
Concept explainers
Interpretation:
The pH values after the addition of each proportion of the base to the acid is to be determined. Also, the titration curve needs to be drawn.
Concept introduction:
Titration curve is drawn to determine the change in pH of an acid or base with respect to the added volume of base or acid to it.
The titration curve can be drawn between a strong/weak acid and strong/weak base. The change in pH shows different patterns for different combinations of acids and bases.

Explanation of Solution
Initial pH of the analyte solution can be calculated as follows:
Lactic acid is a weak acid that forms an equilibrium mixture when dissolved in water. The equilibrium is as follows.
The initial molarity of lactic acid is 0.1 M.
The amount of lactic acid at the beginning can be calculated from. By constructing an ICE table, the concentration of lactate ion in the solution after the acid dissociation can be determined.
Reaction | Lactic acid | Lactate | H+ |
Initial | 0.1 | 0 | 0 |
Change | -x | +x | +x |
Equilibrium | (0.1-x) | x | x |
The acid dissociation constant can be represented as follows:
Solving this quadratic equation gives the amount of hydrogen ions in the solution.
Thus, the concentration of hydrogen ion is 0.00185 and pH of the solution can be calculated as follows:
Addition of
Total amount of lactic acid to be neutralized can be calculated from its molarity and volume as follows:
Or,
Now, the amount of base added can be calculated as follows:
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0004 | ||
Change | -0.0004 | -0.0004 | 0.0004 | 0.0004 |
Equilibrium | 0.0021 | 0 | 0.0004 | 0.0004 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0008 | ||
Change | -0.0008 | -0.0008 | 0.0008 | 0.0008 |
Equilibrium | 0.0017 | 0 | 0.0008 | 0.0008 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.00125 | ||
Change | -0.00125 | -0.00125 | 0.00125 | 0.00125 |
Equilibrium | 0.00125 | 0 | 0.00125 | 0.00125 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.002 | ||
Change | -0.002 | -0.002 | 0.002 | 0.002 |
Equilibrium | 0.0005 | 0 | 0.002 | 0.002 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0024 | ||
Change | -0.0024 | -0.0024 | 0.0024 | 0.0024 |
Equilibrium | 0.0001 | 0 | 0.0024 | 0.0024 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.00245 | ||
Change | -0.00245 | -0.00245 | -0.00245 | -0.00245 |
Equilibrium | 0.00005 | 0 | -0.00245 | -0.00245 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.00249 | ||
Change | -0.00249 | -0.00249 | -0.00249 | -0.00249 |
Equilibrium | 0.00001 | 0 | -0.00249 | -0.00249 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
Applying the Henderson-Hasselbalch equation,
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0025 | ||
Change | -0.0025 | -0.0025 | -0.0025 | -0.0025 |
Equilibrium | 0.0000 | 0 | -0.0025 | -0.0025 |
Concentration of lactic acid after addition of base
Concentration of lactate ion
At this point, there is no excess acid or base. Therefore, the only possible reaction here is the dissociation of the conjugate base of the lactic acid (that is lactate ion).
Thereafter, by obtaining the Kb value for lactate ion, the amount of hydroxide ions in the solution can be determined to get the pH value at this point.
Reaction | Lactic acid | Lactate | OH- |
Initial | 0.05 | 0 | 0 |
Change | -X | x | x |
Equilibrium | (0.05-x) | x | x |
Then the pH can be calculated as follows:
Thereafter, this quadratic equation can be solved to determine the hydroxide ion concentration, thereby, the pOH and the pH can be determined.
The calculated value of x is concentration of hydroxide ion. The pOH of the solution will be:
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0028 | ||
Change | -0.0025 | 0.0025 | 0 | 0 |
Equilibrium | 0 | 0.0003 | 0 | 0 |
Concentration of hydroxide
Addition of
Total amount of lactic acid to be neutralized
Amount of base added
Then the ICE table after the addition of base is created in order to determine the pH of the solution using Henderson-Hasselbalch equation.
Reaction | Lactic acid | OH- | Lactate | H+ |
Initial | 0.0025 | 0 | 0 | 0 |
Add | 0 | 0.0030 | ||
Change | -0.0025 | 0.0025 | 0 | 0 |
Equilibrium | 0 | 0.0005 | 0 | 0 |
Concentration of hydroxide
Thus, the value of pH with respect to added volume of base is as follows:
Volume (in mL) | pH |
0 | 2.73 |
4 | 3.14 |
8 | 3.53 |
12.5 | 3.86 |
20 | 4.46 |
24 | 5.24 |
24.5 | 5.6 |
24.9 | 6.3 |
25.0 | 8.28 |
25.1 | 10.3 |
26.0 | 11.30 |
28.0 | 11.75 |
30.0 | 11.96 |
The titration curve can be drawn as follows:
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