Chemistry weak bases

Question

Trimethylamine, (CH3) 3N is a weak base (Kb = 6.3 × 10–5). What volume of this gas, measured at STP, must be dissolved in 2.5 L of solution to give that solution a pOH of 2.50?

Answer 1

(CH₃)₃N + H2O ==> (CH₃)₃NH⁺ + OH^-

Kb = 6.3x10^-5 = [(CH₃)₃NH⁺][OH^-] / [(CH₃)₃N]

From pOH = 2.50, we can find [OH-] = [(CH₃)₃NH⁺]

[OH-] = [(CH₃)₃NH⁺] = 1x10^-2.50 = 3.16x10^-3

Solving for (CH₃)₃N] we have...

6.3x10^-5 = (3.16x10^-3)² / [(CH₃)₃N] (note: I've omitted subtracting 3.16x10^-3 from denominator)

[(CH₃)₃N] = 9.99x10^-6 /6.3x10^-5

[(CH₃)₃N] = 0.159 M

In 2.5 L the moles = 0.159 mol/L x 2.5 L = 0.398 moles

At STP, 1 mole = 22.4 L

Volume of (CH₃)₃N needed = 0.398 moles x 22.4 L/mol = 8.9 L (2 sig. figs.)