Question

The empirical formula of alum is (1) \(\mathrm{K}_{2} \mathrm{SO}_{4} \cdot \mathrm{A}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot 24 \mathrm{H}_{2} \mathrm{O}\) (2) \(\mathrm{KA} 1\left(\mathrm{SO}_{4}\right)_{2} \cdot 12 \mathrm{H}_{2} \mathrm{O}\) (3) \(2 \mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2} \cdot 12 \mathrm{H}_{2} \mathrm{O}\) (4) None

Short answer

Option (3) \(\text{2 KAl}\text{SO}_{4}_{2} \text{ } 12 \text{H}_{2}\text{O}\).

Step-by-step solution

- Identify the Components of Alum

Alum typically contains potassium (K), aluminum (Al), sulfate (SO4), and water of crystallization (H2O). The empirical formula will reflect these components in a stoichiometric ratio.

- Analyze each option

Review each of the given formulas to identify which one correctly combines potassium, aluminum, sulfate, and water according to common ratios observed in alum compounds.

- Verify Formula (1)

Option (1) \(\text{K}_{2} \text{SO}_{4} \text{ A}_{2}\text{SO}_{4}_{3} \text{ } 24 \text{H}_{2}\text{O}\) does not correctly reflect the combination of one mole of potassium (\text{K}), one mole of aluminum (\text{Al}), two moles of sulfate (\text{SO}_{4}), and twelve moles of water (\text{H}_{2}\text{O}). Hence, this is not correct.

- Verify Formula (2)

Option (2) \(\text{KA} 1\text{SO}_{4}_{2} \text{ } 12 \text{H}_{2}\text{O}\) is not a standard way of representing the ratio of potassium, aluminum, sulfate, and water for an alum.

- Verify Formula (3)

Option (3) \(\text{2 KAl}\text{SO}_{4}_{2} \text{ } 12 \text{H}_{2}\text{O}\) represents the correct ratio of 2 moles of potassium (\text{K}), 2 moles of aluminum (\text{Al}), 4 moles of sulfate (\text{SO}_{4}), and 24 moles of water (\text{H}_{2}\text{O}) in pairs; which simplifies down to the conventional formula of alum.

- Confirm Answer

After reviewing all the options, formula (3) \(\text{2 KAl}\text{SO}_{4}_{2} \text{ } 12 \text{H}_{2}\text{O}\) is the accurate empirical composition for alum.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry. It involves calculating the relationships between the quantities of reactants and products in a chemical reaction.
It helps us understand how much of each substance is necessary for a reaction to occur.
Stoichiometry uses balanced chemical equations to make these calculations.
For example, if we know the formula of a compound like alum, we can use stoichiometry to determine the quantities of potassium, aluminum, sulfate, and water of crystallization present.
This helps in verifying if a given empirical formula is accurate by ensuring the ratios are consistent with known chemical principles.

Empirical Formula

An empirical formula represents the simplest whole-number ratio of elements in a compound.
It is obtained by dividing the moles of each element by the smallest number of moles present in the compound.
For example, the empirical formula of water is \(\text{H}_2\text{O}\), showing a 2:1 ratio of hydrogen to oxygen.
In the case of alum, the empirical formula shows how many moles of potassium, aluminum, sulfate, and water molecules are present.
In the given problem, the correct empirical formula is \(\text{2 KAl}\text{SO}_{4}_2 \text{ } 12 \text{H}_2 \text{O}\), which correctly represents the ratio of components in alum.

Inorganic Chemistry

Inorganic chemistry deals with inorganic compounds, which include minerals, metals, and other non-carbon-containing substances.
It focuses on compounds not covered by organic chemistry, including salts, metals, and minerals.
Alums are a significant topic in inorganic chemistry.
They are double salts composed of two different cations like potassium and aluminum combined with sulfate and water of crystallization.
Understanding the empirical formula of inorganic compounds like alum helps us grasp their chemical behavior and applications in various fields.

Chemical Compounds

Chemical compounds are substances formed from two or more elements in a definite ratio.
This fixed ratio determines the compound's properties and behavior.
In alum, the compound's formula reflects the specific number of potassium, aluminum, sulfate ions, and water molecules grouped together.
Compounds can be identified by their empirical formulas, which provide crucial information on the ratio and type of atoms within them.
Correctly identifying the empirical formula is critical for understanding the compound's structure and chemical interactions.