Answer:
pH = 5.85
Explanation:
The reaction of methylamine with HCl is:
CH₃NH₂ + HCl → CH₃NH₃⁺ + Cl⁻
As the titration was made with two solutions with the same molarity, the final concentration of the CH₃NH₃⁺ ion is 0.100M ([CH₃NH₃⁺] = 0.100M)
Then, the conjugate acid will be in equilibrium with water as follows:
CH₃NH₃⁺(aq) + H₂O(l) ⇄ CH₃NH₂(aq) + H₃O⁺(aq)
And the equilibrium constant, Ka, of this reaction is:
Kw/Kb = Ka = 1.0x10⁻¹⁴ / 5.0x10⁻⁴= 2x10⁻¹¹
2x10⁻¹¹ = [CH₃NH₂] [H₃O⁺] / [CH₃NH₃⁺]
As both CH₃NH₂ and H₃O⁺ comes from the same equilibrium we can say:
[CH₃NH₂] = [H₃O⁺] = X
And as we know [CH₃NH₃⁺] = 0.100M:
2x10⁻¹¹ = [X] [X] / [0.100M]
2x10⁻¹² = X²
X = 1.414x10⁻⁶M = [H₃O⁺]
And as pH= -log [H₃O⁺]
