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Acid-base titrations in analytical chemistry

Acid-base titrations are widely used in analytical chemistry to determine the concentration of an unknown acid or base solution. This technique is based on the neutralization reaction between the acid and the base, where the concentration of one of the species is known and the other is unknown. The process involves slowly adding a solution of known concentration to a solution of unknown concentration until the equivalence point is reached. The equivalence point is the point where the number of moles of acid and base in the solution are stoichiometrically equal.

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Acid-base titrations in analytical chemistry

There are various types of acid-base titrations depending on the properties of the acid and base being used. In a strong acid-strong base titration, both the acid and base are completely dissociated in solution. This means that the equivalence point is reached when the solution is neutral, and the pH is 7.

In a weak acid-strong base titration, the acid is only partially dissociated in solution, so the equivalence point is reached when the pH is greater than 7. In this type of titration, it is important to use a pH indicator that changes color at a pH close to the equivalence point. The most commonly used indicator for this type of titration is phenolphthalein.

In a strong acid-weak base titration, the base is only partially dissociated in solution, so the equivalence point is reached when the pH is less than 7. This type of titration is not commonly used in analytical chemistry because it is difficult to prepare and standardize a solution of a weak base.

One of the most important applications of acid-base titrations in analytical chemistry is in the pharmaceutical industry. Acid-base titrations are used to determine the purity and concentration of drugs, as well as to identify and quantify impurities. In addition, acid-base titrations are used to measure the pH of biological fluids such as blood, urine, and saliva, which is important in the diagnosis of many diseases.

Overall, acid-base titrations are an essential tool in analytical chemistry for the determination of the concentration of acids and bases. They are versatile and widely applicable, making them an important technique in many fields including pharmaceuticals, environmental science, and biochemistry.

pH changes during the titration of a weak acid (acetic acid) with a strong base (sodium hydroxide)

During the titration of a weak acid such as acetic acid with a strong base such as sodium hydroxide, the pH of the solution changes in a characteristic manner. At the beginning of the titration, the pH of the solution is determined by the weak acid, which only partially dissociates in water. Acetic acid, for example, is a weak acid that dissociates according to the following equilibrium:

CH3COOH + H2O ⇌ CH3COO- + H3O+

This means that only a small fraction of the acetic acid molecules have dissociated into acetate ions (CH3COO-) and hydronium ions (H3O+). As a result, the pH of the solution is slightly acidic, typically around 4.7 for a 0.1 M solution of acetic acid.

As the strong base sodium hydroxide is added to the solution, it reacts with the weak acid to form water and the conjugate base of the weak acid. In the case of acetic acid, sodium hydroxide reacts with the hydronium ion to form water and the acetate ion:

CH3COOH + NaOH → CH3COO- + H2O

As more sodium hydroxide is added, the concentration of acetate ions in the solution increases, and the pH gradually increases as well. The pH at any point in the titration can be calculated using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

where pKa is the dissociation constant of the weak acid, [A-] is the concentration of the acetate ion, and [HA] is the concentration of the undissociated acetic acid.

When the equivalence point is reached, all the acetic acid has reacted with the sodium hydroxide and the solution contains only acetate ions and water. At this point, the pH of the solution is determined solely by the concentration of acetate ions in the solution, which is determined by the amount of sodium hydroxide added.

After the equivalence point, any additional sodium hydroxide added to the solution will increase the pH of the solution, making it increasingly basic. At the equivalence point, the pH of the solution is equal to the pKa of the weak acid, which for acetic acid is 4.76. However, if the amount of strong base added is significantly greater than the amount required to reach the equivalence point, the pH of the solution may exceed 7, becoming strongly basic.

Question:

Calculate the pH in the titration of 25.0 mL of 0.100M acetic acid by sodium hydroxide after the addition to the acid solution of
(a) 10.0 mL of 0.100MNaOH
(b) 25.0 mL of 0.100MNaOH
(c) 35.0 mL of 0.100MNaOH

Answer :

Approach for the solution:

To calculate the pH of the solution at each point in the titration, we need to use the principles of acid-base chemistry and stoichiometry. During the titration of acetic acid with sodium hydroxide, a neutralization reaction occurs, resulting in the formation of sodium acetate and water. The balanced chemical equation for this reaction is:

CH3COOH + NaOH → CH3COONa + H2O

At the beginning of the titration, the solution contains only acetic acid. As sodium hydroxide is added, it reacts with the acetic acid to form sodium acetate and water. The pH of the solution changes as the amount of sodium hydroxide added increases.

To calculate the pH at each point, we need to determine the amount of acid and base in the solution, and use the principles of equilibrium chemistry to determine the concentration of hydronium ions (H+) and hydroxide ions (OH-) in the solution. From there, we can use the pH formula (pH = -log[H+]) to calculate the pH of the solution.

