Answer in Organic Chemistry for Sandra #118043

Solution:

Since methylamine (CH₃NH₂) is a weak base, the major species in solution are CH₃NH₂ and H₂O.

Both are bases; however, since water can be neglected as a source of OH^–, the dominant equilibrium is:

CH₃NH₂(aq) + H₂O(l) = CH₃NH₃⁺(aq) + OH^–(aq)

and

The concentrations are as follows:

[OH^–] = [CH₃NH₃⁺] = x

[CH₃NH₂] = 1.0 – x

Then,

Assume that 1 >> x, then:

(1.0 – x) = 1.0

K_b = x² / 1.0

x² = K_b

x = (K_b)^0.5 = (4.38×10^-4)^0.5 = 0.0209

x= [OH^–] = 0.0209 M

We can convert between [OH^–] and pOH using the following equations:

pOH = – log[OH^–]

pOH = – log(0.0209) = 1.68

pOH = 1.68

For any aqueous solution at 25^∘C:

pH + pOH = 14

pH = 14 – pOH = 14 – 1.68 = 12.32

pH = 12.32

Answer: pH = 12.32