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) \(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{g} \cdot \mathrm{xH}_{2} \mathrm{O}\) (c) \(\mathrm{Na}_{2} \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot \mathrm{xH}_{2} \mathrm{O}\) (d) \(\mathrm{CaB}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot \mathrm{xH}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

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

Step 1: Understanding Permutit

Permutit is a type of synthetic zeolite used in water softening. In its exhausted form, it contains calcium ions initially present in the hardness of water.

Step 2: Identification of Exhausted Form

In its exhausted form, permutit often exchanges its initial sodium ions with calcium ions. Thus, the exhausted form will contain calcium instead of sodium.

Step 3: Examining the Options

Look at the provided formulas to identify which one contains calcium ions in place of sodium ions as in the original form of permutit.

Step 4: Matching the Formula

The exhausted permutit should have calcium replacing sodium from the original sodium-based permutit structure. That structure is represented by option (b): \(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} 3 \mathrm{xH}_{2} \mathrm{O}\).

Key Concepts

Synthetic Zeolite

Synthetic zeolites are engineered minerals often made from aluminum, silicon, and oxygen, structured into a porous network. These materials are commonly utilized in water softening processes. Due to their highly porous nature, synthetic zeolites have a vast surface area with void spaces that enable them to capture and hold a variety of ions. This capability facilitates the removal of "hardness" ions such as calcium ( Ca^{2+} ) and magnesium ( Mg^{2+} ) from water. With their uniform pore size and strong ion-exchange capabilities, synthetic zeolites are a preferred choice in many industrial applications. Their efficiency in trapping unwanted metal ions while releasing sodium ions makes them an effective alternative to other water-softening agents.

Exhausted Permutit

When permutit, a specific type of synthetic zeolite employed in ion exchange processes, is used repeatedly to soften water, it becomes "exhausted." The term exhausted refers to the state when most of the initial sodium ions ( Na^{+} ) in the permutit are replaced by calcium ions ( Ca^{2+} ) through the ion exchange process. This transformation indicates that the permutit can no longer effectively soften water until it is regenerated. Regeneration involves flushing the zeolite with a concentrated sodium chloride ( NaCl ) solution. This process replaces the calcium ions back with sodium ions, thus rejuvenating the permutit and allowing it to be reused for further water softening.

Ion Exchange

Ion exchange is a reversible chemical process where unwanted dissolved ions in water are replaced by other ions of a similar charge. This method is vital in water softening where calcium ( Ca^{2+} ) and magnesium ions ( Mg^{2+} ) are exchanged for sodium ions ( Na^{+} ). The process relies heavily on the properties of zeolites and resins that act as ion-exchange mediums. Here's how it typically works:

• The hard water flows through a bed of synthetic zeolites or ion-exchange resins.
• Calcium and magnesium ions present in the water are attracted and bind to the zeolite.
• Sodium ions, initially present in the zeolite, are released into the water to maintain electrical neutrality.

This cycle continues until the zeolite is exhausted, at which point it undergoes regeneration to restore its ion-exchange capacity.

Calcium Ions

Calcium ions ( Ca^{2+} ) are a key component of water "hardness," a term used to describe water with high mineral content. In many regions, the presence of calcium in drinking water is quite common, primarily derived from limestone and other mineral deposits. While not harmful to human health, calcium ions in water can cause undesirable effects such as soap scum formation, scale buildup in pipes and appliances, and decreased efficiency of soaps and detergents. By using ion exchange processes, calcium ions are removed or replaced by less problematic ions, such as sodium, improving water quality and extending the lifespan of plumbing systems. This not only benefits household utilities but also industrial processes that rely on water free from calcium deposits.