Solution:

Acetic acid is a weak acid, and it reacts with sodium hydroxide in a neutralization reaction. The balanced equation for the reaction is:

CH3COOH + NaOH -> CH3COONa + H2O

Before any NaOH is added, the acetic acid is present in the solution as CH3COOH. As NaOH is added, it reacts with the acetic acid to form CH3COONa and water. The pH of the solution depends on the amount of NaOH that has been added and the resulting concentration of the CH3COO- ion, which is the conjugate base of acetic acid.

(a) After adding 10.0 mL of 0.100 M NaOH:

The number of moles of NaOH added is:

n(NaOH) = M(NaOH) × V(NaOH) = 0.100 mol/L × 0.010 L = 0.001 mol

The number of moles of acetic acid originally present in the solution is:

n(CH3COOH) = M(CH3COOH) × V(CH3COOH) = 0.100 mol/L × 0.025 L = 0.0025 mol

The number of moles of acetic acid that have reacted with NaOH is equal to the number of moles of NaOH added, since the balanced equation has a 1:1 mole ratio between NaOH and CH3COOH:

n(CH3COOH reacted) = n(NaOH) = 0.001 mol

The number of moles of CH3COOH remaining in the solution is:

n(CH3COOH remaining) = n(CH3COOH) – n(CH3COOH reacted) = 0.0025 mol – 0.001 mol = 0.0015 mol

The concentration of the CH3COO- ion in the solution is equal to the number of moles of CH3COO- divided by the total volume of the solution:

[CH3COO-] = n(CH3COO-) / V(total) = n(CH3COO-) / (V(CH3COOH) + V(NaOH)) = 0.001 mol / (0.025 L + 0.010 L) = 0.025 mol/L

The pH of the solution can be calculated using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

The pKa of acetic acid is 4.76. In this case, the acid is CH3COOH and the conjugate base is CH3COO-. Therefore,

[HA] = [CH3COOH] = 0.0015 mol / 0.025 L = 0.06 mol/L [A-] = [CH3COO-] = 0.025 mol/L

Substituting these values into the Henderson-Hasselbalch equation gives:

pH = 4.76 + log(0.025/0.06) = 4.63

Therefore, the pH of the solution after adding 10.0 mL of 0.100 M NaOH is 4.63.

(b) After adding 25.0 mL of 0.100 M NaOH:

The number of moles of NaOH added is:

n(NaOH) = M(NaOH) × V(NaOH) = 0.100 mol/L × 0.025 L = 0.0025 mol

The number of moles of acetic acid that have reacted with NaOH is equal to the number of moles of NaOH added, since

the balanced equation has a 1:1 mole ratio between NaOH and CH3COOH:

n(CH3COOH reacted) = n(NaOH) = 0.0025 mol

The number of moles of CH3COOH remaining in the solution is:

n(CH3COOH remaining) = n(CH3COOH) – n(CH3COOH reacted) = 0.0025 mol – 0.0025 mol = 0 mol

This means that all of the acetic acid has reacted, and the solution now contains only the CH3COO- ion. The concentration of the CH3COO- ion in the solution is equal to the number of moles of CH3COO- divided by the total volume of the solution:

[CH3COO-] = n(CH3COO-) / V(total) = n(NaOH) / (V(CH3COOH) + V(NaOH)) = 0.0025 mol / (0.025 L + 0.025 L) = 0.05 mol/L

The pH of the solution can be calculated using the equation for the pOH of a solution of a strong base and weak acid:

pOH = pKb + log([B]/[HB+])

The pKb of the CH3COO- ion is equal to 14 – pKa = 14 – 4.76 = 9.24. In this case, the base is CH3COO- and the conjugate acid is HAc (acetic acid). Therefore,

[B] = [CH3COO-] = 0.05 mol/L [HB+] = [HAc] = 0 mol/L

Substituting these values into the equation for pOH gives:

pOH = 9.24 + log(0.05/0) = 9.24

The pH of the solution is:

pH = 14 – pOH = 14 – 9.24 = 4.76

Therefore, the pH of the solution after adding 25.0 mL of 0.100 M NaOH is 4.76.

