Question

White phosphorus, \(P_{4},\) is produced by the reduction of phosphate rock, \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\). If exposed to oxygen, the waxy, white solid smokes, bursts into flames, and releases a large quantity of heat: $$ \mathrm{P}_{4}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)+\text { heat } $$ Does this reaction have a large or small equilibrium constant? Explain.

Short answer

This reaction has a large equilibrium constant because it produces a solid from gases and is highly exothermic.

Step-by-step solution

Identify reaction components

The reaction involves the conversion of gaseous phosphorus \(\mathrm{P}_{4}(g)\) and oxygen \(\mathrm{O}_{2}(g)\) to solid tetraphosphorus decoxide \(\mathrm{P}_{4}\mathrm{O}_{10}(s)\) with the release of heat.

Determine reaction type

This reaction is exothermic because it releases heat.

Examine physical states of reactants and products

Gaseous reactants \(\mathrm{P}_{4}(g)\) and \(\mathrm{O}_{2}(g)\) combine to form a solid product \(\mathrm{P}_{4}\mathrm{O}_{10}(s)\), indicating a significant decrease in entropy (disorder).

Consider the equilibrium concept

The reaction proceeds to form a solid from gases and produces heat. Both factors (lower entropy and exothermic nature) drive the reaction toward the product side.

Predict the equilibrium constant

Because the reaction strongly favors the formation of the product \(\mathrm{P}_{4}\mathrm{O}_{10}(s)\) and is exothermic, the equilibrium constant \(K\) is likely to be very large. This indicates that the concentration of products at equilibrium is much higher than that of reactants.

Key concepts

Exothermic Reaction

An exothermic reaction is a type of chemical reaction that releases energy in the form of heat. This heat is given off to the surroundings, causing the temperature of the surroundings to rise. In the reaction of white phosphorus with oxygen, `\(\text{P}_4(g) + 5\text{O}_2(g) \rightarrow \text{P}_4\text{O}_{10}(s)\)`, heat is released, as indicated in the equation.

Exothermic reactions are characterized by negative enthalpy changes (\(\text{ΔH})\). This means that the energy of the products is lower than the energy of the reactants. In simpler terms, the system loses energy during the reaction. Examples of exothermic reactions include combustion (like burning wood or gasoline) and many oxidation reactions. Understanding this concept helps in predicting the behavior of chemical systems and the direction in which the reaction will proceed.

Entropy

Entropy is a measure of the disorder or randomness in a system. In chemical reactions, changes in entropy (\(S\)) indicate how the arrangement of particles changes. When gaseous reactants form solid products, as in the reaction `\(\text{P}_4(g) + 5\text{O}_2(g) \rightarrow \text{P}_4\text{O}_{10}(s)\)`, the system becomes more ordered, resulting in a decrease in entropy.

Decreasing entropy makes sense because gases have more freedom of movement and higher entropy compared to solids. In our reaction, the gaseous molecules of \(\text{P}_4\) and \(\text{O}_2\) come together to form a solid \(\text{P}_4\text{O}_{10}\). The move from a high-entropy state (gases) to a low-entropy state (solid) influences the direction of the reaction and contributes to a high equilibrium constant.

Phosphorus Chemistry

Phosphorus is an essential element in chemistry and is widely studied for its unique properties and reactions. White phosphorus, denoted as \(\text{P}_4\), is a common allotrope that appears as a waxy, white solid. It is highly reactive and can spontaneously combust in air, forming phosphorus pentoxide (tetraphosphorus decoxide), \(\text{P}_4\text{O}_{10}\).

In its reactions, white phosphorus acts as a reducing agent, meaning it donates electrons to other substances. The reaction \(\text{P}_4(g) + 5\text{O}_2(g) \rightarrow \text{P}_4\text{O}_{10}(s)\) exemplifies this behavior, as phosphorus reacts readily with oxygen.

Phosphorus chemistry is significant in many environmental and biological processes. Phosphates are essential components in DNA, RNA, and ATP, the energy currency of cells. Understanding phosphorus reactions and their equilibrium properties is crucial for mastering both fundamental and applied chemistry topics.