Question

When \(10 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid \((\mathrm{pKa}=5.0)\) is titrated against \(10 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) ammonia solution \((\mathrm{pKb}=5.0)\) the equivalence point occurs at \(\mathrm{pH}\) : (a) \(5.0\) (b) \(6.0\) (c) \(9.0\) (d) \(7.0\)

Short answer

The pH at the equivalence point is 5.0, option (a).

Step-by-step solution

Understand the Components

You have two substances: acetic acid, with a given pKa value, and ammonia, with a given pKb value. You are to determine the pH at the equivalence point for their titration.

Recall Equivalence Point Definition

The equivalence point in a titration is where the number of moles of the acid equals the number of moles of the base. Here, both solutions have equal concentrations and volumes, so they neutralize each other perfectly.

Characteristics of a Weak Acid and Weak Base Reaction

When a weak acid is titrated with a weak base, the pH at the equivalence point is not 7, but is determined by the average of the pKa and pKb values of the substances involved.

Apply the pH Formula

Use the formula for the equivalence point in titration involving weak acids and weak bases, where \( \text{pH} = \frac{\text{pKa} + \text{pKb}}{2} \). Here: \[ \text{pH} = \frac{5.0 + 5.0}{2} \]

Calculate the pH

Calculate the pH using the values from the previous step:\[ \text{pH} = \frac{5.0 + 5.0}{2} = 5.0 \] This is the pH at the equivalence point.

Key concepts

Equivalence Point

In a titration, the equivalence point is reached when the exact amount of acid has reacted with the exact amount of base, or vice versa. This means the moles of the titrant (the solution being added) are exactly enough to neutralize the moles of the substance in the solution being titrated.
The equivalence point isn't necessarily the same as the endpoint, which is when you stop adding titrant based on an observable change (such as a color change if an indicator is used).
In the context of a weak acid and weak base titration, like the one involving acetic acid and ammonia, the equivalence point is determined not by neutrality (pH = 7) but by the average of the \( ext{pKa}\) of the acid and the \( ext{pKb}\) of the base. This results from the fact that neither the acid nor the base fully dissociates in water, leading to a pH that reflects the balance of both strengths.

Weak Acid and Weak Base Reaction

Reactions between weak acids and weak bases differ significantly from those involving strong acids or bases. In a typical reaction involving a weak acid like acetic acid and a weak base such as ammonia, neither reactant completely dissociates in solution.

• A weak acid, like acetic acid, only partially donates its protons.
• Similarly, a weak base, like ammonia, does not fully accept protons.

Because of this partial dissociation, these solutions do not completely neutralize as they would with strong acids or bases. This leads to the distinct characteristic where the pH at the equivalence point is neither very acidic nor very basic, but somewhere in between, depending on the acid and base's strength, and thus their \( ext{pKa}\) and \( ext{pKb}\) values.

pH Calculation

Calculating the pH at the equivalence point for a titration involving a weak acid and a weak base involves averaging their respective \( ext{pKa} \) and \( ext{pKb} \). This formula is derived based on the equilibrium nature and the dissociation constants of the acid and base involved.To calculate:

• Take the \( ext{pKa} \) value of the weak acid.
• Take the \( ext{pKb} \) value of the weak base.
• Average these two values using the formula: \[ ext{pH} = \frac{\text{pKa} + \text{pKb}}{2} \]

For example, if you have acetic acid (\( ext{pKa} = 5.0 \)) and ammonia (\( ext{pKb} = 5.0 \)), the calculation would be perfect and simple: \ [ \ \text{pH} = \frac{5.0 + 5.0}{2} = 5.0 ] \This calculation shows that the pH at the equivalence point for this reaction is 5.0, reflecting a neutral balance tailored to the specific strengths of the weak acid and weak base used.