Calculating pH at Different Volumes of KOH

Oct 13, 2025 by miodeya.com 67 views

Introduction

Titration is a laboratory technique used to determine the concentration of a substance by reacting it with a known amount of another substance. In this article, we will consider the titration of 100.0 mL of 0.200 M acetic acid ( $K_{a} = 1.8 \times 10^{-5}$ ) by 0.100 M KOH. We will calculate the pH of the resulting solution after the following volumes of KOH have been added.

Theoretical Background

Acetic acid (CH3COOH) is a weak acid that partially dissociates in water to produce hydrogen ions (H+) and acetate ions (CH3COO-). The dissociation reaction is as follows:

CH3COOH ⇌ H+ + CH3COO-

The acid dissociation constant ( $K_{a}$ ) is a measure of the strength of the acid and is defined as the ratio of the concentrations of the products to the reactants:

$K_{a} = \frac{[H^{+}][CH_{3}COO^{-}]}{[CH_{3}COOH]}$

For acetic acid, $K_{a} = 1.8 \times 10^{-5}$ .

Calculating pH at Different Volumes of KOH

To calculate the pH of the resulting solution after the addition of different volumes of KOH, we need to consider the following steps:

Initial pH: Calculate the pH of the initial solution of acetic acid.
Addition of KOH: Calculate the pH after the addition of a certain volume of KOH.
Equivalence Point: Calculate the pH at the equivalence point, where the amount of KOH added is equal to the amount of acetic acid present.

Initial pH

The initial pH of the acetic acid solution can be calculated using the formula:

pH = -log[H+]

where [H+] is the concentration of hydrogen ions in the solution.

For acetic acid, the concentration of hydrogen ions can be calculated using the acid dissociation constant ( $K_{a}$ ):

$K_{a} = \frac{[H^{+}][CH_{3}COO^{-}]}{[CH_{3}COOH]}$

Since the dissociation of acetic acid is a weak acid, we can assume that the concentration of hydrogen ions is small compared to the concentration of acetic acid. Therefore, we can simplify the equation to:

$K_{a} = \frac{[H^{+}]^{2}}{[CH_{3}COOH]}$

Rearranging the equation to solve for [H+], we get:

$[H^{+}] = \sqrt{K_{a} \times [CH_{3}COOH]}$

Substituting the values of $K_{a}$ and [CH3COOH], we get:

$[H^{+}] = \sqrt{1.8 \times 10^{-5} \times 0.200} = 1.3 \times 10^{-3}$

Therefore, the initial pH of the acetic acid solution is:

pH = -log(1.3 \times 10^{-3}) = 2.89

Addition of KOH

When KOH is added to the acetic acid solution, it reacts with the acetic acid to form water and acetate ions. The reaction is as follows:

CH3COOH + KOH → CH3COOK + H2O

The concentration of hydrogen ions in the solution decreases as the amount of KOH added increases. To calculate the pH after the addition of a certain volume of KOH, we need to consider the following:

The amount of KOH added is equal to the amount of acetic acid present.
The concentration of hydrogen ions in the solution is equal to the concentration of KOH added.

Let's consider the addition of 50.0 mL of 0.100 M KOH.

The amount of KOH added is:

n(KOH) = C(KOH) * V(KOH) = 0.100 M * 50.0 mL = 5.00 mmol

The amount of acetic acid present is:

n(CH3COOH) = C(CH3COOH) * V(CH3COOH) = 0.200 M * 100.0 mL = 20.0 mmol

Since the amount of KOH added is equal to the amount of acetic acid present, the reaction is complete, and the concentration of hydrogen ions in the solution is equal to the concentration of KOH added.

Therefore, the pH after the addition of 50.0 mL of 0.100 M KOH is:

pH = -log(0.100) = 1.00

Equivalence Point

The equivalence point is reached when the amount of KOH added is equal to the amount of acetic acid present. At this point, the concentration of hydrogen ions in the solution is zero, and the pH is equal to 14.

To calculate the pH at the equivalence point, we need to consider the following:

The amount of KOH added is equal to the amount of acetic acid present.
The concentration of hydrogen ions in the solution is zero.

Let's consider the addition of 100.0 mL of 0.100 M KOH.

The amount of KOH added is:

n(KOH) = C(KOH) * V(KOH) = 0.100 M * 100.0 mL = 10.0 mmol

The amount of acetic acid present is:

n(CH3COOH) = C(CH3COOH) * V(CH3COOH) = 0.200 M * 100.0 mL = 20.0 mmol

Since the amount of KOH added is equal to the amount of acetic acid present, the reaction is complete, and the concentration of hydrogen ions in the solution is zero.

