Titration of HCl with NaOH

Problem

100 mL of 0.1 molar HCl solution should be titrated with 1 molar NaOH. Calculate the titration curve (i.e. pH as a function of added NaOH).

Preparatory Work

We calculate the titration curve step by step starting with 0 mL up to 12 mL NaOH. Each calculation is then characterized by the following “mixing concentration” of HCl with NaOH:

(1)   HCl = 100 mM ∙ V0 / (V0 + V1)
(2)   NaOH = 1000 mM ∙ V1 / (V0 + V1)

where V0 = 100 mL is the volumen of the HCl solution and V1 is the volumen of the NaOH solution. In this way we otain the following table (which provides the input concentrations for the subsequent aqion calculations):

V0 in mL V1 in mL HCl in mM NaOH in mM
100 0 100.00 0.00
100 1 99.01 9.90
100 2 98.04 19.61
100 3 97.09 29.13
100 4 96.15 38.46
100 5 95.24 47.62
100 6 94.34 56.60
100 7 93.46 65.42
100 8 92.59 74.07
100 9 91.74 82.57
100 9.9 90.99 90.08
100 9.99 90.92 90.83
100 10 90.91 90.91
100 10.01 90.90 90.99
100 10.1 90.83 91.73
100 11 90.09 99.10
100 12 89.29 107.14

pH Calculations (Titration Curve)

The pH calculations with aqion are easy. Start with pure water (button New) and switch to molar units (activate checkbox mmol/L). Now enter the NaOH and HCl concentrations from the first line of the above table into the fields Na and Cl. Click on Start and adjust with pH. The calculated pH will be immediately displayed.

Then, repeat this procedure with the second line, and so on. The results are listed here:

NaOH addition (V1 in mL) pH
0 1.08
1 1.13
2 1.19
3 1.25
4 1.32
5 1.40
6 1.51
7 1.63
8 1.81
9 2.12
9.9 3.12
9.99 4.13
10 7.00
10.01 9.80
10.1 10.85
11 11.85
12 12.14

Approximation

If you ignore activity corrections and perform the calculations with a pocket calculator you would obtain the following approximated pH values

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Indeed, there are significant deviations from the exact values in the above table.

9 mL NaOH   →   pH = 2
9.9 mL NaOH   →   pH = 3
9.99 mL NaOH   →   pH = 4
[last modified: 2013-08-05]