Question

From the reaction \(P_{\text {white }} \longrightarrow P_{\text {red }} ; \Delta H=18.4 \mathrm{~kJ}\) follows that (1) Red \(\mathrm{P}\) is readily formed from white \(\mathrm{P}\). (2) White \(\mathrm{P}\) is readily formed from \(\mathrm{red} \mathrm{P}\). (3) White P cannot be converted to red \(P\). (4) Whitc P can be converted into red \(\mathrm{P}\) and red \(\mathrm{P}\) is more stable.

Short answer

Option (4) is correct: White P can be converted into red P and red P is more stable.

Step-by-step solution

- Understand the Reaction

The reaction given is the conversion of white phosphorus (\text{white }P) to red phosphorus (\text{red }P). This process has an enthalpy change \(\text{ΔH} = 18.4 \text{ kJ} \).

- Analyze the Enthalpy Change

Typically, a positive \(\text{ΔH}\) indicates that the reaction absorbs heat from the surroundings, making it endothermic. Given that \(\text{ΔH} > 0\), the energy required to convert white phosphorus to red phosphorus is 18.4 kJ. This means white phosphorus is less stable than red phosphorus.

- Interpret the Stability

Since white phosphorus requires energy input to convert to red phosphorus, red phosphorus is the more stable form. The stability of a substance is often associated with its energy state; lower energy states are more stable.

- Evaluate the Options

Option (4) states that white phosphorus can be converted into red phosphorus and that red phosphorus is more stable. This aligns with the fact that the conversion absorbs energy and results in a more stable product. The other options do not correctly reflect the enthalpy change and stability.

Key concepts

Endothermic Reactions

In chemistry, endothermic reactions are those that absorb energy from their surroundings. This energy absorption can be measured and is usually expressed as an enthalpy change, noted with the symbol \(\text{ΔH}\). For endothermic reactions, \(\text{ΔH}\) is positive. That means the system is taking in heat. Now let's consider the reaction where white phosphorus (\text{white }P) converts to red phosphorus (\text{red }P) with \(\text{ΔH} = 18.4 \text{ kJ}\). Here, the positive sign of \(\text{ΔH}\) indicates that the reaction is endothermic. This signifies white phosphorus requires heat energy from its surroundings to transform into the more stable red phosphorus. So, in practical terms, if you were to perform this reaction, you would need to supply 18.4 kJ of energy for every mole of white phosphorus you convert to red phosphorus.

Stability of Phosphorus Allotropes

Phosphorus exists in different forms known as allotropes. The two main allotropes are white phosphorus and red phosphorus. The stability of these allotropes is an essential factor in many reactions. When the enthalpy change \(\text{ΔH}\) for a reaction is positive, it indicates that energy is needed to carry out the transformation. This tells us that the product is more stable than the reactant. In our reaction, we see that red phosphorus is more stable than white phosphorus. Why? Because converting white phosphorus to red phosphorus requires 18.4 kJ of energy. Stability in chemistry is often associated with being in a lower energy state. So, since white phosphorus requires energy input to change into red phosphorus, we can deduct that red phosphorus exists in a lower, more stable energy state. This conclusion aligns with the fact that red phosphorus is generally safer and less reactive than white phosphorus.

Energy Absorption in Phase Transitions

Phase transitions involve the conversion of substances from one physical state to another, and these transformations can either absorb or release energy. When discussing the conversion of white phosphorus to red phosphorus, it's important to understand that this is not just a simple chemical reaction; it is also a phase transition.
In this particular transition, energy absorption is critical. The enthalpy change of 18.4 kJ tells us how much energy from the surroundings is needed to make this change happen. So, if you're converting one mole of white phosphorus to red phosphorus, you'd need to supply that much energy.
Understanding energy absorption in phase transitions helps explain many natural and industrial processes. For example:

• Heating water to become steam involves endothermic phase transition.
• Freezing water to form ice releases energy, which is an exothermic phase transition.

In our case, the absorption of 18.4 kJ during the conversion of phosphorus essentially means you are investing energy to create a more stable form of phosphorus.