Therefore, the pH at the equivalence point is:

pH = 14

pH at Different Volumes of KOH

To calculate the pH at different volumes of KOH, we need to consider the following:

The amount of KOH added is less than the amount of acetic acid present.
The concentration of hydrogen ions in the solution is equal to the concentration of KOH added.

Let's consider the addition of 25.0 mL of 0.100 M KOH.

The amount of KOH added is:

n(KOH) = C(KOH) * V(KOH) = 0.100 M * 25.0 mL = 2.50 mmol

The amount of acetic acid present is:

n(CH3COOH) = C(CH3COOH) * V(CH3COOH) = 0.200 M * 100.0 mL = 20.0 mmol

Since the amount of KOH added is less than the amount of acetic acid present, the reaction is not complete, and the concentration of hydrogen ions in the solution is equal to the concentration of KOH added.

Therefore, the pH after the addition of 25.0 mL of 0.100 M KOH is:

pH = -log(0.025) = 1.60

Similarly, we can calculate the pH at different volumes of KOH.

Volume of KOH (mL)	pH
0.0	2.89
25.0	1.60
50.0	1.00
100.0	14

Conclusion

In this article, we have calculated the pH of the resulting solution after the addition of different volumes of KOH to 100.0 mL of 0.200 M acetic acid. We have considered the initial pH, the addition of KOH, and the equivalence point. The results show that the pH decreases as the amount of KOH added increases, and the pH at the equivalence point is 14.

References

Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
Chang, R. (2010). Physical chemistry for the biosciences. University Science Books.
Levine, I. N. (2012). Physical chemistry (6th ed.). McGraw-Hill.
Q&A: Titration of Acetic Acid with Potassium Hydroxide =====================================================

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to the titration of acetic acid with potassium hydroxide.

Q: What is the purpose of titration?

A: The purpose of titration is to determine the concentration of a substance by reacting it with a known amount of another substance.

Q: What is the acid dissociation constant (Ka)?

A: The acid dissociation constant (Ka) is a measure of the strength of an acid and is defined as the ratio of the concentrations of the products to the reactants.

Q: How is the pH of a solution calculated?

A: The pH of a solution is calculated using the formula:

pH = -log[H+]

where [H+] is the concentration of hydrogen ions in the solution.

Q: What is the equivalence point in titration?

A: The equivalence point in titration is reached when the amount of titrant added is equal to the amount of analyte present. At this point, the concentration of hydrogen ions in the solution is zero, and the pH is equal to 14.

Q: How is the pH of a solution affected by the addition of a strong base?

A: The pH of a solution is affected by the addition of a strong base in the following way:

The addition of a strong base increases the concentration of hydroxide ions (OH-) in the solution.
The increase in the concentration of hydroxide ions decreases the concentration of hydrogen ions (H+) in the solution.
The decrease in the concentration of hydrogen ions increases the pH of the solution.

Q: What is the effect of the concentration of the titrant on the pH of the solution?

A: The effect of the concentration of the titrant on the pH of the solution is as follows:

A higher concentration of the titrant results in a more rapid increase in the pH of the solution.
A lower concentration of the titrant results in a more gradual increase in the pH of the solution.

Q: How is the pH of a solution affected by the presence of a buffer?

A: The pH of a solution is affected by the presence of a buffer in the following way:

A buffer is a solution that resists changes in pH when an acid or base is added.
The presence of a buffer in a solution prevents the pH from changing rapidly when an acid or base is added.
The pH of a solution with a buffer remains relatively stable over a wide range of pH values.

Q: What is the significance of the pH of a solution?

A: The pH of a solution is significant because it determines the chemical properties of the solution. For example:

A solution with a high pH is basic and can react with acids to form salts and water.
A solution with a low pH is acidic and can react with bases to form salts and water.
A solution with a neutral pH is neither acidic nor basic and can react with acids and bases to form salts and water.

Conclusion

In this article, we have answered some frequently asked questions related to the titration of acetic acid with potassium hydroxide. We have discussed the purpose of titration, the acid dissociation constant (Ka), the calculation of pH, the equivalence point, and the effect of the concentration of the titrant and the presence of a buffer on the pH of a solution. We have also discussed the significance of the pH of a solution and its effect on the chemical properties of the solution.

References

Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
Chang, R. (2010). Physical chemistry for the biosciences. University Science Books.
Levine, I. N. (2012). Physical chemistry (6th ed.). McGraw-Hill.