Methylamine is a weak base. The hydrolysis equation is:

The base, CH₃NH₂, abstracts a proton from water. The conjugate acid is CH₃NH₃⁺. This is a basic solution because hydroxide ion is produced. The base hydrolysis constant for this reaction, K_b is:

Here, we will relate K_a, K_b, and K_w. Consider the following equations:

 
Sum the equations:

 
We see that K_a x K_b = K_w = 1.0 x 10^-14

If K_a is known, we can find K_b. If K_b is known, we can find K_a.

For example acetic acid has K_a equal to 1.8 x 10^-5. We can calculate K_b

Weak bases will undergo hydrolysis with water to produce the conjugate acid and hydroxide ion. For example, fluoride ion will react with water to produce hydrofluoric acid and hydroxide ion.

Let’s calculate the pH of a solution that is 0.25 M CH₃NH₂. K_b = 4.4 x 10^-4.

First write the hydrolysis reaction.

CH₃NH₂ (aq) + H₂O (l) ⇄ CH₃NH₃⁺ (aq) + OH^– (aq)   \( K_b=\frac{[\mathrm{CH_3NH_3^+}][\mathrm{OH^-}]}{[\mathrm{CH_3NH_2}]}=4.4\times 10^{-4}\)
 
Set up an ICE table.

Assume x is neglible and 0.25 M – x ≅ 0.25 M

\(\displaystyle \frac{x^2}{0.25}\;=\;1.5\times 10^{-11}\)
 
Solve for x.

\(\displaystyle x\;=\;\sqrt{0.25\times\;(1.5\times 10^{-11})}\;=\;1.9\times\;10^{-6}\;M\)
 
Check assumption.

\(\displaystyle \frac{1.9\times 10^{-6}\;M}{0.25\;M}\times\;100\;=\;0.00076\%\)
 
The assumption is valid.

The [OH^–] = 1.9 x 10^-6 M. Use pOH to calculate the pH.

pH = 14.00 – (-log(1.9 x 10^-6) = 8.28

The solution is basic as we expected.

Watch the following video.

Exercises

Exercise 1. Calculate K_b for NH₃ if K_a for NH₄⁺ is equal to 5.6 x 10^-10.

Check Solution to Exercise 1

Exercise 2. Write a balanced net ionic equation and the equilibrium constant expression for the weak base ethlyamine, C₂H₅NH₂, in water. K_{a (C2H5NH3⁺)} = 8.6 x 10^-4.

Check Solution to Exercise 2

Exercise 3. Pyridine is a base with K_b = 2.0 x 10^-9. What is the pH of a 0.75 M pyridine solution?

Check Solution to Exercise 3

Exercise 4. Ammonia, NH₃ has a K_b = 1.8 x 10^-5. What is the pH of an aqueous solution that is 0.35 M NH₃?

Check Solution to Exercise 4

Exercise 5. A 0.75 M aqueous solution of methylamine, CH₃NH₂, has a pH of 12.26. Calculate K_b and the equilibrium concentrations of [CH₃NH₂], [CH₃NH₃⁺], and [OH^–].

Check Solution to Exercise 5

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