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 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 correct volume is \( \left(V_2 - V_1\right) \mathrm{mL}\). Option (c).

Step 1: Identifying the Reaction Stages

When titrating with phenolphthalein, the reaction \\[ \text{Na}_2\text{CO}_3 + \text{HCl} \rightarrow \text{NaHCO}_3 + \text{NaCl} \] completes. Upon using methyl orange, the reaction \\[ \text{NaHCO}_3 + \text{HCl} \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{NaCl} \] begins and finishes. At the point where methyl orange indicates, both reactions are complete.

Step 2: Understanding Total HCl Required

The volume \( V_1 \) corresponds to the moles of \( \text{HCl} \) needed to convert the entire \( \text{Na}_2\text{CO}_3 \) to \( \text{NaHCO}_3 \). The total \( V_2 \) volume completes both full reactions for \( \text{Na}_2\text{CO}_3 \) to \( \text{CO}_2 \) via \( \text{NaHCO}_3 \).

Step 3: Determining Volume for \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) Alone

The volume of \( \text{HCl} \) needed solely for \( \text{Na}_2\text{CO}_3 \) to convert directly to other products (without involving \( \text{NaHCO}_3 \)) is the difference \( V_2 - V_1 \). This accounts for the moles used in the second step of \( \text{NaHCO}_3 \) to \( \text{CO}_2 \).

Step 4: Conclusion

Hence, the volume of \( \text{HCl} \) needed for the reaction with \( \text{Na}_2\text{CO}_3 \) alone is \( V_2 - V_1 \). Therefore, the answer is option (c).

Key Concepts

Phenolphthalein Indicator

Phenolphthalein is a fascinating and widely used indicator in acid-base titrations. This chemical compound changes color at specific pH levels. It's particularly splendid because it remains colorless in acidic solutions but turns a vibrant pink to deep fuchsia as the solution becomes basic.
Essentially, phenolphthalein is used when we expect the pH to change from slightly acidic to neutral or slightly basic.
During a titration involving sodium carbonate (Na_2CO_3) and hydrochloric acid (HCl), phenolphthalein helps identify the endpoint where Na_2CO_3 has been converted to NaHCO_3.
This transition occurs in a basic environment, where phenolphthalein vividly signals the completion of the first stage of the reaction.

• The color change typically occurs around a pH of 8.2 to 10.
• In the context of our original exercise, phenolphthalein signifies the point where all the Na_2CO_3 has reacted with HCl.
• This change doesn't signal all reactions are complete, only that initial transition from Na_2CO_3 to NaHCO_3.

Methyl Orange Indicator

Unlike phenolphthalein, methyl orange behaves differently in acid-base titrations. This indicator is most useful for stronger acids and is known for its efficient pH sensitivity in the acidic range.
Methyl orange switches from red in acidic solutions to yellow as conditions become neutral or slightly alkaline. This color change occurs in a more acidic pH range, between 3.1 and 4.4, making it ideal for strong acid titrations.
In the specific NaHCO_3 and Na_2CO_3 reactions, methyl orange marks the endpoint where all remaining NaHCO_3 has transformed into carbon dioxide (CO_2) and water (H_2O) completing the second reaction stage.

• Methyl orange ensures that titrations reach full completion by accurately pinpointing the final equivalence point.
• It is essential for correctly calculating the total amount of acid needed for titration.
• In our exercise, methyl orange confirms the consumption of HCl from both reactions of NaHCO_3 to CO_2.

NaHCO3 and Na2CO3 Reactions

The reactions involving NaHCO_3 and Na_2CO_3 are classic examples of how acid-base chemistry operates. Sodium bicarbonate (NaHCO_3), also known as baking soda, and sodium carbonate (Na_2CO_3) are both alkalies reacting with HCl.
The sequence of reactions in a titration is important: - **First Stage:** - Na_2CO_3 + HCl → NaHCO_3 + NaCl - Here, Na_2CO_3, a more basic salt, reacts first to form a less basic product, NaHCO_3.
- **Second Stage:** - NaHCO_3 + HCl → CO_2 + H_2O + NaCl - When all Na_2CO_3 absorbs HCl, NaHCO_3 is subsequently converted fully to CO_2 and water.

• These progressive stages of neutralization require accurate indicators to be detected correctly.
• Understanding each step helps in determining the exact amount of HCl consumed.
• These consecutive reactions illustrate why V_2 is typically greater than V_1 in our titration exercise.

Equivalence Point

The equivalence point in a titration is where the amount of titrant added exactly neutralizes the analyte solution. Every acid-base reaction seeks this balance.
It's different from the endpoint; the endpoint refers to the perceived completion by indicator change, while the equivalence point marks the actual stoichiometric end.
For Na_2CO_3 and HCl titration, both equivalence and endpoint nearly align with phenolphthalein; whereas, with methyl orange, the end-solution is fully composed of the acid's and base's reaction products.

• In our given problem, V_1 indicates the first equivalence point, mostly for Na_2CO_3 with HCl.
• V_2 covers the full titration process including NaHCO_3 conversion.
• The distinction between these points helps in understanding precise titration results.
• Choosing the correct indicator maximizes accuracy of identifying the true equivalence points.