Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

The molecular formula of potash alum is (a) \(\mathrm{K}_{2} \mathrm{Al}_{2} \mathrm{~S}_{2} \mathrm{H}_{43} \mathrm{O}_{39}\) (b) \(\mathrm{KAl}_{2} \mathrm{~S}_{2} \mathrm{H}_{48} \mathrm{O}_{40}\) (c) \(\mathrm{K}_{2} \mathrm{AlS}_{2} \mathrm{H}_{43} \mathrm{O}_{40}\) (d) \(\mathrm{K}_{2} \mathrm{Al}_{2} \mathrm{~S}_{2} \mathrm{H}_{48} \mathrm{O}_{40}\)

Step-by-Step Solution

Answer

The molecular formula of potash alum is option (d): \(\mathrm{K}_2\mathrm{Al}_2\mathrm{S}_2\mathrm{H}_{48}\mathrm{O}_{40}\).

Step 1: Identify the Composition

Potash alum is a double sulfate of potassium and aluminum. Its composition includes potassium (K), aluminum (Al), sulfate (SO₄), and water of crystallization.

Step 2: Determine Known Molecular Formula

The accepted molecular formula for potash alum is \([\text{K}_2\text{SO}_4 \cdot \text{Al}_2(SO_4)_3 \cdot 24\text{H}_2\text{O}]\). This indicates that there are two K, two Al, four S, and 48 hydrogen atoms from water, totaling 24 water molecules.

Step 3: Analyze the Options

Review each option to see if it matches the formula derived in the previous step: - Option (a): K2 Alࢸ2 Sₜ2 H₁43 O₃9 - Option (b): KAlۣ2 S₂ HF48 O₀0 - Option (c): Kۣ2 AlS₂ H⟳43 O⠇40 - Option (d): Kۣ2 Alۣ2 S₂ H⠊48 O₀0.

Step 4: Select the Correct Formula

Compare the options with the known formula. Option (d) \[\text{K}_2\text{Al}_2\text{SO}_4\text{S}_2\text{H}_{48}\text{O}_{40}\] correctly represents potash alum: \[\text{K}_2\text{Al}_2(SO_4)_3\cdot 24\text{H}_2\text{O}.\]

Key Concepts

Molecular Formula

Potash alum, a widely used compound, has a precise molecular formula that reflects its unique chemical structure and properties. The correct molecular formula for potash alum is

• \( ext{K}_2 ext{SO}_4 \)
• \( ext{Al}_2(SO_4)_3\)
• \(24 ext{H}_2 ext{O}\)

This formula indicates it is composed of potassium sulfate and aluminum sulfate, further united with water molecules (water of crystallization).

Each component of the molecular formula plays a key role in the structure:

• Two potassium ions (\( ext{K}^+\)) contribute to the overall charge balance.
• The \( ext{Al}_2(SO_4)_3\) part indicates two aluminum ions (\( ext{Al}^{3+}\)) combined with three sulfate ions (\( ext{SO}_4^{2-}\)).
• Water molecules (24 \( ext{H}_2 ext{O}\)) are involved as water of crystallization, stabilizing the solid structure.

Double Sulfate

Potash alum belongs to the class of compounds known as double sulfates. These compounds contain two different cations combined with sulfate anions. In the case of potash alum, the cations are potassium (\( ext{K}^+ \)) and aluminum (\( ext{Al}^{3+} \)) ions.

Double sulfates are characterized by having the general formula

• \( ext{M'}_2 ext{SO}_4 ext{ · M''}_2( ext{SO}_4)_3\), where
• \( ext{M}' \) and \( ext{M}'' \) are different cationic elements.

In potash alum, \( ext{M}' \) is potassium and \( ext{M}'' \) is aluminum.

Double sulfates reinforce the material's crystalline structure, which is critical for its formation and applications, especially in the purification and refining processes or as a mordant in dyeing.

Crystallization Water

Water of crystallization is an integral part of the potash alum's structure, as seen in its formula

• \(24 ext{H}_2 ext{O}\).

These water molecules are trapped within the crystal lattice during the crystallization process.

Crystallization water:

• Helps maintain the compound's solid form.
• Aids in stabilizing the crystal structure by hydrogen bonding with sulfate ions.

Each water molecule within the crystal is held relatively loosely compared to water in liquid form, and can be released by heating.

This feature is particularly useful in experiments that require a pure solid compound since it can be easily weighed and heated without decomposing.

Chemical Composition

Understanding the chemical composition of potash alum involves knowing the types and quantities of ions present. Potash alum's composition is expressed through its empirical formula, along with the knowledge of its constituent ions.

The major components of potash alum are:

• ## Potassium Ions\( ext{K}^+\): Essential for balancing the negative charges from sulfate anions.
• ## Aluminum Ions\( ext{Al}^{3+}\): Crucial for the formation of the aluminum sulfate complex.
• ## Sulfate Ions\( ext{SO}_4^{2-}\): Acts as the anionic framework joining the cations together.
• ## Water of CrystallizationWater molecules that stabilize the whole compound.

In application contexts, the chemical composition of potash alum not only influences its structural integrity but also its solubility, reactivity, and practical uses in various industries.