donates a lone pair on nitrogen to form a coordinate bond with H⁺.
This dual role explains how methylamine satisfies both definitions of a base.