Answer:
Percent dissociated = 3.92%
Explanation:
The equilibrium of the weak acid, HA, is:
HA ⇄ H⁺ + A⁻
<em>Where Ka = 8x10⁻⁴ is: [H⁺] [A⁻] / [HA]</em>
<em> </em>
As both H⁺ and A⁻ comes from the same equilibrium we can write the concentrations of the species as follows:
[H⁺] = X
[A⁻] = X
[HA] = 0.50M - X
<em>Where X is reaction coordinate</em>
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Replacing:
8x10⁻⁴ = X² / 0.50-X
4x10⁻⁴ - 8x10⁻⁴X - X² = 0
Solving for X:
X = -0.02M. False solution. There is no negative concentrations
X = 0.0196M. Right solution.
Replacing:
[A⁻] = 0.0196M
Percent of the acid that is dissociated is:
[A⁻] / [HA]₀ * 100
<em>[HA]₀ is its initial concentration = 0.50M</em>
0.0196M / 0.50M * 100
<h3>Percent dissociated = 3.92%</h3>