Answer to Question #118043 in Organic Chemistry for Sandra

Question

Calculate the pH of a 1.0 M solution of methylamine (Kb = 4.38 x 104
).

Answer 1

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