Problem 253 - A Complete Resource Book in Chemistry for JEE Main

Question

Calculate \(\mathrm{pH}\) at which an acid indicator HIn with concentration \(0.1 \mathrm{M}\) changes its colour \(\left(\mathrm{K}_{\mathrm{a}}\right.\) for \(\mathrm{HIn}=\) \(\left.1 \times 10^{-5}\right)\)

Step-by-Step Solution

Answer

The indicator changes color around pH 5, specifically within pH 4 to 6.

Step 1: Understand the Problem

The task is to determine the pH level at which the acid indicator HIn changes its color. For an indicator in the form of HIn, the color changes near its pK_a value.

Step 2: Identify Given Values

We know the concentration of the indicator HIn is 0.1 M and its dissociation constant, \(K_a = 1 \times 10^{-5}\).

Step 3: Calculate pKa

The \(pK_a\) of a substance is calculated by the formula \(pK_a = -\log_{10}(K_a)\). Substitute the given value of \(K_a\):\[pK_a = -\log_{10}(1 \times 10^{-5}) = 5\].

Step 4: Determine the pH Range for Color Change

An indicator changes color around its \(pK_a\) value, which is typically within ±1 of its \(pK_a\), that is between 4 and 6.

Key Concepts

Understanding Acid-Base Indicators

Acid-base indicators are special chemical substances that change color depending on the pH level of their environment. This color change happens because these indicators can exist in different ionic forms, each of which has a distinct color. Essentially, they are weak acids or bases that dissociate in water to give an ion and a neutral molecule, and as this dissociation occurs, the color changes. This makes them useful in experiments to study pH changes in solutions.

- **Role of Indicators**: They help in detecting the end point in titrations. - **Types of Indicators**: Include natural indicators like litmus and synthetic indicators such as phenolphthalein.

Defining Dissociation Constant

The dissociation constant, often represented as \(K_a\) for acids, gives insight into the strength of an acid in solution. It is a crucial value that determines how well an acid dissociates into its constituents in water. For example, in our problem, the dissociation constant of HIn is given as 1 \(\times\) 10^{-5}.

- **Understanding \(K_a\) value**: A lower \(K_a\) implies a weaker acid, which won't dissociate fully in water.- **Interpreting \(K_a\)**: Knowing \(K_a\) helps in predicting the pH range over which an indicator will change color.

Exploring Color Change

The fascinating color change in acid-base indicators is a visible sign of a reaction occurring at a molecular level. This change is usually sudden and noticeable within the indicator's specific range. This is because the molecular structure of an indicator changes in response to the hydrogen ion concentration in the surrounding environment.

- **Observation**: As pH changes, the balance between the differently colored forms of the indicator changes. - **Practical Application**: This property is used in labs to determine unknown pH values simply by observing the color.

Indicator Range Explained

The indicator range is the pH range over which an indicator changes color. This usually spans one pH unit on either side of the indicator's \(pK_a\). For instance, if an indicator's \(pK_a\) is 5, the range would be from 4 to 6.- **Importance**: A successful laboratory titration hinges on choosing the right indicator.- **Choosing the Right Indicator**: It should have a color change range as close as possible to the expected pH of the desired endpoint.

Understanding pKa Determination

The \(pK_a\) is a crucial property of an acid-base indicator that reflects its strength or weakness. It is the negative logarithm of the dissociation constant \(K_a\). In our solution, we calculated the \(pK_a\) of HIn using the formula: \(pK_a = -\log_{10}(K_a)\).

- **Calculation**: If \(K_a\) is known, \(pK_a\) can be easily derived.- **Significance**: It points to the pH level at which equilibrium between the different ionic forms of the indicator is achieved, which is crucial for understanding its behavior.