Question

Gifblaar is a small South African shrub and one of the most poisonous plants known because it contains fluoroacetic acid (FCH2COOH), which has a pKa of 2.59. Calculate the concentration of fluoroacetic acid in a solution that has the same pH as a 0.00395 M solution of HCl.

Answer 1

HCl is a strong acid while fluoroacetic acid is weak acid. The former implies that on dissolution or in aqueous medium, that species will completely dissociate into protons and its conjugate base. Weak acids meanwhile, are those which do not ionize completely in aqueous medium and instead stay in an equilibrium with their unionized species always. Therefore, a solution containing 0.00395M HCl will contain 0.00395M concentration of protons.

pH = -log[H⁺]. So for a 0.00395M HCl solution, pH will be -log[0.00395] = 2.4034.

Now, we know that 0.00395M protons are required from fluoroacetic acid solution to give the desired pH. pKa is related to the dissociation constant Ka of acids as pKa = -logKa. The dissociation constant is a parameter which shows the extent to which the acid is ionized in water. This Ka is an equilibrium constant whose expression is [H⁺][A^-]/[HA] where HA is the representation of the acid where A is its conjugate base - the species formed upon dissociation of its protons.

Since fluoroacetic acid gives only one proton per molecule, the ratio of protons and fluoroacetate ion in the medium is in the ratio 1:1, which can be taken as x. From the Ka of the acid as Ka = 10^-pKa = 2.5704x10^-3, the concentration of fluoracetic acid required for 0.00395M of protons can be given as [HA] x Ka = x². This gives the concentration of acid as 1.56025x10^-5/2.5704x10^-3 = 6.07x10^-3M.

Thus, a 6.07mM (millimolar i.e. 1mM = 0.001M) solution of fluoroacetic acid will have the same pH as a 3.95mM solution of HCl.