Problem 32 - A Complete Resource Book in Chemistry for JEE Main

Question

Which allotrope of phosphorus is thermodynamically most stable? (a) red (b) black (c) white (d) yellow

Step-by-Step Solution

Answer

Black phosphorus is thermodynamically the most stable allotrope.

Step 1: Identify the Allotropes of Phosphorus

Phosphorus exists in several allotropes. The most common ones are red, white, and black phosphorus. Yellow phosphorus is less commonly referred to, but typically it is another form of white phosphorus.

Step 2: Understand Stability in Terms of Thermodynamics

A thermodynamically stable substance is one that has the lowest free energy state under a given set of conditions, such as ambient temperature and pressure. It favors less reactive and more stable forms.

Step 3: Consider the Stability of Each Allotrope

- White phosphorus has a low melting point and is highly reactive, making it less stable. - Red phosphorus is more stable than white and is less reactive. - Black phosphorus is the least reactive and most stable thermodynamically due to its layered structure and strong covalent bonding, similar to graphite in carbon.

Step 4: Select the Most Stable Allotrope

The black allotrope of phosphorus is thermodynamically the most stable form under standard conditions because it is the least reactive and has the lowest free energy.

Key Concepts

Thermodynamic Stability

When we talk about thermodynamic stability, we are referring to how stable a substance is under a set of given conditions, typically at room temperature and pressure. Imagine a substance as a ball in a bowl — the deeper and smoother the bowl, the more stable the ball is. This is similar to how stable substances operate. They exist in a low-energy state, like a ball settled at the bottom of a deep bowl.

Thermodynamic stability is influenced by factors such as energy and reactivity. Substances that are less reactive usually have lower energy, making them more stable. The allotropes of phosphorus, specifically red, white, and black, each have different levels of stability.

• Black phosphorus is the most stable because it resides in the lowest energy state and is less reactive compared to the other forms.
• White phosphorus, on the other hand, is highly reactive and thus less stable.
• Red phosphorus is more stable than white but not as stable as black. This gradient of stability is vital in understanding the practical applications and behaviors of these substances.

Covalent Bonding

Covalent bonding is the type of chemical bond where atoms share electron pairs. In phosphorus allotropes, the structure and strength of the covalent bonds greatly affect their properties. Much like glue holding pieces together, these bonds determine the allotrope's stability and reactivity.

Black phosphorus' structure features strong covalent bonds within its layers, resembling graphite in carbon. This structure provides it with superior thermodynamic stability and low reactivity. The layers are tightly bound by covalent bonds, resulting in a robust and rigid structure, making it the least reactive allotrope.

• White phosphorus consists of a network of weaker P-P bonds, making it highly reactive and less stable.
• Red phosphorus has a polymeric net-like structure with stronger covalent bonds than white phosphorus, making it more stable.

These variations in bonding highlight the importance of covalent bonding in determining the properties of allotropes.

Reactivity in Chemistry

Reactivity is a chemical property that describes how readily a substance undergoes a chemical reaction. For phosphorus allotropes, reactivity is a key factor in determining stability and potential applications.

The reactivity of phosphorus allotropes can be compared to their predilection for engaging in chemical reactions. White phosphorus is highly reactive, forming reactive P4 tetrahedra that readily ignite in air. It’s akin to a whiz kid eager but uncontrolled, reacting with many other substances quickly.

• Red phosphorus is less reactive and more controlled, making it safer to handle. It is commonly used in safety matches due to this lesser reactivity.
• Black phosphorus, being the least reactive, does not readily engage in chemical reactions under normal conditions, thus demonstrating its exceptional stability.

Understanding reactivity helps in determining safe handling, storage, and application of these allotropes. It plays a crucial role in scientific and industrial fields, guiding how materials are selected and used in various chemical processes.