Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the molecular formula of white phosphorus? (a) \(\mathrm{P}_{2}\) (c) \(\mathrm{P}_{3}\) (b) \(\mathrm{P}_{4}\) (d) \(\mathrm{P}_{16}\)

Step-by-Step Solution

Answer

The molecular formula of white phosphorus is \(\mathrm{P}_4\).

Step 1: Identifying White Phosphorus

White phosphorus is one of the allotropes of the element phosphorus. It is important to recognize the specific molecular structure associated with white phosphorus in order to determine its molecular formula.

Step 2: Recognizing the Molecular Structure

White phosphorus typically exists in a tetrahedral structure known as a tetra-phosphorus molecule. This structure involves four phosphorus atoms forming a tetrahedral shape.

Step 3: Determining the Molecular Formula

Given that white phosphorus has a tetrahedral molecular structure comprising four phosphorus atoms, the molecular formula representing this allotrope must be \((\mathrm{P}_4)\).

Step 4: Matching to Given Options

From the options provided: (a) \((\mathrm{P}_{2})\), (b) \((\mathrm{P}_{3})\), (c) \((\mathrm{P}_{4})\), and (d) \((\mathrm{P}_{16})\), the correct molecular formula for white phosphorus is option (c) \((\mathrm{P}_4)\).

Key Concepts

Molecular Formula

White phosphorus is an interesting form of phosphorus with a specific molecular formula. When we discuss the molecular formula, we're talking about the symbols and numbers that tell us which elements make up a molecule and in what proportions. For white phosphorus, the molecular formula is \( \mathrm{P}_4 \). This means that each molecule of white phosphorus is made up of four phosphorus atoms. White phosphorus is not formed by random or additional atoms; it is precisely this set of four that defines it.

Understanding the molecular formula helps us recognize the composition and properties of the substance. For example, knowing that white phosphorus is \( \mathrm{P}_4 \) can tell chemists about the chemical reactions it may undergo and its physical characteristics, like how it glows faintly in the dark (a property known as chemiluminescence).

White phosphorus is often stored under water because it is reactive, especially with oxygen, making this simple tetraatomic formula \( \mathrm{P}_4 \) practically significant in handling and chemical applications.

Allotropes of Phosphorus

Phosphorus is a fascinating element because it can rearrange itself into different forms known as allotropes. This means, despite being the same elemental phosphorus, it can exist in distinct structural forms. These different forms have unique properties. The three most known allotropes of phosphorus are:

• White Phosphorus: Known for its high reactivity and tetrahedral \( \mathrm{P}_4 \) structure.


• Red Phosphorus: More stable than white phosphorus; it's often used in safety matches and is composed of a network of phosphorus atoms.


• Black Phosphorus: The least reactive and stable, resembling graphite, used in electronics due to its semiconducting properties.

Each of these allotropes has a different arrangement of phosphorus atoms, affecting how they interact with the environment. While white phosphorus must be handled carefully, red and black phosphorus are more stable, allowing for different industrial applications.
Understanding these allotropes is crucial for utilizing phosphorus effectively in practical applications across different industries.

Tetrahedral Structure

The tetrahedral structure is a key concept in understanding the physical and chemical properties of white phosphorus. In this structure, four phosphorus atoms are arranged at the corners of a tetrahedron, a three-dimensional shape with four triangular faces.

To visualize, imagine a triangular pyramid where each corner is occupied by a phosphorus atom. This formation allows the phosphorus atoms to be as far apart from each other as possible while sharing a space, which can contribute to the instability and reactivity of white phosphorus.
- The angles between the phosphorus atoms in this tetrahedral formation are around 60°, creating notable angular strain. - This angular strain is one reason white phosphorus is highly reactive, especially compared to other phosphorus allotropes. The beauty of the tetrahedral structure lies in its symmetry and the unique reactivity it provides to white phosphorus, making it not only a topic of study for chemistry enthusiasts but also a fascinating material for practical applications once tamed and understood.