Final answer:
To calculate the percent ionization of a 0.219 M solution of formic acid with a Ka of 1.77 × 10⁻⁴, we use an ICE table and the assumption that the concentration of ionized formic acid is small compared to the initial concentration. We solve for the equilibrium concentration of H+ and use it to calculate the percent ionization.
Step-by-step explanation:
To calculate the percent ionization of formic acid in a 0.219 M solution, we start with the equilibrium equation for the ionization of formic acid (HCO₂H):
HCO₂H → H+ + HCO₂-
We use the given acid dissociation constant (Ka) of formic acid, which is 1.77 × 10⁻⁴, and set up a table of initial concentrations, changes in concentration, and equilibrium concentrations (ICE table). Assuming x is the concentration of ionized formic acid, the equilibrium concentrations will be 0.219-x for HCO₂H, x for H+, and x for HCO₂-.
Now, plug these values into the expression for Ka:
Ka = [H+][HCO₂-] / [HCO₂H]
1.77 × 10⁻⁴ = x² / (0.219 - x)
We can simplify by assuming that x is much smaller than 0.219 M, hence 0.219 - x ≈ 0.219. Solving for x gives us the concentration of HCO₂- which is approximately equal to the concentration of H+. We then use the definition of percent ionization:
Percent Ionization = (x / 0.219) × 100%
By solving the quadratic equation we obtained, we can find x and thus calculate the percent ionization. When solving, x should represent the equilibrium concentration of HCO₂- or H+, and our answer should be one of the provided options, which best corresponds to the calculated value.
It's important to verify the assumptions we've made by ensuring x is indeed much smaller than the initial concentration of the acid, otherwise, we might need to solve the quadratic equation without approximations.