Final answer:
To calculate the pH of a 0.010 M aluminum chloride solution, we use the hydrolysis reaction of the hydrated aluminum ion. The concentration of H₃O⁺ ions is 6 times the concentration of the hydrated aluminum ions. Using the equation pH = -log[H₃O⁺], we find the pH to be approximately 1.22.
Step-by-step explanation:
The aluminum chloride (AlCl3) dissociates in water to form hydrated aluminum ions [Al(H2O)6]³⁺ and chloride ions (Cl⁻). The hydrated aluminum ions can undergo hydrolysis to produce hydronium ions (H₃O⁺) and aluminum hydroxide.
The equation for the hydrolysis reaction is:
[Al(H2O)6]³⁺ + 3H₂O ⇌ Al(OH)3 + 6H₃O⁺
The equilibrium constant (Ka) for this reaction is given as 1.4 x 10⁻⁵.
To calculate the pH of the solution, we need to determine the concentration of H₃O⁺ ions. Since 1 mole of [Al(H2O)6]³⁺ produces 6 moles of H₃O⁺ ions, the concentration of H₃O⁺ ions is 6 times the concentration of [Al(H2O)6]³⁺.
Given that the concentration of [Al(H2O)6]³⁺ is 0.010 M, the concentration of H₃O⁺ ions is 6 x 0.010 M = 0.060 M.
Lastly, we can calculate the pH using the formula pH = -log[H₃O⁺].
pH = -log(0.060) ≈ 1.22