(c) After adding 35.0 mL of 0.100 M NaOH:

The number of moles of NaOH added is:

n(NaOH) = M(NaOH) × V(NaOH) = 0.100 mol/L × 0.035 L = 0.0035 mol

The number of moles of acetic acid that have reacted with NaOH is equal to the number of moles of NaOH added, since the balanced equation has a 1:1 mole ratio between NaOH and CH3COOH:

n(CH3COOH reacted) = n(NaOH) = 0.0035 mol

The number of moles of CH3COOH remaining in the solution is:

n(CH3COOH remaining) = n(CH3COOH) – n(CH3COOH reacted) = 0.0025 mol – 0.0035 mol = -0.001 mol

This means that there is no more acetic acid remaining in the solution and that there is an excess of the CH3COO- ion. The concentration of the CH3COO- ion in the solution is equal to the number of moles of CH3COO- divided by the total volume of the solution:

[CH3COO-] = n(CH3COO-) / V(total) = n(NaOH) / (V(CH3COOH) + V(NaOH)) = 0.0035 mol / (0.025 L + 0

035 L) = 0.07 mol/L

The excess OH- ions in the solution react with water to form hydroxide ions and hydronium ions according to the equation:

OH- + H2O ↔ H2O + OH-

The equilibrium constant for this reaction is Kw = [H+][OH-] = 1.0 x 10^-14 at 25°C.

Since the [OH-] concentration is known, we can use the Kw expression to calculate the [H+] concentration:

Kw = [H+][OH-]

1.0 x 10^-14 = [H+][0.14]

[H+] = 7.1 x 10^-14 mol/L

Therefore, the pH of the solution after adding 35.0 mL of 0.100 M NaOH is:

pH = -log[H+] = -log(7.1 x 10^-14) = 13.15

So, the pH of the solution after adding 35.0 mL of 0.100 M NaOH is 13.15.

Summary

To calculate the pH during the titration of a weak acid with a strong base, we use stoichiometry and acid-base chemistry principles to determine the amount of acid and base in the solution at each point. We then use equilibrium chemistry to determine the concentration of hydronium and hydroxide ions, and calculate the pH of the solution using the pH formula.

In this specific problem, we are asked to calculate the pH after adding 10.0 mL, 25.0 mL, and 35.0 mL of 0.100 M NaOH to 25.0 mL of 0.100 M acetic acid. The calculations involve determining the amount of acetic acid and NaOH in the solution, calculating the moles of NaOH that reacted with the acetic acid, and using the dissociation constant for acetic acid to determine the concentration of acetate and hydronium ions. Finally, we use the Kw expression to calculate the hydroxide ion concentration and the pH formula to calculate the pH of the solution.

FAQ

Some frequently asked questions related to the topic of calculating pH during acid-base titrations:

Q: What is an acid-base titration?

A: An acid-base titration is a technique used to determine the concentration of an unknown acid or base by reacting it with a known concentration of an acid or base.

Q: What is the equivalence point in an acid-base titration?

A: The equivalence point is the point in an acid-base titration where the moles of acid and base are stoichiometrically equal. At this point, all the acid has reacted with the base or vice versa.

Q: How is the pH calculated during an acid-base titration?

A: The pH during an acid-base titration is calculated using the principles of stoichiometry and acid-base chemistry to determine the amount of acid and base in the solution at each point. The concentration of hydronium and hydroxide ions is then determined using equilibrium chemistry, and the pH is calculated using the pH formula (pH = -log[H+]).

Q: What is the pH of a buffer solution?

A: A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added. The pH of a buffer solution is determined by the concentration of the weak acid and its conjugate base or the weak base and its conjugate acid.

Q: What is the difference between a strong acid and a weak acid?

A: A strong acid is an acid that completely dissociates in water, meaning that all the acid molecules ionize into hydronium ions and anions. A weak acid, on the other hand, only partially dissociates in water, meaning that only some of the acid molecules ionize into hydronium ions and anions.

Q: What is the significance of the equivalence point in the titration of a weak acid with a strong base?

A: The equivalence point is the point at which the moles of acid and base are equal. At this point, all of the acid has reacted with the base and the solution contains only the conjugate base of the weak acid and water. The pH at the equivalence point is determined by the dissociation constant of the weak acid and is independent of the amount of strong base added. Therefore, the equivalence point is a critical point in the titration and is used to determine the concentration of the acid.

Q: Why does the pH of the solution change during the titration of a weak acid with a strong base?

A: The pH of the solution changes during the titration because of the reaction between the weak acid and the strong base. As the base is added, it reacts with the acid to form the conjugate base of the acid and water. The concentration of the conjugate base increases, leading to an increase in the pH of the solution.

Q: How can the pH of the solution be determined during the titration of a weak acid with a strong base?

A: The pH of the solution can be determined by measuring the amount of base added and calculating the concentration of the conjugate base of the weak acid. The Henderson-Hasselbalch equation can be used to calculate the pH of the solution at any point in the titration.

Q: What happens to the pH of the solution after the equivalence point?

A: After the equivalence point, the pH of the solution increases rapidly because any additional strong base added to the solution will react with water to form hydroxide ions, making the solution increasingly basic. The pH of the solution can exceed 7 and become strongly basic if a large excess of strong base is added.