Question

Soda-water is made by saturating \(\mathrm{H}_{2} \mathrm{O}\) with \(\mathrm{CO}_{2}\). If one titrates soda-water with alkali using phenolphthalein as indicator, one obtains a fading end-point. What does this suggest?

Short answer

The fading endpoint suggests the presence of a reversible reaction where \(\mathrm{CO}_2\) forms carbonic acid, which dissociates and reforms, affecting the phenolphthalein color change.

Step-by-step solution

Understanding the Setup

We are considering a solution of soda-water, which is essentially water saturated with carbon dioxide (\(\mathrm{CO}_2\)). This setup involves an acidic component due to the presence of \(\mathrm{CO}_2\) in water.

Chemical Reaction Insight

When \(\mathrm{CO}_2\) is dissolved in water, it forms carbonic acid (\(\mathrm{H}_2\mathrm{CO}_3\)) via the reaction: \(\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{H}_2\mathrm{CO}_3\). Carbonic acid is a weak acid, which can dissociate to release \(\mathrm{H}^+\) ions in water.

Role of Indicator

Phenolphthalein is used as an indicator in titrations and changes color in the pH range of about 8.2 to 10. It shifts from colorless in acidic solutions to pink in basic solutions.

Titration with Alkali

During titration, an alkali (base) is added to neutralize the acid present in soda-water. As the base neutralizes the \(\mathrm{H}^+\) ions, the pH increases from acidic towards basic levels, prompting the phenolphthalein to change color.

Fading Endpoint Explanation

The endpoint fades because carbonic acid (which forms from \(\mathrm{CO}_2\) and water) is a weak, equilibrium-limited acid. After reaching the endpoint, any additional \(\mathrm{CO}_2\) dissolved in the solution can re-establish equilibrium, causing more \(\mathrm{H}_2\mathrm{CO}_3\) to form, thus lowering the pH once again and causing the indicator to revert to its colorless state.

Key concepts

Carbonic Acid

Carbonic acid is a simple molecule formed when carbon dioxide \(\mathrm{CO}_2\) dissolves in water. The reaction is described as: \[ \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{H}_2\mathrm{CO}_3 \] Carbonic acid is quite weak because it partially disassociates into hydrogen ions \(\mathrm{H}^+\) and bicarbonate ions \(\mathrm{HCO}_3^-\). This reversible reaction means carbonic acid doesn't fully release all its hydrogen ions.
This characteristic makes it an essential component in various equilibrium-related reactions in the body and environment.
When involved in reactions, carbonic acid can make solutions slightly acidic. This is crucial in the context of neutralization reactions such as in an acid-base titration.

Phenolphthalein Indicator

Phenolphthalein is a popular acid-base indicator used mostly in titrations.

• Its color changes in a pH range of 8.2 to 10, transitioning from colorless in acidic environments to pink in basic ones.
• Since phenolphthalein only shows a visible color change at a higher pH, it is ideal for detecting when a solution transitions from slightly acidic to basic.

In a titration like the one described with soda-water, the indicator is indispensable for visually marking the endpoint.
Watching the color change helps chemists judge when the titration has achieved the desired state.
However, in weakly acidic environments such as with carbonic acid, the change might not be stable.

Titration Endpoint

The titration endpoint is a critical moment in titration experiments. It’s when the amount of titrant added is stoichiometrically equivalent to the quantity of the substance being titrated.
In the case of soda-water titrated with an alkali, the endpoint indicates when the carbonic acid has been neutralized by the base.

• For weak acids like carbonic acid, reaching the endpoint can be particularly elusive.
• Since phenolphthalein indicates in a basic range, achieving a stable endpoint with weak acids is tricky. Signs include a temporary pink color that fades when further conversions of carbonic acid occur.

This momentary endpoint can be confusing, showing how careful one needs to be with weak acid titrations.

Equilibrium Chemistry

Equilibrium chemistry involves reactions that can proceed in both directions, creating a balance or equilibrium between reactants and products. For carbonic acid, the reaction \[ \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{H}_2\mathrm{CO}_3 \] is a prime example.

• This equilibrium can shift towards either reactants or products based on conditions such as pH or concentrations.
• In soda-water, when \(\mathrm{H}_2\mathrm{CO}_3\) forms, it lightly acidifies the solution until equilibrium is reached.

The re-establishment of equilibrium explains why, after a titration endpoint is perceived, the solution might revert changes.
This shifting background dynamic is why understanding equilibrium is key—especially for grasping titrations involving weak acids like carbonic acid.