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 [2015] (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, which corresponds to (a) 18 mg.

Step 1: Calculate Initial Moles of Acetic Acid

First, we will calculate the initial moles of acetic acid in the solution before adsorption. We start with the formula for normality:\[ N = \frac{moles}{volume (L)} \]Given initial normality of the solution is \(0.06 \mathrm{~N}\) and the volume of the solution is \(50 \mathrm{~mL}\) or \(0.050 \mathrm{~L}\):\[ 0.06 = \frac{moles}{0.050} \]Thus, moles of acetic acid = \(0.06 \times 0.050 = 0.003 \) moles.

Step 2: Calculate Moles of Acetic Acid After Filtration

Next, we calculate the moles of acetic acid in the solution after the filtration. The new normality is given as \(0.042 \mathrm{~N}\), using the same formula:\[ 0.042 = \frac{moles'}{0.050} \]So, moles of acetic acid remaining after adsorption = \(0.042 \times 0.050 = 0.0021 \) moles.

Step 3: Calculate Moles of Acetic Acid Adsorbed

Now, we determine the moles of acetic acid adsorbed by subtracting the moles of acetic acid after filtration from the initial moles:\[ moles_{adsorbed} = 0.003 - 0.0021 = 0.0009 \, ext{moles} \]

Step 4: Convert Moles to Milligrams of Acetic Acid Adsorbed

The molecular weight of acetic acid is \(60 \, \text{g/mol}\). To find the mass of acetic acid adsorbed, convert moles to grams and then to milligrams:\[ ext{grams} = 0.0009 \, ext{moles} \times 60 \, \text{g/mol} = 0.054 \, \text{g} \]\[ ext{milligrams} = 0.054 \, ext{g} \times 1000 = 54 \, ext{mg} \]

Step 5: Calculate Mass Adsorbed per Gram of Charcoal

Since the total adsorption was over \(3 \, \text{g}\) of charcoal, the amount adsorbed per gram is:\[ ext{mg/g} = \frac{54 \, ext{mg}}{3 \, ext{g}} = 18 \, ext{mg/g} \]

Key Concepts

Acetic Acid

Acetic acid is a simple organic compound with the formula \( \text{CH}_3\text{COOH} \). It is a colorless liquid with a distinctive sour smell and taste, widely known as the main component of vinegar. In chemistry, acetic acid is used in various applications, including as a polar protic solvent. Its ability to react with bases makes it an essential reagent in chemical syntheses.

Properties of acetic acid include:

• Boiling point: Approximately \(118 \degree C\)
• Molecular weight: \(60.05 \text{g/mol}\)
• Weak acid: It only partially dissociates in water.

In laboratory and industrial settings, understanding the behavior of acetic acid in various solutions is crucial. For instance, its adsorption on activated charcoal can help purify acetic acid-containing solutions by removing impurities through the charcoal's porous structure.

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 material is extensively used in water purification, air filters, and chemical purification.

Key characteristics of activated charcoal include:

• High surface area: Effective for adsorption processes.
• Porous structure: Contains numerous microscopic holes.
• Usable in filtering impurities, including colored substances and odors.

When used in chemical reactions, activated charcoal adsorbs impurities by trapping molecules in its intricate network of pores. This process is reversible, meaning the adsorbed substances can often be desorbed under certain conditions, making activated charcoal a powerful tool in laboratories and industries.

Normality

Normality is a measure of concentration equivalent to the molarity of a reactive species in a solution. It specifically considers the reactive capacity of a solute in a reaction. For example, in acid-base reactions, normality takes into account the number of hydrogen ions (\( \text{H}^+ \)) that one mole of an acid can donate.

Key points about normality:

• Formula: \( N = \frac{\text{equivalents}}{\text{volume of solution in liters}} \)
• Dependent on the type of chemical reaction being observed.
• Utilized for titration and other chemical quantifications.

Understanding normality is essential in various chemistry applications, especially when calculating reactive species involved in the reaction. In our exercise, the normality of acetic acid before and after adsorption provides insight into how much acid was adsorbed onto activated charcoal.

Moles Calculation

Moles calculation is a fundamental technique in chemistry used to determine the amount of a substance in terms of its basic unit, the mole. This concept is pivotal for converting between mass, volume, and number of particles. The mole concept allows chemists to relate easily measurable quantities like mass and volume to the number of molecules or atoms present in a material.

In our exercise, finding the moles of acetic acid involved these steps:

• Initial moles: Calculated using the initial normality and volume of the acetic acid solution.
• Moles after adsorption: Determined from the new normality after the reaction with activated charcoal.
• Moles adsorbed: The difference between initial moles and post-reaction moles.

Such calculations enable accurate quantification of chemical reactions, offering insights into the stoichiometry of reactants and products in reaction mixtures.