When a typical diprotic acid H2A (Ka1 = 10^-4, Ka2 = 10^-10) is t...

Question

When a typical diprotic acid H2A (Ka1 = 10^-4, Ka2 = 10^-10) is titrated with NaOH, the principal A-containing species at the first equivalence point is HA-. (b) Assuming that this is the principal reaction, show that the pH at the first equivalence point equals the average of pKa1 and pKa2. (c) How many A2- ions are present in 50.0 mL of 1.0 M NaHA?

Accepted Answer

Step 1: Understand the concept of equivalence point in a titration. At the first equivalence point of a diprotic acid titration, all the initial H2A has been converted to HA-. This is because the amount of NaOH added is stoichiometrically equivalent to the amount of H2A initially present.. Step 2: Calculate the pKa values from the given Ka values. Use the formula $$ 	ext{pKa} = -\log(	ext{Ka})  to $$find pKa1 and pKa2. For Ka1 = $$10^{-4}$$, pKa1 = 4. For Ka2 = $$10^{-10}$$, pKa2 = 10.. Step 3: Determine the pH at the first equivalence point. At this point, the solution contains HA- ions, which can act as both an acid and a base. The pH is approximately the average of pKa1 and pKa2 because HA- is a weak acid and a weak base, and the solution is a buffer. Calculate the average: $$ 	ext{pH} = \frac{	ext{pKa1} + 	ext{pKa2}}{2} .. $$Step 4: Calculate the number of $$A^{2-}$$ ions in 50.0 mL of 1.0 M NaHA. First, determine the number of moles of NaHA: $$ 	ext{moles of NaHA} = 	ext{volume (L)} 	imes 	ext{molarity} = 0.050 	imes 1.0 .. $$Step 5: Recognize that in a solution of NaHA, the HA- ions can dissociate to form $$A^{2-}$$ ions. However, the extent of this dissociation is determined by the second dissociation constant, Ka2. Use the equilibrium expression for the dissociation of HA- to calculate the concentration of $$A^{2-}$$ ions.

주요 개념

Diprotic Acids and Their Ionization

Equivalence Point in Titration

pH and pKa Relationship