Answer :
The percent ionization of a 1.55 M aqueous acetic acid solution is approximately 0.34%. This is calculated using the dissociation constant (Ka) and simplifying the equilibrium expression for the weak acid dissociation.
To calculate the percent ionization of a 1.55 M aqueous acetic acid solution, given the dissociation constant (Ka) for acetic acid as 1.8 × 10⁻⁵, follow these steps:
Write the dissociation equation for acetic acid:
CH₃COOH(aq) ⇌ H₃O⁺(aq) + CH₃COO⁻(aq)
Let x be the concentration of H₃O⁺ and CH₃COO⁻ at equilibrium. The initial concentration of acetic acid is 1.55 M.
At equilibrium, the concentrations are as follows:
[CH₃COOH] = 1.55 - x, [H3O+] = x, [CH₃COO⁻] = x
Since Ka = 1.8 × 10⁻⁵ = [H₃O⁺][CH3COO⁻] / [CH₃COOH], substitute the values:
1.8 × 10⁻⁵ = (x)(x) / (1.55 - x).
Assume x is very small compared to 1.55, so 1.55 - x ≈ 1.55.
The equation simplifies to 1.8 × 10⁻⁵ ≈ x² / 1.55.
Solve for x:
x² ≈ (1.8 × 10⁻⁵) * 1.55, x² ≈ 2.79 × 10⁻⁵, x ≈ √(2.79 × 10⁻⁵), x ≈ 5.28 × 10⁻³ M.
The percent ionization is given by:
( [CH₃COO⁻] / [CH₃COOH]initial ) × 100 = (5.28 × 10⁻³ / 1.55) × 100%
Calculate the percent ionization: ≈ 0.34%
Thus, the percent ionization of a 1.55 M aqueous acetic acid solution is approximately 0.34%.
Final answer:
To calculate the percent ionization of an aqueous acetic acid solution, use the equilibrium constant expression and the ICE approach.
Explanation:
The percent ionization of a 1.55 M aqueous acetic acid solution can be calculated using the equilibrium constant expression for acetic acid, which is represented by the equation:
CH3CO2H(aq) + H2O(l) ⇌ H3O+(aq) + CH3CO2^-(aq)
To calculate the percent ionization, we need to know the initial concentration of acetic acid, which is 1.55 M in this case, and the equilibrium constant Ka for acetic acid, which is 1.8 x 10^-5. Using the ICE approach and the given information, we can calculate the concentration of H3O+ at equilibrium. Finally, the percent ionization is given by (H3O+ concentration at equilibrium / initial acetic acid concentration) x 100%.
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