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) \(\left(\hat{V}_{2}-\mathrm{V}_{1}\right) \mathrm{mL}\) (d) \(\left(\mathrm{V}_{1} / 3\right) \mathrm{mL}\)

Short answer

The answer is (c) \((\hat{V}_{2}-\text{V}_{1})\) mL.

Step-by-step solution

Understanding the Titration Process

In a titration involving  ext{NaHCO}_{3} and  ext{Na}_{2} ext{CO}_{3} with  ext{HCl}, the experiment involves two stages. Phenolphthalein as an indicator is used for the reaction with  ext{Na}_{2} ext{CO}_{3} and turns colorless when it reacts completely with  ext{HCl}. The volume at this point is  ext{V}_{1} mL. When methyl orange is used, it indicates the endpoint of the reaction with both  ext{NaHCO}_{3} and  ext{Na}_{2} ext{CO}_{3}, requiring  ext{V}_{2} mL of  ext{HCl}.

Equations for the Titration Reactions

The first equivalence point with phenolphthalein indicates the completion of  ext{Na}_{2} ext{CO}_{3} reaction:  ext{Na}_{2} ext{CO}_{3} + ext{HCl} ightarrow ext{NaHCO}_{3} + ext{NaCl}. Next, all the remaining carbonate plus bicarbonate react with  ext{HCl} at the methyl orange endpoint:  ext{NaHCO}_{3} + ext{HCl} ightarrow ext{H}_{2} ext{O} + ext{CO}_{2} + ext{NaCl}. The full set of reactions is completed by  ext{V}_{2} mL of  ext{HCl}.

Calculating  ext{HCl} for  ext{Na}_{2} ext{CO}_{3}

The amount of  ext{HCl} used for both reactions is  ext{V}_{2}. The difference ( ext{V}_{2} - ext{V}_{1}) represents the  ext{HCl} used only for the conversion of  ext{NaHCO}_{3} to  ext{H}_{2} ext{O} and  ext{CO}_{2}. Therefore, the volume of  ext{HCl} for  ext{Na}_{2} ext{CO}_{3} reaction alone is the initial phenolphthalein value:  ext{V}_{1} mL.

Key concepts

Phenolphthalein Indicator

Phenolphthalein is a common acid-base indicator used in titrations to determine the equivalence point of a reaction. In acid-base titration, phenolphthalein is particularly useful because it changes color within a specific pH range, providing a clear visual cue when a reaction has reached its endpoint. This is crucial for accurately measuring the amount of titrant needed to completely react with the analyte.

Phenolphthalein is insoluble in water but becomes soluble in alcohol-based solutions, making it ideal for titrations where the endpoint involves a sharp change in pH. In basic solutions, it exhibits a pink hue, but as the solution becomes more acidic, phenolphthalein turns colorless at a pH less than 8.2.

This characteristic transformation aids in detecting when all carbonate in a sodium bicarbonate and carbonate mixture has reacted with hydrochloric acid (HCl). The point at which phenolphthalein turns colorless indicates the completion of the conversion of sodium carbonate (\(\mathrm{Na}_2\mathrm{CO}_3\)) to sodium bicarbonate (\(\mathrm{NaHCO}_3\)), allowing for precision in titration readings.

• In titration with phenolphthalein, always add the indicator before the titration process begins.
• Monitor the solution color change carefully to conclude at the right moment.

Methyl Orange Indicator

Methyl orange is another acid-base indicator used in titration. However, unlike phenolphthalein, methyl orange works effectively over a lower pH range. It is beneficial for reactions that occur in more acidic environments, displaying a distinct color change from yellow to red.

This indicator is sensitive to pH changes from 3.1 to 4.4 and is perfect for titrations involving strong acids. Methyl orange displays a clear transition which makes it easy to observe when the reaction has reached the essential endpoint involving both bicarbonate and carbonate in a sample.

Upon completion of the reaction between hydrochloric acid (HCl) and both \(\mathrm{NaHCO}_3\) and \(\mathrm{Na}_2\mathrm{CO}_3\), methyl orange will change color as the last bit of \(\mathrm{NaHCO}_3\) converts completely into \(\mathrm{CO}_2\) and \(\mathrm{H}_2\mathrm{O}\). The volume of HCl at this endpoint is noted as \(V_2\) mL, which combined with the phenolphthalein reading, helps in deducing the overall reaction dynamics.

• Methyl orange is a more suitable choice for titrations requiring observation in acidic environments.
• It is crucial to recognize the exact color transition to ensure precise measurements.

Sodium Bicarbonate and Carbonate Mixture

The mixture of sodium bicarbonate (\(\mathrm{NaHCO}_3\)) and sodium carbonate (\(\mathrm{Na}_2\mathrm{CO}_3\)) in a solution can be analyzed through acid titration to understand the individual reactions and consumption of reactants. In this context, the solution undergoes two main reactions during titration with hydrochloric acid (HCl).

The first reaction involves \(\mathrm{Na}_2\mathrm{CO}_3\) with HCl in the presence of phenolphthalein as an indicator. This reaction transforms \(\mathrm{Na}_2\mathrm{CO}_3\) into \(\mathrm{NaHCO}_3\). The phenolphthalein indicator changes from pink to colorless, marking the endpoint of this stage and denoting the volume \(V_1\) mL of HCl used for this reaction.

As titration continues using methyl orange as an indicator, the \(\mathrm{NaHCO}_3\) present reacts with HCl, forming \(\mathrm{CO}_2\), \(\mathrm{H}_2\mathrm{O}\), and \(\mathrm{NaCl}\). The methyl orange indicator shifts its color, highlighting that all bicarbonate and carbonate have been fully reacted. The total volume \(V_2\) mL signifies the point at which all reactions within the mixture are complete.

• The difference \((\mathrm{V}_2 - \mathrm{V}_1)\) indicates the volume of HCl used solely for converting \(\mathrm{NaHCO}_3\) in the second reaction.
• Understanding these transitions helps in calculating the quantities of each substance in the original mixture based on the titrations.