Final answer:
To calculate the Ka value for acetic acid, one must use the equation Ka = [H+][CH₃COO˟] / [CH₃COOH], substituting the equilibrium concentrations of H+ and the initial concentration of acetic acid, leading to a calculation of Ka = 3.61 x 10^-5.
Step-by-step explanation:
The question asks us to calculate the Ka value for acetic acid given its concentration and the equilibrium concentration of hydrogen ions. To solve this, we first need to write down the equilibrium expression for the dissociation of acetic acid (CH₃COOH).
The equilibrium equation is:
CH₃COOH(aq) ⇆ H+(aq) + CH₃COO˟(aq)
The Ka expression is given by:
Ka = [H+][CH₃COO˟] / [CH₃COOH]
Since acetic acid is a weak acid and only partially ionizes in water, the concentration of acetate ions (CH₃COO˟) at equilibrium will be same as the concentration of hydrogen ions [H+]. Therefore, we can substitute [CH₃COO˟] with 0.0019M assumed being equal to [H+], and the initial concentration of acetic acid [CH₃COOH] as 0.20M.
Ka = [0.0019][0.0019] / [0.20 - 0.0019]
We subtract the concentration of hydrogen ions from the initial concentration of acetic acid to get the equilibrium concentration of acetic acid. Now we simply plug in the values to find Ka.
Ka = (0.0019 × 0.0019) / (0.20 - 0.0019)
Ka = 3.61 x 10^-5