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

Question

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

Step-by-Step Solution

Answer

The correct molecular formula of potash alum is (d) \(\mathrm{K}_{2}\mathrm{Al}_{2}\mathrm{~S}_{2}\mathrm{H}_{48}\mathrm{O}_{40}\).

Step 1: Understanding Potash Alum

Potash alum is a specific double sulfate salt. It is structurally represented by the general formula of alums, which is \\[ ext{M}^+ ext{M'}^{3+}( ext{SO}_4)_2 imes 12 ext{H}_2 ext{O} \]. \In potash alum (potassium alum), M is potassium (K) and M' is aluminum (Al). This will help in figuring out the molecular formula.

Step 2: Constructing the Molecular Formula

Using the alum formula, where M is K and M' is Al, the molecular formula for potash alum is built as follows: \\[ ext{KAl(SO}_4)_2 imes 12 ext{H}_2 ext{O} \]. \Breaking it down, we have: \a. 2 potassium ions (K), one for each potassium sulfate molecule. \b. 2 aluminum ions (Al), one for each aluminum sulfate molecule. \c. 2 sulfate ions (SO}_4), ensuring the 12 total water molecules remain attached as water of crystallization.

Step 3: Detailed Analysis of Each Option

Examine each given option against the constructed formula above: \a. Option (a) \\( ext{K}_2 ext{Al}_2 ext{S}_2 ext{H}_{48} ext{O}_{39} \) has incorrect numbers of hydrogens and oxygens.\b. Option (b) \\( ext{KAl}_2 ext{S}_2 ext{H}_{43} ext{O}_{40} \) has incorrect potassium, hydrogens, and aluminum counts.\c. Option (c) \\( ext{K}_2 ext{AlS}_2 ext{H}_{48} ext{O}_{40} \) has insufficient aluminum content.\d. Option (d) \\( ext{K}_2 ext{Al}_2 ext{S}_2 ext{H}_{48} ext{O}_{40} \) accurately represents the formula for potash alum.

Step 4: Selecting the Correct Formula

Based on the molecular structure and breakdown of the options, the correct molecular formula of potash alum is option (d).

Key Concepts

Molecular Formula

Potash alum, also known as potassium alum, has a specific and important molecular formula. This formula helps us to understand the precise chemical composition of the compound. The molecular formula for potash alum is \( \mathrm{K}_2 \mathrm{Al}_2(SO_4)_2 \cdot 12 \mathrm{H}_2O \). This formula means that each unit of potash alum contains:

• Two potassium ions (\( \mathrm{K}^+ \)).
• Two aluminum ions (\( \mathrm{Al}^{3+} \)).
• Two sulfate ions (\( \mathrm{SO}_4^{2-} \)).
• Twelve molecules of water (\( \mathrm{H}_2\mathrm{O} \)) embedded within its structure.

Understanding this formula is crucial because it provides insight into the role of each component within the compound. Potash alum is often used in various applications such as water purification and in the dye industry. Knowing the molecular formula allows scientists and industries to calculate quantities needed for reactions and processes.

Double Sulfate Salt

Potash alum belongs to a class of compounds known as double sulfate salts. This means it contains two different cations with sulfate anions (- One of the cations in potash alum is potassium (\( \mathrm{K}^+ \)).- The other cation is aluminum (\( \mathrm{Al}^{3+} \)). Potash alum is an interesting example of how different cations can share the sulfate ions, forming a stable and synergistic structure. The double sulfate nature of potash alum allows for certain unique properties, such as its ability to dissolve in water and reform its crystalline structure upon evaporation. This process is beneficial in various industrial and chemical applications. Overall, the double sulfate allows potash alum to be a versatile substance with wide-ranging uses across different fields.

Water of Crystallization

Water of crystallization is a fascinating concept in chemistry. It refers to water molecules that are integrated into the crystalline structure of a compound. In potash alum, there are 12 water molecules for every formula unit (\( \text{K}_2 \text{Al}_2(SO_4)_2 \cdot 12 \text{H}_2 \text{O} \)).These water molecules are crucial as they stabilize the crystal lattice:

• They contribute to the overall weight and volume of the compound.
• They impact properties such as melting point, solubility, and the compound's ability to store and release water.

This water doesn't evaporate easily because it's not just loosely associated but is intrinsic to the maintenance of the compound's solid structure. It is through the presence of these water molecules that potash alum can maintain its specific crystalline form, which is essential for its applications in industries such as tanning, medicine, and water purification.