We are given:
Initial concentration of HA: 0.200 Molar
The acid is 9.4% ionized
Dissociation constant (α) = (Percent Ionized) / 100 = 0.094
Molar concentration of H+ = 0.0188
Let's Chill! (making the ICE box):
Reaction: HA ⇄ H⁺ + A⁻
Initial: 0.200M - -
Equilibrium: 0.200(1-α) 0.200α 0.200α
while we're here, let's confirm the given equilibrium concentration of H⁺ ions
from the table here, we can see that the equilibrium concentration of H⁺ ions is 0.200α, we know that α = 0.094
[H⁺] = 0.200α = 0.200 * 0.094 = 0.0188 M
which means that we're on the right track
We're basically scientists at this point (finding the dissociation constant):
Acid dissociation is nothing but the equilibrium constant, but for the dissociation of Acids
From the reaction above, we can write the equation of the acid dissociation constant:
Ka = [H⁺][A⁻] / [HA]
now, let's take the values from the 'equilibrium' row of the ice box the plug those in this equation
Ka = (0.200α)(0.200α) / [0.200(1-α)]
Ka = (0.200α)²/[0.200(1-α)]
plugging the value of α
Ka = (0.200*0.094)² / [0.200(0.906)]
Ka = (0.0188)² / 0.1812
Ka = 1.95 * 10⁻³
