16.6: Titration Calculations: Strong Acid – Strong Base

Calculating pH for Titration Solutions: Strong Acid/Strong Base

A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:

(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:

(b) Titrant volume = 12.50 mL. Since the acid sample and the base titrant are both monoprotic and equally concentrated, this titrant addition involves less than a stoichiometric amount of base, and so it is completely consumed by reaction with the excess acid in the sample. The concentration of acid remaining is computed by subtracting the consumed amount from the initial amount and then dividing by the solution volume:

(c) Titrant volume = 25.00 mL. This titrant addition involves a stoichiometric amount of base (the equivalence point), and so only products of the neutralization reaction are in solution (water and NaCl). Neither the cation nor the anion of this salt undergo acid-base ionization; the only process generating hydronium ions is the autoprotolysis of water. The solution is neutral, having a pH = 7.00.

(d) Titrant volume = 37.50 mL. This involves the addition of titrant in excess of the equivalence point. The solution pH is then calculated using the concentration of hydroxide ion:

This text is adapted from Openstax, Chemistry 2e, Section 14.7: Acid-base Titrations.

When a strong acid is titrated with a strong base or vice versa, the pH throughout the titration can be calculated by determining the concentration of the remaining hydronium or hydroxide ions.

For example, 50 mL of 0.10 M hydrochloric acid dissociates into 0.10 M hydronium and chloride ions with an initial pH of one.

If 25 mL of 0.10 M sodium hydroxide is added, the new concentration of hydronium ions can be calculated by subtracting the total moles of hydroxide ions from the total moles of hydronium ions and dividing it by the total volume—75 mL or 0.075 L.

50 mL of 0.10 M hydrochloric acid contains 0.0050 moles of hydronium, while 25 mL of 0.10 M sodium hydroxide has 0.0025 moles of hydroxide ions. Substituting these values into the equation, the hydronium ion concentration equals 0.033 M. Therefore, the pH of the solution has risen to 1.48.

If the addition of sodium hydroxide is continued up to 50 mL, all the hydronium ions from hydrochloric acid get neutralized, and the equivalence point is reached when the pH rises to seven.

Above the equivalence point, the pH of the solution is determined by the hydroxide ions, as the hydrochloric acid has been completely neutralized.

If 70 mL of sodium hydroxide solution containing 0.0070 moles of hydroxide ions is added into the solution, the final concentration of hydroxide ions can be determined by subtracting the initial moles of hydronium ions from the total moles of hydroxide ions and dividing it by the total volume of the solution.  

As the final hydroxide ion concentration is 0.017 M, the pOH and pH of the solution equal 1.78 and 12.22, respectively.