Chemistry multiple choice with working please??? pH?

No. of H⁺ ions added = No. of moles of HCl added = (0.200 mol/L) × (100/1000 L) = 0.02 mol

CH₃NH₂(aq) + H⁺(aq) → CH₃NH₃⁺(aq)
Mole ratio CH₃NH₂ : H⁺ : CH₃NH₃⁺ = 1 : 1 : 1
Hence, 0.02 mole of CH₃NH₂ reacts with 0.02 mole of H⁺ to give 0.02 mole of CH₃NH₃⁺.
After reaction, [CH₃NH₃⁺] = (0.02 mol/L) / (100/1000 L) = 0.2 M

Ka of CH₃NH₃⁺ = Kw / (Kb of CH₃NH₂) = (1.0 × 10⁻¹⁴) / (4.4 × 10⁻⁴) = 2.3 × 10⁻¹¹

Consider the dissociation of CH₃NH₃⁺ :
__________ CH₃NH₃⁺(aq) __ ⇌ __ CH₃NH₂(aq) __ + __ H⁺(aq) ___ Ka = 2.3 × 10⁻¹¹
Initial: _______ 0.2 M __________ 0 M __________ 0 M
Change: ______ -y M __________ +y M _________ +y M
At eqm: ___ (0.2 - y) M _________ y M ___________ y M

As Ka is very small, the dissociation of CH₃NH₃⁺ would be to a very small extent.
It is assumed that 0.2 ≫ y, i.e. [H₂A] at equilibrium = (0.2 + y) M ≈ 0.2 M



Ka = [CH₃NH₂] [H⁺] / [CH₃NH₃⁺]
2.3 × 10⁻¹¹ = y² / 0.2
y = √[0.2 × (2.3 × 10⁻¹¹)]
y = 2.1 × 10⁻⁶

pH = -log[H⁺] = -log(2.1 × 10⁻⁶) = 5.7

The answer: A- 5.7