Problem 109 - General Chemistry: Principles and Modern Applications

Question

If an indicator is to be used in an acid-base titration having an equivalence point in the pH range 8 to 10 , the indicator must (a) be a weak base; (b) have \(K_{\mathrm{a}}=1 \times 10^{-9} ;(\mathrm{c})\) ionize in two steps; (d) be added to the solution only after the solution has become alkaline.

Step-by-Step Solution

Answer

The characteristic for the indicator that should be correct is (d): The indicator should be added to the solution only after it has become alkaline.

Step 1: Analyze the Possible Characteristics

Identify each statement and analyze whether this relates to the features of an indicator suitable for a titration with the equivalence point in the pH range 8 to 10. It's important to consider the nature of acid-base reaction and the properties of weak base, ionization steps, and the process of titration.

Step 2: Analyze Statement (a)

The statement 'indicator must be a weak base' does not necessarily have to be true. Indicators can be either weak acids or weak bases. Therefore, (a) is not a required characteristic.

Step 3: Analyze Statement (b)

The statement 'indicator must have \(K_a = 1 \times 10^{-9}\)' is not mandatory. Acidic or basic indicators can have various \(K_a\) values, which do not need to match with the pH range of the titration.

Step 4: Analyze Statement (c)

The statement 'indicator must ionize in two steps' is not necessary. The most commonly used indicators usually ionize in one step. Therefore, (c) is not a required characteristic.

Step 5: Analyze Statement (d)

The statement 'indicator must be added to the solution only after the solution has become alkaline' is correct. In this case, where the equivalence point is in a basic (or alkaline) pH range (8-10), adding the indicator after the solution has become basic ensures an accurate color change during titration.

Key Concepts

Equivalence Point pH Range

Understanding the equivalence point pH range is critical in acid-base titrations. The equivalence point is the juncture in the titration process where the amount of acid equals the amount of base in solution, meaning the solution is neutralized. For a titration with an equivalence point in the pH range of 8 to 10, we're dealing with a weak acid reacting with a strong base. The resulting pH is higher than 7 due to the basic nature of the salt formed in the reaction.

Selection of an appropriate indicator for this pH range is essential. The indicator must show a distinct color change within this alkaline pH range. It should have a pKa close to the pH at the equivalence point, so its color change aligns correctly with the neutralization point of the titration.

Acid-Base Indicator Properties

Indicators are substances that display different colors depending on the pH of the solution they are in. Acid-base indicators have specific properties that define their behavior and suitability in titrations.

• Indicators are either weak acids or weak bases themselves.
• They undergo ionization, which is where the color change comes from.
• The point of color change, known as the endpoint, is defined by the indicator's pKa or pKb values and the solution pH.
• An ideal indicator changes color sharply and distinctly at its endpoint.

An indicator doesn't have to be a weak base or ionize in two steps. Its Ka can be any value, as long as the pH of its color change matches the pH range of the equivalence point for the given titration.

Titration Process

The titration process is a technique used to determine the concentration of a solution by reacting it with a standard solution of known concentration. A typical acid-base titration involves the following steps:

• Preparing the analyte solution and placing it into a titration flask.
• Adding a few drops of the chosen indicator to the analyte solution.
• Gradually adding the titrant from a burette to the analyte while swirling until the endpoint is reached, indicated by a permanent color change.

Throughout the titration, the pH changes gradually until it jumps sharply at the equivalence point. It's here, with the correct indicator, that the color change becomes evident, signaling the end of the titration.

Indicator Ionization

Indicator ionization is a nuanced concept crucial for understanding the color change during titration. Indicators ionize, meaning they can lose or gain hydrogen ions (protons), which causes them to change their structure and as a consequence, their color.

For example, a weak acid indicator, in its non-ionized form, shows one color, while its ionized form shows a different color. As the pH of the solution changes, the equilibrium between the ionized and non-ionized forms of the indicator shifts, leading to the visible color change. Hence, selecting an indicator with a pKa close to the solution's equivalence point pH ensures the indicator's color change will occur right at the equivalence point of the titration.