If 1 mM solution of ethylamine produces pH=9, then the ionization constant (K_b) of ethylamine is 10⁻ˣ. The value of x is _________ (nearest integer).
[The degree of ionization of ethylamine can be neglected with respect to unity.]

Solution

Chemistry ma’am · 4 steps

Ethylamine is a base, so turn pH into pOH first, then [OH⁻]²/C gives K_b straight away.

1. Find hydroxide. pOH = 14 - 9 = 5, so [OH⁻] = 10⁻⁵ M. The concentration is 1 mM = 10⁻³ M.
2. Set up equilibrium. In C₂H₅NH₂ + H₂O ⇌ C₂H₅NH₃⁺ + OH⁻, each ionized molecule gives one C₂H₅NH₃⁺ and one OH⁻. Since α is negligible, the unionized amine stays at C = 10⁻³ M.

   K_b = [C₂H₅NH₃⁺][OH⁻]/[C₂H₅NH₂] = (10⁻⁵)²/10⁻³ = 10⁻⁷

3. Check the approximation. α = 10⁻⁵/10⁻³ = 0.01, which is small compared with 1, so the shortcut holds.
4. So. K_b = 10⁻⁷, so x = 7.

The common slip: 15. Using [H⁺] = 10⁻⁹ in place of [OH⁻] gives K_b = 10⁻¹⁵, so x = 15. For a base, find pOH first.

The idea to keep. For a weak base, K_b = [OH⁻]²/C. Always convert pH to pOH before you find [OH⁻], and convert mM to M.

Answer from the NTA final answer key. Solution by PrepWiser.