Problem 44 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Read the following statement and explanation and answer as per the options given below: Statement(S) : In the titration of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) with HCl using methyl orange indicator, the volume required at the equivalence point is twice that of the acid required using phenolphthalein indicator. explanation(E) : Two moles of \(\mathrm{HCl}\) are required for the complete neutralization of one mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) [1991 - 2 Marks] (a) Both \(\mathrm{S}\) and \(\mathrm{E}\) are true, and \(\mathrm{E}\) is the correct explanation of \(\mathrm{S}\). (b) Both \(S\) and \(E\) are true, but \(E\) is not the correct explanation of \(S\). (c) \(\mathrm{S}\) is true but \(\mathrm{E}\) is false. (d) \(\mathrm{S}\) is false but \(\mathrm{E}\) is true.

Step-by-Step Solution

Answer

(a) Both S and E are true, and E is the correct explanation of S.

Step 1: Understanding the Reaction

Sodium carbonate \(\mathrm{Na}_2 \mathrm{CO}_3\) reacts with hydrochloric acid \(\mathrm{HCl}\) in a two-step reaction.1. \[ \mathrm{Na}_2 \mathrm{CO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaHCO}_3 + \mathrm{NaCl} \]2. \[ \mathrm{NaHCO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]

Step 2: Titration with Phenolphthalein

In the presence of phenolphthalein, the end point corresponds to the neutralization of one mole of \(\mathrm{HCl}\) with one mole of \(\mathrm{Na}_2 \mathrm{CO}_3\), forming \(\mathrm{NaHCO}_3\). This is the first equivalence point. Therefore, only one mole of HCl is needed.

Step 3: Titration with Methyl Orange

Methyl orange indicates the complete neutralization reaction, where the \(\mathrm{NaHCO}_3\) formed is further neutralized by another mole of \(\mathrm{HCl}\). Thus, a total of two moles of \(\mathrm{HCl}\) are required per mole of \(\mathrm{Na}_2 \mathrm{CO}_3\). This is the second equivalence point.

Step 4: Evaluate the Statement and Explanation

The statement that the volume required at the equivalence point when using methyl orange is twice that when using phenolphthalein is true. The explanation is also true, as it correctly states that two moles of \(\mathrm{HCl}\) are needed for complete neutralization. Both \(S\) and \(E\) are true, and \(E\) directly explains \(S\).

Key Concepts

Equivalence Point

The equivalence point in a titration is a crucial concept to grasp. It refers to the moment in the reaction when the quantity of titrant added is precisely enough to completely neutralize the analyte solution. Both the titrant and the analyte are present in stoichiometrically equal amounts, meaning their reacting ratio is perfectly balanced according to the chemical equation.
For example, in the titration of sodium carbonate ( (a_2)CO_3) with hydrochloric acid (HCl), there are two distinct equivalence points. The first occurs after one mole of HCl has reacted with one mole of (a_2)CO_3, forming sodium bicarbonate (NaHCO_3). The second equivalence point is reached when an additional mole of HCl has fully reacted, neutralizing the NaHCO_3 to form sodium chloride (NaCl), carbon dioxide (CO_2), and water (H_2O). This complete reaction illustrates how equivalence points are key to identifying how many moles of a titrant are required to achieve full neutralization. Understanding these points helps ensure accurate measurements in titration experiments.

Indicators in Titration

Indicators play a vital role in titration, acting as the visual cue that signals the arrival at an endpoint. The endpoint, ideally, is very close to the equivalence point of the reaction. Different indicators are suitable for different reactions, depending on the pH change that occurs at the equivalence point.
In our example, phenolphthalein and methyl orange are two indicators used for sodium carbonate titration.

• Phenolphthalein changes color at a pH around 8.2, suitable for detecting the first equivalence point when (a_2)CO_3 turns into (aHCO_3).
• Methyl orange changes color at a lower pH around 3.1, making it suitable for signaling the second equivalence point, where the complete conversion of (aHCO_3) happens to form (aCl), CO_2, and H_2O.

Choosing the correct indicator ensures the titration results are as accurate as possible.

Neutralization Reaction

Neutralization reactions are the foundation of acid-base titrations. They involve the reaction between an acid and a base to produce water and a salt. These reactions are typically exothermic and result in a significant change in pH, which can be measured and used to determine the concentration of an unknown solution.
In the titration of sodium carbonate ( (a_2)CO_3) with hydrochloric acid (HCl), the neutralization occurs in two stages:

• The first stage involves the reaction of one mole of HCl with (a_2)CO_3 to form sodium bicarbonate (NaHCO_3), resulting in a significant change in pH.
• The second stage completes the neutralization when an additional mole of HCl reacts with the NaHCO_3, resulting in the formation of sodium chloride (NaCl), carbon dioxide (CO_2), and water (H_2O).

Understanding these reactions aids in comprehending how indicators determine their endpoints, reflecting the completion of the neutralization process.