Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is used as the indicator in the \(\mathrm{Fe}^{2 \oplus}-\) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2 \oplus}\) titration in acidic medium. The end point of the titration can be noted (a) By the appearance of colour of the titrated solution with the indicator (b) By the appearance of a transient blue colour after the end point (c) By failure of the indicator to give a colour with the titrated solution (d) By a sudden change of colour from deep blue to intense green at the end point.

Step-by-Step Solution

Answer

The endpoint is noted by the failure of the indicator to give a colour with the titrated solution (choice c).

Step 1: Understanding the Problem

We need to determine how the endpoint of the titration between \[ \mathrm{Fe}^{2+} \] and \[ \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \] in the presence of \[ \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \] as an indicator is observed. The endpoint refers to the point during a titration at which there is a noticeable change that signifies the completion of the reaction.

Step 2: Analyze Indicator Behavior

\[ \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \] is known to form a Prussian blue color when it reacts with \[ \mathrm{Fe}^{2+} \]. In a titration setup, the indicator shows the endpoint by either a color change or disappearance according to its interaction mechanics during the reaction.

Step 3: Identify the Endpoint Signal

In the context of this titration, the endpoint is reached when all \( \mathrm{Fe}^{2+} \) ions have reacted with \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) ions, meaning no free \( \mathrm{Fe}^{2+} \) are present to react with the indicator. Therefore, the indicator will fail to develop a blue color, giving us a signal for endpoint detection.

Step 4: Conclude the Observation

Since no \( \mathrm{Fe}^{2+} \) remains to form Prussian blue, the indication of endpoint being reached is the lack of any color formation with the indicator, which corresponds to choice (c): 'By failure of the indicator to give a colour with the titrated solution.'

Key Concepts

Endpoint Detection

Endpoint detection in a redox titration is a crucial step that indicates when the reaction between the analyte and the titrant is complete. In simpler terms, it is the moment when the exact amount of titrant has been added to completely react with the analyte present in the solution. One needs to be very precise in noticing this point, as it determines the accuracy of the titration results.
Often, the endpoint is marked by some observable physical changes within the solution, such as a color shift or the formation of a precipitate. These changes are typically caused by the interaction of the titrant with a carefully chosen chemical indicator. For the successful detection of an endpoint, the indicator used must provide a noticeable signal that accurately corresponds to the completion of the reaction.
In the case of the titration between \( \mathrm{Fe}^{2+} \) and \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) in acidic medium, the endpoint is detected when the indicator fails to produce a blue color. This happens because all the \( \mathrm{Fe}^{2+} \) ions have been oxidized by \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \), leaving none to react with the indicator \( \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \). Once this is observed, the endpoint has been reached.

Chemical Indicators

In the context of titrations, a chemical indicator signals the endpoint of a titration by undergoing a distinct color change. Selecting the appropriate indicator is vital for ensuring the accuracy of the titration results. Typically, the choice of indicator depends on the specific titration reaction and the expected reaction conditions, such as pH levels and types of chemicals involved.
For the \( \mathrm{Fe}^{2+} \) and \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) reaction, \( \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \) acts as the indicator by producing a characteristic blue color (known as Prussian blue) in the presence of \( \mathrm{Fe}^{2+} \). This color forms only when unused \( \mathrm{Fe}^{2+} \) ions are available, as they interact with the indicator and create a complex.
Therefore, when the endpoint is reached and there are no \( \mathrm{Fe}^{2+} \) ions left to interact with the indicator, it results in the absence of any color change, signifying the completion of the titration. Choosing effective indicators like \( \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \) helps in clearly identifying the endpoint without ambiguity, ensuring the precision of the titration process.

Color Change in Titrations

Color change in titrations is among the most intuitive methods for observing the endpoint of a chemical reaction. The change is usually the result of a reaction between the titrant or the analyte with the indicator, leading to a distinct change in color that signals reaction completion.
For the titration involving \( \mathrm{Fe}^{2+} \) and \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \), the indicator \( \mathrm{K}_{3}[\mathrm{Fe}(\mathrm{CN})_{6}] \) provides a clear signal through color change. When \( \mathrm{Fe}^{2+} \) is entirely oxidized by \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \), no Prussian blue is formed, thus the absence of color signals the endpoint. This is a helpful feature because it provides an unambiguous cue that the reaction is complete.
Understanding the mechanism of color change not only helps in accurate endpoint detection but also ensures that the titration provides reliable results. It allows chemists to visually verify that the correct stoichiometric amounts have reacted, reducing errors during the titration process.