Problem 87 - A Complete Resource Book in Chemistry for JEE Main

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) \(7.0\)

Step-by-Step Solution

Answer

The pH at the equivalence point is 7.0, so the correct answer is (d) 7.0.

Step 1: Understand the Reactions

We are dealing with a titration of a weak acid (acetic acid) and a weak base (ammonia). Both have the same concentration and balance in terms of moles because \\(\text{Moles of acetic acid} = \text{Moles of ammonia} = 0.001 \space \text{mol}\).

Step 2: Calculate pH at Halfway Point

Initially, for weak acid and weak base titrations such as this, at the halfway point, \\(\text{pH} = \frac{\text{pKa} + \text{pKb}}{2}\).\Using \(\text{pKa} = 5.0\) and \(\text{pKb} = 5.0\), \\(\text{pH} = \frac{5.0 + 5.0}{2} = 5.0\).

Step 3: Determine pH at Equivalence Point

At the equivalence point, the weak acid and weak base are completely neutralized, forming water and the salt of the acid and base. Since both acetic acid and ammonia are weak and have equal strength, the solution's pH will be neutral. Thus, \\(\text{pH} = 7.0\).

Step 4: Identify the Correct Answer

Based on the calculation from Step 3, the pH at the equivalence point in this titration is \(7.0\). Therefore, the correct option is (d) \(7.0\).

Key Concepts

Equivalence Point in Titration

The equivalence point in a titration is the moment during the process where the amount of acid equals the amount of base in terms of moles. The reaction is complete, and the acid and base have been completely neutralized by one another. In this specific exercise, it involves titration between a weak acid, acetic acid, and a weak base, ammonia. The equivalence point is a crucial aspect as it tells us when the titration is complete. This point can significantly vary depending on the strength of the acids and bases involved. For instance, in strong acid-strong base reactions, the equivalence point typically falls at pH 7. However, with combinations involving weak acids or weak bases, the equivalence point can differ substantially. Here, because we deal with both a weak acid and weak base with similar strength, the equivalence point results in a neutral pH of 7.

Understanding Weak Acids and Weak Bases

Weak acids, like acetic acid, and weak bases, such as ammonia, do not completely dissociate into ions when dissolved in water. This partial dissociation is what defines them as 'weak'. Their strengths are represented by their dissociation constants, pKa and pKb, respectively.

• The pKa of acetic acid is 5.0, indicating a relatively low strength as an acid.
• Similarly, the pKb for ammonia is 5.0, reflecting its low basic strength.

This characteristic impacts the titration process, as the reaction dynamics are different compared to strong acids or bases. The balance or neutrality achieved at the equivalence point here highlights that neither the acidic nor the basic properties dominate, which is an important nuance of weak acid-weak base interactions.

Calculating pH in Titration

Calculating the pH at various stages of titration is essential to understand the progress and endpoint of the process. During titration of a weak acid with a weak base, the pH can be anticipated both at the halfway point and at the equivalence point.

• At the halfway point, when equal volumes but not moles of acid and base have reacted, the pH can be found using the equation \(\text{pH} = \frac{\text{pKa} + \text{pKb}}{2}\).
• Using the exercise's values, this results in a pH of 5.0 halfway.

At the equivalence point, as both concentrations of acid and base are the same, and their weak nature ensures neutrality, the pH is 7.0. This is contrary to strong acid-base reactions, where distinct changes in pH are noted.

Role of Neutralization Reaction

Neutralization is the chemical reaction forming the backbone of titration between acids and bases. It involves the hydrogen ions from the acid reacting with the hydroxide ions from the base to form water. In a weak acid and weak base setup like our exercise, after neutralization, a salt is formed. Here, acetic acid and ammonia neutralize to form ammonium acetate and water. However, because both the acid and base are weak, the resulting solution at the equivalence point doesn’t create excess hydrogen ions or hydroxide ions that would significantly affect the pH. This neutralization supports the formation of a neutral pH 7 at the equivalence point. Understanding this process helps grasp why weak acid and weak base titrations have different pH characteristics than those involving strong acids and bases.