A 0.30M solution of a weak monoprotic acid is 0.41% ionized. what is the acid-ionization constant, Ka for this acid?

Use. HA + H2O <==> H3O + A to figure out X for H3O and A

0.30M x 0.0041 = 0.00123

...........HA ==> H^+ + A^-
I..........0.30...0.......0
C.......-0.00123.0.00123.0.00123
E......0.299....0.00123.0.00123

Substitute the E line into the Ka expression and solve for Ka.

To find the acid-ionization constant (Ka) for the weak monoprotic acid, we can use the given information about the concentration of the acid solution and the percentage of ionization.

The given equation for the acid-ionization is:
HA + H2O ⇌ H3O+ + A-

Let's assume that initially, the concentration of the weak monoprotic acid (HA) is [HA] M.

Since the percentage of ionization is given as 0.41%, it means that only 0.41% of the initial concentration of HA ionizes. Therefore, the concentration of ions formed can be calculated as:
[H3O+] = 0.0041 * [HA] (0.41% = 0.0041 as a decimal)

The remaining concentration of the un-ionized acid can be calculated as:
[HA-remaining] = [HA] - [H3O+]

We know that the initial concentration of HA is 0.30M. Therefore, substituting the values, we have:
[HA-remaining] = 0.30M - (0.0041 * 0.30M) = 0.30M - 0.00123M = 0.2988M

At equilibrium, the concentration of H3O+ and A- will be the same. So, let's assume that the concentration of H3O+ and A- at equilibrium is X M.

Now we can write the equilibrium expression (Ka) using the concentrations:
Ka = [H3O+] * [A-] / [HA-remaining]

Substituting the known values and X for [H3O+] and [A-], we have:
Ka = X * X / 0.2988

Now, we need to solve for X. To do this, we can use the fact that only 0.41% of the initial concentration of HA ionizes, which means the change in [HA] concentration is small compared to the initial concentration. This allows us to assume that [HA-remaining] ≈ [HA] = 0.30M.

Therefore, the equation becomes:
Ka = X * X / 0.30

Now we can solve for X by rearranging the equation:
X * X = Ka * 0.30

Taking the square root of both sides of the equation, we get:
X = √(Ka * 0.30)

Now we have an expression for X. To solve for Ka, we need the value of X. However, the given information does not provide a direct means of calculating the value of X or Ka.

To find the value of Ka, we would need additional experimental data or information, such as the pH of the solution or the equilibrium constant (Kw) for water.