Final answer:
To calculate the pH of a 0.11 M solution of diethylamine, we can use the base ionization constant (Kb) to find the concentration of hydroxide ions. Then, we can use the concentration of hydroxide ions to calculate the concentration of hydrogen ions and finally the pH. The pH of the 0.11 M diethylamine solution is approximately 11.99.
Step-by-step explanation:
To calculate the pH of a solution of diethylamine, we need to first determine the concentration of hydroxide ions (OH-) in the solution. Diethylamine is a weak base, so it will react with water to form hydroxide ions and its conjugate acid, diethylammonium ions. The equilibrium constant for this reaction is given by the base ionization constant (Kb).
To find the concentration of hydroxide ions, we can use the equation Kb = [OH-][diethylammonium ions]/[diethylamine]. We know the concentration of diethylamine, 0.11 M, and the value of Kb, 8.6 × 10⁻⁴. We can set up the equation 8.6 × 10⁻⁴ = x²/0.11, where x is the concentration of hydroxide ions. Solving this equation will give us the concentration of hydroxide ions, which we can then use to calculate the pH using the equation pH = -log[H+], where [H+] is the concentration of hydrogen ions.
Let's solve the equation 8.6 × 10⁻⁴ = x²/0.11:
8.6 × 10⁻⁴ * 0.11 = x²
x² = 9.46 × 10⁻⁵
x = sqrt(9.46 × 10⁻⁵)
x ≈ 0.00972 M
The concentration of hydroxide ions is approximately 0.00972 M. Now, we can calculate the concentration of hydrogen ions using the equation [H+] = Kw/[OH-]. The value of Kw (the equilibrium constant for water) is 1.0 × 10⁻¹⁴. Substituting the values, we get [H+] = (1.0 × 10⁻¹⁴)/(0.00972) = 1.03 × 10⁻¹² M. Finally, we can calculate the pH using pH = -log[H+].
pH = -log(1.03 × 10⁻¹²) ≈ 11.99