Question

Determine Ka for hydrogen sulfate ion, HSO₄⁻. In a 0.10-M solution, the acid is 29% ionized.

a) 2.9 x 10⁻²
b) 1.0 x 10⁻²
c) 8.1 x 10⁻³
d) 2.9 x 10⁻³

Answer 1

The Ka for hydrogen sulfate ion (HSO4-) in a 0.10 M solution that is 29% ionized is calculated to be approximately 1.2 x 10^-2, which closely matches the provided option b) 1.0 x 10^-2.

Step-by-step explanation:

To determine the acid ionization constant (Ka) for the hydrogen sulfate ion (HSO4-), we can use the given information that in a 0.10 M solution, the acid is 29% ionized. First, we calculate the concentration of ionized HSO4- by multiplying the initial concentration by the percent ionized, which gives us 0.29 x 0.10 M = 0.029 M. Thus, [H3O+] and [SO42-] are both 0.029 M, as ionization produces one mole of H3O+ and SO42- for each mole of HSO4- that dissociates.

The remaining concentration of HSO4- is the initial concentration minus the ionized amount, which is 0.10 M - 0.029 M = 0.071 M. We then use the formula for Ka :

Ka = [H3O+][SO42-]/[HSO4-]

Substituting the concentrations, we get:

Ka = (0.029 M * 0.029 M) / 0.071 M = 0.0292 / 0.071 = 0.000841 / 0.071 ≈ 1.2 x 10-2

Therefore, the correct answer is 1.2 x 10-2, which closely matches option b) 1.0 x 10-2.