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) \(\mathrm{KAl}_{2} \mathrm{~S}_{2} \mathrm{H}_{48} \mathrm{O}_{40}\) (c) \(\mathrm{K}_{2} \mathrm{AlS}_{2} \mathrm{H}_{48} \mathrm{O}_{40}\) (d) \(\mathrm{K}_{2} \mathrm{Al}_{2} \mathrm{~S}_{2} \mathrm{H}_{48} \mathrm{O}_{40}\)

Short 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-by-step solution

Understand the Molecular Composition

A potash alum is a type of alum, which is a double sulfate salt. Typically, potash alum includes potassium, aluminum, sulfur, hydrogen, and oxygen in its chemical makeup.

Recall the General Formula for Potash Alum

The general formula for potash alum is \[ ext{KAl(SO}_4 ext{)}_2 \cdot 12 ext{H}_2 ext{O}\]. Upon expanding this structure, the formula should reflect the composition of its components by showing their correct proportion and counts of atoms.

Count Atoms in General Formula

Using the general formula of potash alum, count the atoms: - Potassium (K): 1- Aluminum (Al): 2- Sulfur (S): 2 (each sulfate group contains one sulfur)- Oxygen (O): 8 (in sulfate) + 24 (in water) = 32- Hydrogen (H): 24 (in water)Thus, the expanded formula is \[ ext{KAl}(SO_4)_2 \text{. } 12H_2O\].

Match with Given Options

When expanded, the formula for potash alum should read \[ ext{K}_2 ext{Al}_2(SO_4)_2 \cdot 24H_2O\], which consists of 2 sulfur atoms, 2 aluminum atoms, 48 hydrogen atoms, 40 oxygen atoms, and 2 potassium atoms. Therefore, the correct option among those given is (d) \[ ext{K}_2 ext{Al}_2 ext{S}_2 ext{H}_{48} ext{O}_{40}\].

Key concepts

Double Sulfate Salt

Potash alum is a fascinating compound, mainly due to its classification as a double sulfate salt. This means it contains two different metallic ions bound together with sulfate ions. In potash alum's case, these are potassium

• Potassium (K) ions
• Aluminum (Al) ions
• Sulfate (SO₄) ions

The dual nature of double sulfate salts is what gives potash alum its unique chemical behavior. It's not just a simple combination but such a specific interaction of components that exhibits characteristic properties. Among these properties are high solubility in water and the ability to form large crystals.

Moreover, double salts like potash alum decomposes in water to give separate cations, making the individual ions available for participation in various chemical reactions. This decomposition provides the ions separately, enabling varied use in industrial and laboratory settings. Double sulfate salts play an essential role in both academic exploration and practical applications.

General Formula of Alum

Alums are a class of important compounds that follow a general chemical structure. They usually adopt a generalized formula expressed as \( ext{M}_2 ext{SO}_4 imes ext{M'}_2( ext{SO}_4)_3 imes 24 ext{H}_2 ext{O}\).Here,

• "M" represents a monovalent cation like potassium (K) or sodium (Na)
• "M'" stands for a trivalent cation such as aluminum (Al), chromium (Cr) or iron (Fe)
• The formula indicates the compound often exists in hydrated form, exhibiting molecules of water bound to it

In the instance of potash alum, the formula becomes \[ ext{KAl(SO}_4)_2 \cdot 12 ext{H}_2 ext{O}\]. This indicates one monovalent potassium ion, one trivalent aluminum ion, two sulfate groups, and twelve molecules of water per formula unit.

Recognizing the general formula of alums helps to decipher their composition quickly, simplifying the understanding of how they interact in solutions. It equips one with a tool to predict the chemical behavior of similar compounds.

Chemical Composition of Potash Alum

Potash alum, a vital compound in various sectors, holds a distinct formula that illustrates its composition. By examining its structure \[ ext{K}_2 ext{Al}_2( ext{SO}_4)_2 \cdot 24 ext{H}_2 ext{O}\], we unravel that it is composed of

• 2 Potassium (K) atoms
• 2 Aluminum (Al) atoms
• 2 Sulfur (S) atoms (as part of sulfate)
• 48 Hydrogen (H) atoms from water molecules
• 40 Oxygen (O) atoms

This comprehensive breakdown reflects the complexity and versatility of potash alum.

Its stable arrangement of atoms affords it properties such as astringency, antiseptic characteristics, and wide utility in fields like water purification, tanning, and dyeing. Understanding how its atoms are assembled highlights why it behaves a certain way and why it remains a valuable resource in chemical and industrial processes.