To find the acid-ionization constant of the weak acid HA, we can use the equation for percent ionization:
Percent ionization = (concentration of ionized acid / initial concentration of HA) * 100
In this case, we are given that the weak acid HA is 0.20% ionized in a 0.04 M solution. To find the concentration of ionized acid, we can use the equation:
Concentration of ionized acid = Percent ionization * initial concentration of HA / 100
Plugging in the given values, we get:
Concentration of ionized acid = 0.20% * 0.04 M / 100 = 0.00008 M
Now, we can use the equation for the acid-ionization constant (Ka):
Ka = (concentration of ionized acid)^2 / (concentration of undissociated acid)
Since the weak acid HA is 0.20% ionized, the concentration of undissociated acid is the initial concentration minus the concentration of ionized acid:
Concentration of undissociated acid = initial concentration of HA - concentration of ionized acid
Plugging in the values, we get:
Concentration of undissociated acid = 0.04 M - 0.00008 M = 0.03992 M
Finally, we can calculate the acid-ionization constant (Ka):
Ka = (0.00008 M)^2 / 0.03992 M = 1.6 x 10^-7
Therefore, the acid-ionization constant of HA is 1.6 x 10^-7.