Problem 115 - A Complete Resource Book in Chemistry for JEE Main

Question

In the titration of a certain solution of a mixture of \(\mathrm{NaHCO}_{3}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) against \(\mathrm{HCl}, \mathrm{V}_{1} \mathrm{~mL}\) of \(\mathrm{HCl}\) is required with phenolphthalein as indicator and \(\mathrm{V}_{2} \mathrm{~mL}\) with methyl orange as indicator for the same volume of the titrated solution. Hence volume of \(\mathrm{HCl}\) for reaction of \(\mathrm{HCl}\) with \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) alone is (a) \(\mathrm{V}_{2} / 4 \mathrm{~mL}\) (b) \(2 \mathrm{~V}_{1} \mathrm{~mL}\) (c) \(\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right) \mathrm{mL}\) (d) \(\left(\mathrm{V}_{1} / 3\right) \mathrm{mL}\)

Step-by-Step Solution

Answer

The volume of \(\mathrm{HCl}\) for \(\mathrm{Na}_2 \mathrm{CO}_3\) alone is \((\mathrm{V}_2 - \mathrm{V}_1)\) mL.

Step 1: Understanding the Problem

In this titration problem, we are dealing with a solution that contains both sodium bicarbonate \((\mathrm{NaHCO}_3)\) and sodium carbonate \((\mathrm{Na}_2 \mathrm{CO}_3)\). The problem provides us with two different volumes of \(\mathrm{HCl}\) used with two different indicators. \(\mathrm{V}_1\) is the volume required to reach the phenolphthalein endpoint, where \(\mathrm{Na}_2 \mathrm{CO}_3\) goes to \(\mathrm{NaHCO}_3\), and \(\mathrm{V}_2\) is for the methyl orange endpoint, where all carbonates are converted to \(\mathrm{CO}_2\). We need to find the volume of \(\mathrm{HCl}\) used for the reaction with \(\mathrm{Na}_2 \mathrm{CO}_3\) alone.

Step 2: Reactions Overview

Two significant reactions occur during the titration. 1. \(\mathrm{Na}_2 \mathrm{CO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaHCO}_3 + \mathrm{NaCl}\) ends at the phenolphthalein endpoint.2. \(\mathrm{NaHCO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2\), and \(\mathrm{Na}_2 \mathrm{CO}_3 + 2\mathrm{HCl} \rightarrow 2 \mathrm{NaCl} + \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2\) fully react to the methyl orange endpoint.\(\mathrm{V}_1\) represents the volume used in the first reaction (partial neutralization) and \(\mathrm{V}_2\) represents the total volume for full neutralization.

Step 3: Phenolphthalein Endpoint Analysis

At the phenolphthalein endpoint, only \(\mathrm{Na}_2 \mathrm{CO}_3\) is partially neutralized to \(\mathrm{NaHCO}_3\), requiring \(\mathrm{V}_1\) mL of \(\mathrm{HCl}\). This reaction converts \(\mathrm{Na}_2 \mathrm{CO}_3\) partially, but not \(\mathrm{NaHCO}_3\).

Step 4: Methyl Orange Endpoint Analysis

At the methyl orange endpoint, the remaining \(\mathrm{NaHCO}_3\) from both sources and the rest of \(\mathrm{Na}_2 \mathrm{CO}_3\) are completely neutralized, requiring \(\mathrm{V}_2\) mL of \(\mathrm{HCl}\). This volume completes the neutralization of \(\mathrm{Na}_2 \mathrm{CO}_3\) and \(\mathrm{NaHCO}_3\).

Step 5: Differentiating \(\mathrm{Na}_2 \mathrm{CO}_3\) Contribution

To find the \(\mathrm{HCl}\) volume that reacts with \(\mathrm{Na}_2 \mathrm{CO}_3\) independently, we consider that the phenolphthalein volume \(\mathrm{V}_1\) accounts for the reaction with \(\mathrm{Na}_2 \mathrm{CO}_3\) as NaHCO_3 is not titrated at this point. Therefore, the additional volume used by methyl orange, \((\mathrm{V}_2 - \mathrm{V}_1)\), must be attributed to \(\mathrm{Na}_2 \mathrm{CO}_3\) reacting fully and \(\mathrm{NaHCO}_3\) participating in more reaction to fully convert both species to CO_2. The volume of HCl for \(\mathrm{Na}_2 \mathrm{CO}_3\) is thus \((\mathrm{V}_2 - \mathrm{V}_1)\).

Key Concepts

Sodium Bicarbonate

Sodium bicarbonate, also known as baking soda, is a chemical compound with the formula \( \mathrm{NaHCO}_3 \). It is a white solid that can dissolve in water to produce an alkaline solution. Sodium bicarbonate acts as a weak base and is often used in baking, cleaning, and neutralizing acids.

In the context of titration, sodium bicarbonate reacts with hydrochloric acid (HCl) to produce sodium chloride (\( \mathrm{NaCl} \)), water, and carbon dioxide (\( \mathrm{CO}_2 \)).

The reaction can be represented as follows:
\[ \mathrm{NaHCO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2 \]

This particular reaction happens after all \( \mathrm{Na}_2 \mathrm{CO}_3 \) is converted to \( \mathrm{NaHCO}_3 \), making it essential in understanding the full neutralization process of carbonates in titration.

Sodium Carbonate

Sodium carbonate, with the chemical formula \( \mathrm{Na}_2 \mathrm{CO}_3 \), is commonly known as washing soda or soda ash. This white substance is soluble in water and is used in glass manufacturing, as well as a cleansing agent.

In titration chemistry, sodium carbonate acts as a base that can react with acids to form sodium bicarbonate first, and then fully convert to \( \mathrm{NaCl} \), water, and \( \mathrm{CO}_2 \).

The two-step reaction with HCl can be shown as:
1. Partial Neutralization:
\[ \mathrm{Na}_2 \mathrm{CO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaHCO}_3 + \mathrm{NaCl} \]
2. Full Neutralization:
\[ \mathrm{NaHCO}_3 + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2 \]

Understanding these reactions helps us interpret the endpoint differences in titration, especially when using different indicators.

Phenolphthalein Endpoint

The phenolphthalein endpoint in titration occurs when an indicator called phenolphthalein changes color, signaling that a certain reaction stage is complete. Phenolphthalein is a weak acid itself, and it appears colorless in acidic solutions but turns pink in basic solutions.

In the context of sodium carbonate titration, phenolphthalein indicates the point when \( \mathrm{Na}_2 \mathrm{CO}_3 \) has been converted to \( \mathrm{NaHCO}_3 \), but not yet to \( \mathrm{CO}_2 \) and water. This partial neutralization occurs when \( \mathrm{V}_1 \) mL of HCl is added. This stage is crucial as it sets the stage for understanding the overall titration process, distinguishing between the two different carbonate forms.

Methyl Orange Endpoint

The methyl orange endpoint represents another key stage in titration, characterized by the use of methyl orange indicator. This indicator turns red in acidic solutions and yellow in neutral environments, marking the transition from the acid state to the completely neutralized base.

During the titration of sodium bicarbonate and sodium carbonate mixture, the methyl orange endpoint indicates complete neutralization. This means that both \( \mathrm{NaHCO}_3 \) and \( \mathrm{Na}_2 \mathrm{CO}_3 \) have fully converted to \( \mathrm{NaCl} \), water, and \( \mathrm{CO}_2 \). The point at which methyl orange changes color is achieved after \( \mathrm{V}_2 \) mL of HCl has been added.

Understanding this endpoint is vital to recognizing when all the carbonate sources in the solution have been fully reacted, providing complete insight into the final stage of titration.