Problem 48 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation [Adv. 2019] (a) \(\frac{1}{8} \mathrm{~S}_{8}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{2}(\mathrm{~g})\) (b) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)\) (c) \(\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{O}_{3}(\mathrm{~g})\) (d) \(2 \mathrm{C}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\)

Step-by-Step Solution

Answer

(a) is the correct reaction.

Step 1: Understanding Standard Enthalpy of Formation

The standard enthalpy of formation is defined as the change in enthalpy when one mole of a compound is formed from its elements in their standard states.

Step 2: Analyzing Reaction (a)

In the reaction \frac{1}{8} \mathrm{~S}_{8}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{2}(\mathrm{~g})\, sulfur and oxygen are in their standard states, and one mole of \( \mathrm{SO}_{2} \) is formed. This satisfies the definition of standard enthalpy of formation.

Step 3: Analyzing Reaction (b)

In the reaction \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)\), the product is two moles of \( \mathrm{H}_{2} \mathrm{O} \), not one. Thus, this does not represent a standard enthalpy of formation of one mole of product.

Step 4: Analyzing Reaction (c)

The reaction \(\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{O}_{3}(\mathrm{~g})\) involves forming ozone \( \mathrm{O}_{3} \) from oxygen in its natural state, but it forms ozone, not typically a natural state or compound formed from pure elements in standard conditions.

Step 5: Analyzing Reaction (d)

In the reaction \(2 \mathrm{C}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\), carbon is in its gaseous state whereas its standard state is solid graphite. Hence, this does not meet the criteria for standard enthalpy of formation.

Step 6: Conclusion: Determining the Correct Option

Only reaction (a) meets all the criteria, as it involves elements in their standard states forming one mole of a product, \( \mathrm{SO}_{2} \), which aligns with the definition of standard enthalpy of formation.

Key Concepts

Chemical Thermodynamics

Chemical thermodynamics is a branch of physical chemistry that deals with the energy changes accompanying chemical reactions. Whenever a chemical reaction occurs, energy is either absorbed or released, which describes its thermodynamic nature. This field helps us understand the direction of a chemical process, its equilibrium state, and how variations in temperature, pressure, or concentration can affect the reaction. Several key concepts relate closely to chemical thermodynamics, including:

• Enthalpy: the heat content of a system at constant pressure.
• Entropy: a measure of disorder or randomness.
• Gibbs free energy: evaluates the capacity of a process to do work and helps predict the spontaneity of reactions.

Understanding these terms is vital because they form the backbone of predicting how and why chemical reactions happen. Thermodynamics does not tell how fast reactions proceed, but rather if they are possible and how much energy is involved.

Enthalpy Change

Enthalpy change is a core concept in understanding how energy is transferred within a chemical reaction. It represents the difference in enthalpy, or total heat content, between the reactants and the products at constant pressure. In the context of a reaction, the enthalpy change (\(\Delta H\)) helps us determine whether a reaction is exothermic or endothermic:

• An exothermic reaction releases heat, making \(\Delta H < 0\). For instance, combustion is typically exothermic as it releases energy into the surroundings.
• An endothermic reaction absorbs heat from its surroundings, so \(\Delta H > 0\). Photosynthesis in plants is a common example of endothermic reaction.

The standard enthalpy of formation is a specific type of enthalpy change, defined as the enthalpy change when one mole of a substance is formed from its elements in their standard states. This concept assists chemists in computing the overall enthalpy changes for various reactions by using standard enthalpies of formation as reference points.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to transform reactants into products. This process often results in changes in chemical energy, depicted as energy diagrams. There are several types of reactions, each with unique characteristics and energy profiles:

• Synthesis Reaction : Two or more substances combine to form a single product, typically exothermic, like the formation of water from hydrogen and oxygen.
• Decomposition Reaction : A compound breaks down into two or more simpler substances, often requiring energy input, making it endothermic.
• Combustion Reaction : A hydrocarbon reacts with oxygen to produce carbon dioxide and water, releasing significant amounts of energy.

The challenge in studying chemical reactions lies in balancing equations to ensure conservation of mass and energy. Enthalpy changes are assessed during these reactions to understand whether they release or absorb energy, helping in applications such as energy-efficient process design.