Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

The formula of exhausted permutit is (a) \(\mathrm{K}_{2} \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot \mathrm{xH}_{2} \mathrm{O}\) (b) \(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \times \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{Na}_{2} \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot \mathrm{xH}_{2} \mathrm{O}\) (d) \(\mathrm{CaB}_{2} \mathrm{Si}_{2} \mathrm{O}_{\mathrm{s}} \cdot \mathrm{xH}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The formula for exhausted permutit is (b) \(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \times \mathrm{H}_{2}\mathrm{O}\).

Step 1: Understanding Permutit

Permutit is a type of water softener used to replace calcium and magnesium ions in water with sodium ions. It is a hydrated sodium aluminum silicate.

Step 2: Identify the Formula for Exhausted Permutit

An exhausted permutit means active sodium ions are replaced by other ions like calcium or magnesium during the softening process.

Step 3: Compare with Given Formulas

Option (a) is potassium-based; option (b) is calcium-based; option (c) is sodium-based, which is the base for a non-exhausted permutit; option (d) is a boron-based compound.

Step 4: Identify Exhausted Condition

Exhausted permutits usually feature calcium ions in place of sodium ions, which is option (b): \(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \times \mathrm{H}_{2} \mathrm{O}\).

Key Concepts

Exhausted Permutit

When we talk about an exhausted permutit, we are referring to a substance used in the water softening process that has reached its capacity in absorbing unwanted minerals from water. The primary function of a permutit is to replace calcium and magnesium ions in water, which cause hardness, with sodium ions, making the water soft. Over time, as a permutit is used, the sodium ions are gradually replaced by calcium and magnesium ions. This change indicates that the permutit has become 'exhausted.' It's a bit like a sponge that has soaked up all it can and needs to be rejuvenated or replaced.
Naturally, when all the sodium ions are swapped for sodium or magnesium, the permutit can no longer effectively soften water. At this stage, the permutit material itself will have its sodium ions exhausted, and in terms of composition, it resembles option (b) in the original exercise, composed of calcium aluminum silicate: \( \mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \times \mathrm{H}_{2} \mathrm{O} \). Understanding this exhaustion process is crucial for ensuring the efficiency of a water softening system over time.

Sodium Aluminum Silicate

Sodium aluminum silicate is a key ingredient in permutit and plays an essential role in the water softening process. It's a type of zeolite, which is a mineral with a microporous structure that can trap and exchange ions. The uniqueness of sodium aluminum silicate lies in its ability to exchange sodium ions for calcium and magnesium ions. The chemical formula for sodium aluminum silicate is \( \mathrm{Na}_{2} \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot \mathrm{xH}_{2} \mathrm{O} \).
In water softening, when hard water passes through a filter containing sodium aluminum silicate, the hard ions like calcium and magnesium are exchanged for sodium ions. This exchange process doesn't just make the water softer but also helps in preventing deposits and buildups in pipes and appliances. Understanding the role of sodium aluminum silicate is important for anyone interested in the chemistry of water treatment and purification systems.

Calcium Ions Replacement

In the context of water softening, the replacement of calcium ions is a critical step performed by a permutit system. Hard water contains high concentrations of calcium and magnesium ions, which can cause various issues like scaling on pipes and reduced efficiency of soap. The aim of water softening is to eliminate these hard ions and replace them with sodium ions.
During this process, when water flows through a permutit material, the sodium ions present in the structure are exchanged with the calcium and magnesium ions found in the hard water. This ion exchange process is efficient and reversible, meaning exhausted permutits can be regenerated by flushing them with a high concentration of sodium chloride, typically found in salt. This rejuvenation process underscores the importance of understanding how calcium ions are replaced in the water softening cycle, ensuring water remains soft and suitable for everyday use.