"Published in Newark, California, USA"
To determine the Ka of a weak acid, a student took 20 mL of a solution of the acid and titrated it with a base. He found out that it took 32 mL of base to neutralize the acid. He then took a new 20 mL of acid and added exactly 10 mL of the same base to it. He measured the pH of this solution and found it to be 4.20. What is the value of Ka for the weak acid?
Solution:
In the given problem, the concentrations of a weak acid and a base are not given but their volumes are given. We can still solve for the value of Ka for the weak acid. Let's assume that the unknown weak acid is a monoprotic acid and the unknown base is a monoprotic base so that it will be easy for us to solve for the value of Ka.
After the titration of 20 mL of a weak acid with 32 mL of a base, the amount of weak acid at the start of the reaction is
where CBase is the concentration or molarity of a base in millimoles of solute per milliliter of solution. Let's assign HA for the weak acid and BOH for the base.
The equilibrium reaction for the ionization of a weak acid is
and the ionization constant is
At equilibrium,
where x is the mmoles of HA that partially ionized. Hence, the above equation becomes
If 10 mL of the same base is added to a new 20 mL of a weak acid, then the amount of weak acid that is converted into salt BA is
From the reaction of a weak acid with the base, salt BA is formed
By using mole to mole relationship of the reactants and products, if
then it follows that
As mentioned earlier that 10 mL of the base is added to a new 20 mL of a weak base. At equilibrium, the amount of weak acid will decrease and the amount of product which is the A ion will increase. The ionization constant for the weak acid becomes
Let's assume that the value of Ka is less than 1 x 10-3 so that we can neglect x at the numerator and denominator as follows
If the pH of the solution is 4.20, then the value of x which is the concentration of [H+] is
Take the inverse logarithm on both sides of the equation, we have
Therefore, the value of Ka for the weak acid is
