The concentration of a solution of a strong base like sodium hydroxide (NaOH) can be determined by titration, a technique where a strong acid like hydrochloric acid (HCl) is added slowly until equivalence is reached (i.e., until the amounts of H

+

and OH−

are equal, and thus exactly the right amount of acid has been added to react with the base). At this point the pH of the solution is 7. We discuss pH more in Section 4.2

.3). Often, a marker is added to the solution, which changes colour when the equivalence point is reached.

If we know that a volume, Vb, of NaOH reacts completely with a volume, Va, of HCl (of known concentration [HCl]), the concentration of NaOH, [NaOH], can be determined from the equation

[NaOH] × Vb = [HCl] × Va.

Suppose that 0.100

± 0.000 5 mol L−1 HCl, is titrated against 25.0

± 0.03 mL of NaOH, of unknown concentration. Also, suppose that we start with 23.72

± 0.005 mL of HCl (in the burette, which is the thing used to add the HCl to the NaOH), and at the equivalence point we are left with only 0.32

± 0.005

mL.

a. Calculate Va.

b. Calculate the absolute uncertainty in the calculation of Va.

c. Calculate [NaOH].

d. Calculate the relative and absolute uncertainties in the value for [NaOH].