The Ka of HC2H3O2 is found by calculating the concentrations of the reactants and products when the solution ionizes and then dividing the concentrations of the products multiplied together over the concentration of the reactant. For HC2H3O2, the formula for Ka is Ka = [H3O+][C2H3O2]/[HC2H3O2].
The concentrations used in the equation for Ka are known as the equilibrium concentrations and can be determined by using an ICE table that lists the initial concentration, the change in concentration and the equilibrium concentration for H3O+, C2H3O2 and HC2H3O2. The concentration is listed in moles per liter.
In the table, the change in concentration for HC2H3O2 is -x, while the concentration of each of the products is x. Then, the equilibrium concentration for HC2H3O2 is the initial molarity of HC2H3O2 minus x, while the concentration of the products is any initial molarity plus x. For example, if the initial HC2H3O2 had a concentration of 0.3 moles per liter, then the equilibrium concentration of HC2H3O2 is 0.3 moles per liter minus x.
Plugging in the values found for the equilibrium concentration as found on the ICE table for the equation Ka = [H3O+][C2H3O2]/[HC2H3O2] allows the value of Ka to be solved in terms of x. To find the Ka, solve for x by measuring out the equilibrium concentration of one of the products or reactants through laboratory techniques. The Ka value for HC2H3O2 is 1.8 x 10^-5.