Problem 196 - A Complete Resource Book in Chemistry for JEE Main

Question

\(3 \mathrm{~g}\) of activated charcoal was added to \(50 \mathrm{~mL}\) of acetic acid solution \((0.06 \mathrm{~N})\) in a flask. After an hou it was filtered and the strength of the filtrate was found to be \(0.042 \mathrm{~N}\). The amount of acetic acid adsorbed (per gram of charcoal) is (a) \(18 \mathrm{mg}\) (b) \(36 \mathrm{mg}\) (c) \(42 \mathrm{mg}\) (d) \(54 \mathrm{mg}\)

Step-by-Step Solution

Answer

The amount of acetic acid adsorbed per gram of charcoal is 18 mg.

Step 1: Determine the Initial Amount of Acetic Acid

First, we will calculate the number of equivalents of acetic acid initially present in the solution. The concentration of the solution is given as \(0.06 \mathrm{~N}\) and the volume of the solution is \(50 \mathrm{~mL}\) or \(0.05 \mathrm{~L}\). The normality equation \(N \times V = \,\text{equivalents}\) is used here: \(0.06 \mathrm{~eq/L} \times 0.05 \mathrm{~L} = 0.003 \mathrm{~equivalents}\).

Step 2: Calculate the Remaining Acetic Acid in the Filtrate

After filtration, the strength of the acetic acid solution is \(0.042 \mathrm{~N}\). The number of equivalents remaining is \(0.042 \mathrm{~eq/L} \times 0.05 \mathrm{~L} = 0.0021 \mathrm{~equivalents}\).

Step 3: Find the Amount of Acetic Acid Adsorbed

Subtract the equivalents of acetic acid in the filtrate from the initial amount to find the adsorbed acetic acid: \(0.003 \mathrm{~equivalents} - 0.0021 \mathrm{~equivalents} = 0.0009 \mathrm{~equivalents}\).

Step 4: Convert Equivalents to Milligrams

To convert equivalents of acetic acid to mass, note that each equivalent of acetic acid corresponds to its molar mass: \(60 \mathrm{~g/mol}\), and considering acetic acid is a monoprotic acid, \(1 \mathrm{~eq} = 60 \mathrm{~g/eq}\). Calculate the mass adsorbed: \(0.0009 \mathrm{~equivalents} \times 60 \mathrm{~g/eq} = 0.054 \mathrm{~g} = 54 \mathrm{~mg}\). This is the total mass adsorbed by 3 g of charcoal.

Step 5: Calculate the Amount Adsorbed per Gram of Charcoal

Finally, to find the amount of acetic acid adsorbed per gram of charcoal, divide the total adsorbed mass by the mass of the charcoal: \(\frac{54 \mathrm{~mg}}{3 \mathrm{~g}} = 18 \mathrm{~mg/g}\).

Key Concepts

Acetic Acid

Acetic acid is a simple carboxylic acid with the formula \( \text{CH}_3\text{COOH} \). It is a colorless liquid with a strong, distinctive smell, commonly recognized as vinegar when diluted.
Acetic acid is a monoprotic acid, meaning it can donate only one proton (\(\text{H}^+\)) per molecule in an aqueous solution.
This characteristic is essential in chemistry for various calculation purposes, such as determining the normality, which directly affects the number of equivalents in any reaction involving acetic acid.

• Used extensively in the production of synthetic fibers and fabrics.
• Serves as an intermediary in the chemical synthesis of various compounds.
• Acts as a solvent and a food preservative, enhancing the taste and shelf life of food.

Acetic acid's reactivity and properties make it a vital chemical both in industrial and household applications.

Activated Charcoal

Activated charcoal, also known as activated carbon, is a form of carbon processed to have small, low-volume pores that increase the surface area available for adsorption.
This high degree of microporosity makes it extremely effective for trapping chemicals and impurities, making it widely used for purification purposes.

• In applications such as water purification, air filters, and medical treatment for overdoses and poisonings.
• Each gram of activated charcoal has a surface area exceeding 500 \(\text{m}^2\), making it highly efficient in adsorbing contaminants.
• It works through adsorption, where adsorption refers to substances sticking to the surface rather than absorbing within.

Activated charcoal's effectiveness in adsorbing acetic acid, as explored in the exercise, showcases its role in various analytical and industrial processes.

Equivalents in Chemistry

In chemistry, the concept of equivalents allows chemists to simplify the stoichiometry of reactions, particularly when dealing with acids, bases, and redox reactions.
An equivalent is the amount of a substance reacting with or supplying one mole of active species, like protons for acids or electrons for redox reactions.
This makes calculations involving chemical reactions more straightforward as it equates different species on the same scale.

• For monoprotic acids like acetic acid, one mole provides one equivalent of hydrogen ions.
• Equivalents help in understanding and conducting titrations effectively, ensuring precise results.
• In this exercise, equivalents were vital in calculating the precise amount of acetic acid adsorbed on the activated charcoal.

Understanding equivalents is crucial for accurate chemical analysis and laboratory practices.

Normality Calculations

Normality is a measure of concentration equivalent to the gram equivalent of solute per liter of solution. It is particularly useful for reactions involving acids and bases because it directly relates to the number of reactive species in a solution.
Normality simplifies calculations like the one in this exercise, where the amount of acetic acid adsorbed by activated charcoal was calculated based on its normality.

• Normality (\(N\)) is calculated as \(N = \frac{\text{equivalents of solute}}{\text{volume of solution in liters}}\).
• It is beneficial in titration calculations, allowing for the determination of concentration after neutralization.
• Reaction stoichiometry is often expressed in terms of normality to maintain the balance of equivalents throughout a chemical process.

Understanding normality helps in accurately measuring and reacting chemical substances without the need for conversions between moles and equivalents, facilitating smoother chemical calculations.