Final answer:
The pH of a 1.0 MNH₄Cl solution can be calculated using the expression for the dissociation constant of NH₄⁺ (Ka). By assuming complete dissociation of NH₄⁺, we can substitute [H₃O⁺] for [NH₄⁺] in the equation. Solving for [H₃O⁺] and taking the negative logarithm gives the pH of the solution.
Step-by-step explanation:
To calculate the pH of a solution of NH₄Cl, we need to consider the dissociation of NH₄Cl into NH₄⁺ and Cl⁻. Since NH₄⁺ is a weak acid and Cl⁻ is the conjugate base of a strong acid, we can assume that NH₄⁺ is the species that will determine the pH of the solution.
We can use the expression for the dissociation constant of NH₄⁺ (Ka) to calculate the concentration of H₃O⁺ in the solution:
Ka = [NH₄⁺][H₃O⁺] / [NH₄Cl]
Since NH₄⁺ is a strong acid, we can assume that it completely dissociates, so [H₃O⁺] = [NH₄⁺]. Therefore, we can substitute [H₃O⁺] for [NH₄⁺] in the equation:
Ka = [H₃O⁺]² / [NH₄Cl]
Since we have a 1.0 M NH₄Cl solution, the concentration of NH₄Cl is 1.0 M. With this information, we can solve for [H₃O⁺]:
5.62 × 10⁻¹⁰ = [H₃O⁺]² / 1.0
Solving for [H₃O⁺] gives us:
[H₃O⁺] = √(5.62 × 10⁻¹⁰) = 7.50 × 10⁻⁶ M
Finally, we can calculate the pH using the expression:
pH = -log[H₃O⁺] = -log(7.50 × 10⁻⁶) = 5.12