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

(a) 18 mg

Step 1: Initial Moles of Acetic Acid

First, we need to calculate the initial moles of acetic acid present in the solution. The normality (0.06 ext{ N}) is equivalent to the molarity for monoprotic acids like acetic acid. Using the formula:\[ ext{moles} = ext{Normality} imes ext{Volume in L} \]So,\[ ext{moles of acetic acid} = 0.06 ext{ N} imes 0.050 ext{ L} = 0.003 ext{ moles} \]

Step 2: Moles of Acetic Acid in Filtrate

Next, calculate the moles of acetic acid remaining in the filtrate after adsorption. The strength of the filtrate is given as 0.042 ext{ N}. Thus:\[ ext{moles of acetic acid in filtrate} = 0.042 ext{ N} imes 0.050 ext{ L} = 0.0021 ext{ moles} \]

Step 3: Moles of Acetic Acid Adsorbed

Find the moles of acetic acid adsorbed by subtracting the moles of acetic acid in the filtrate from the initial moles:\[ ext{moles adsorbed} = 0.003 ext{ moles} - 0.0021 ext{ moles} = 0.0009 ext{ moles} \]

Step 4: Convert Moles to Mass

Convert the moles of acetic acid adsorbed to mass. The molar mass of acetic acid (CH_3COOH) is approximately 60 ext{ g/mol}.\[ ext{mass of acetic acid adsorbed} = 0.0009 ext{ moles} imes 60 ext{ g/mol} = 0.054 ext{ g} = 54 ext{ mg} \]

Step 5: Mass Adsorbed per Gram of Charcoal

Since 3 ext{ g} of charcoal was used, calculate the amount of acetic acid adsorbed per gram of charcoal:\[ ext{mass adsorbed per gram} = \frac{54 ext{ mg}}{3 ext{ g}} = 18 ext{ mg/g}\]

Key Concepts

Acetic Acid

Acetic acid is a simple organic compound often recognized by its chemical formula, \( \text{CH}_3\text{COOH} \). It is a key ingredient in vinegar and is best known for its tangy taste and pungent smell. In chemistry, acetic acid is classified as a weak monoprotic acid, meaning it can donate one proton or hydrogen ion (\( \text{H}^+ \)) per molecule. This characteristic is crucial in dictating how it behaves in aqueous solutions. When mixed with water, acetic acid partially dissociates to form acetate ions and hydrogen ions. This partial dissociation is important for calculations involving normality and molarity, two concepts often used to express the concentration of a solution.

Activated Charcoal

Activated charcoal is a form of carbon processed to have tiny, low-volume pores that increase its surface area available for adsorption. This high surface area makes it incredibly effective at trapping and holding molecules, ions, or particles on its surface. Because of this property, it is often used in various filtration processes, including water purification and detoxification products. In the exercise, activated charcoal is used to adsorb acetic acid from the solution. The efficiency of such adsorption processes depends on factors like the surface area of the charcoal, the temperature, and the concentration of the compound being adsorbed.

Molar Mass Calculation

Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). To find the molar mass of acetic acid, calculate the sum of the atomic masses of all atoms in a molecule of \( \text{CH}_3\text{COOH} \). Using the periodic table:

• Carbon (C): 12.01 g/mol, and there are two carbons.
• Hydrogen (H): 1.01 g/mol, and there are four hydrogens.
• Oxygen (O): 16.00 g/mol, and there are two oxygens.

So, the molar mass is \((2 \times 12.01) + (4 \times 1.01) + (2 \times 16.00) = 60.05 \text{ g/mol}\). This calculation is crucial when converting from moles to mass and vice versa, as seen in the step-by-step solution.

Normality and Molarity

Normality and molarity are two ways to express the concentration of a solution. Molarity is defined as the number of moles of a solute per liter of solution, typically expressed as mol/L. Normality, on the other hand, is the measure of concentration equivalent to the molar concentration divided by an equivalence factor. For acids like acetic acid, which is monoprotic, its normality is the same as its molarity because it donates one proton per molecule. When you know the normality of a solution, you can use it to determine the number of moles present by multiplying by the volume in liters (\[\text{moles} = \text{Normality} \times \text{Volume in L} \]). This equivalence simplifies calculations in reactions involving acid-base titrations.

Filtration Process

Filtration is a common mechanical or physical process used to separate solids from liquids or gases. It involves passing a mixture through a medium that allows the fluid (liquid or gas) to pass while retaining the solid particles. In the context of this exercise, after the activated charcoal has adsorbed acetic acid from the solution, the mixture was filtered. The purpose of this step was to remove the charcoal and any acetic acid it had adsorbed, leaving behind a filtrate with a reduced concentration of acetic acid. The effectiveness of a filtration process can be influenced by the size of the pores in the filter medium and the nature of the substances being separated. This is a critical step in ensuring that the separation process removes the desired components effectively.