Problem 18 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The species which by definition has ZERO standard molar enthalpy of formation at \(298 \mathrm{~K}\) is [2010] (a) \(\mathrm{Br}_{2}(\mathrm{~g})\) (b) \(\mathrm{Cl}_{2}(\mathrm{~g})\) (c) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{CH}_{4}\) (g)

Step-by-Step Solution

Answer

The correct answer is (b) \(\mathrm{Cl}_{2}(\mathrm{~g})\).

Step 1: Understanding the Concept

The standard molar enthalpy of formation of a substance, by definition, is the change in enthalpy when one mole of the substance is formed from its elements in their most stable forms at 1 atmosphere and 298 K. For a pure element in its standard state, the standard enthalpy of formation is zero.

Step 2: Identifying the Species

Examine the options to find the one where the species is in its standard state. The options are: (a) \(\mathrm{Br}_{2}(\mathrm{~g})\) (b) \(\mathrm{Cl}_{2}(\mathrm{~g})\) (c) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{CH}_{4}\) (g)

Step 3: Checking Standard States

For diatomic gases like bromine and chlorine, the standard state at 298 K is the gaseous form for chlorine (\(\mathrm{Cl}_{2}(\mathrm{~g})\)) and liquid form for bromine (\(\mathrm{Br}_{2}(\mathrm{~l})\)). Water and methane have their standard states different from the ones given in this problem.

Step 4: Conclusion

The only option where the molecule is an elemental form in its standard state is chlorine gas \(\mathrm{Cl}_{2}(\mathrm{~g})\). Therefore, chlorine gas has a standard molar enthalpy of formation of zero at 298 K, according to the definition.

Key Concepts

Standard State

In chemistry, the term "standard state" refers to the state in which a chemical element exists at a stable equilibrium under standard conditions. These conditions are typically set at a pressure of 1 atmosphere and a temperature of 298 K (25 degrees Celsius), which is easily reproducible in laboratory settings.
When referring to a standard state, it’s essential to understand that it depends on the element being pure and existing in its most stable physical form at the given temperature and pressure. For example:

• Metals usually have their standard state in the solid form.
• Noble gases and many other nonmetals are gases in their standard states.
• Bromine is unique amongst most non-metals as it is a liquid at the standard state.
• Elements like sulfur can form multiple allotropes, but only the most stable one at 298 K is considered its standard state.

It is crucial to remember that the standard state does not imply a particular reactivity or chemical behavior. Instead, it provides a basis for comparing different substances using thermodynamic data like the standard enthalpy of formation.

Enthalpy Change

The concept of enthalpy change in a chemical reaction is a measure of the heat absorbed or released during the transformation. In simple terms, it is the difference in energy between the products and reactants, enabling us to understand whether a reaction is endothermic or exothermic.
Enthalpy change is denoted by the symbol \( \Delta H \), and when it is specifically referred to as standard enthalpy change, it means the measurement was taken under standard conditions. Calculating the standard enthalpy of formation involves:

• Determining the energy change when one mole of a compound is formed from its elements in standard states.
• The standard enthalpy of formation for elements in their standard states is always zero.

This zero-value reference point for elements in their standard states is fundamental in calculating reactions' enthalpies accurately. It allows chemists to predict the energy changes in chemical reactions, giving a glimpse into feasibility and reaction spontaneity.

Diatomic Molecules

Diatomic molecules are a simple yet crucial concept in chemistry, particularly when studying elements in their natural forms. These molecules are composed of two atoms of the same or different chemical elements joined by a chemical bond. In the context of the standard enthalpy of formation, certain non-metals naturally occur as diatomic molecules because this arrangement is the most stable energetically.
Common examples of diatomic molecules include:

• Hydrogen (\( \text{H}_2 \))
• Oxygen (\( \text{O}_2 \))
• Nitrogen (\( \text{N}_2 \))
• Florine (\( \text{F}_2 \))
• Chlorine (\( \text{Cl}_2 \))

These diatomic forms are their standard states at 298 K, highlighting a special case where the molecule is elemental, yet diatomic, which simplifies synchronization in thermodynamic calculations.
The existence of elements as diatomic molecules is essential in defining their standard state, direct applications in calculating properties like standard molar enthalpy of formation, and understanding reactions involving these common reactants.