Problem 30 - A Complete Resource Book in Chemistry for JEE Main

Question

Standard molar enthalpy of formation of \(\mathrm{CO}_{2}\) is equal to (a) zero (b) the standard molar enthalpy of combustion of gaseous carbon. (c) the sum of standard molar enthalpies of formation Of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) (d) the standard molar enthalpy of combustion of carbon (graphite)

Step-by-Step Solution

Answer

Both (b) and (d) are correct; it is the same as the combustion of carbon.

Step 1: Understanding the Problem

We need to determine which of the given options correctly defines the standard molar enthalpy of formation for carbon dioxide \( \mathrm{CO}_2 \). The standard molar enthalpy of formation is defined as the enthalpy change when one mole of a substance is formed from its elements in their standard states.

Step 2: Interpreting Key Concepts

Option (a) suggests that the standard molar enthalpy of formation is zero, but this is only true for elements in their standard state, like \( \mathrm{O}_2 \) or carbon as graphite. \( \mathrm{CO}_2 \) is a compound, so this option is incorrect.

Step 3: Evaluating Option (b)

The standard molar enthalpy of formation of \( \mathrm{CO}_2 \) is indeed equivalent to the standard molar enthalpy of combustion of gaseous carbon because forming \( \mathrm{CO}_2 \) from carbon and oxygen is essentially the same reaction as burning carbon in oxygen.

Step 4: Addressing Option (c)

This option suggests that the enthalpy of formation of \( \mathrm{CO}_2 \) is the sum of \( \mathrm{CO} \) and \( \mathrm{CO}_2 \) enthalpies. This doesn't align with the process definition, so it is incorrect.

Step 5: Evaluating Option (d)

Option (d) presents that the enthalpy of \( \mathrm{CO}_2 \) formation is the same as the combustion of carbon in its graphite form, which parallels forming \( \mathrm{CO}_2 \) from carbon and oxygen. Thus, this option is true, presenting an equivalent reaction.

Step 6: Conclusion of Analysis

We conclude that both options (b) and (d) correctly define the standard molar enthalpy of formation of \( \mathrm{CO}_2 \) because they interpret the reaction of forming \( \mathrm{CO}_2 \) from its elements, which is essentially the combustion of carbon.

Key Concepts

Enthalpy Change

Enthalpy change is a concept that involves the heat exchange of a system during a chemical reaction. It reflects the difference in heat content between the products and reactants. This change can be categorized as either:

• Exothermic: Where heat is released and the enthalpy change is negative.
• Endothermic: Where heat is absorbed, resulting in a positive enthalpy change.

In the context of standard molar enthalpy of formation, it specifically refers to the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. For carbon dioxide (\(\mathrm{CO}_2\)), this involves the reaction of carbon and oxygen. The enthalpy change is a crucial indicator of the energy dynamics in reactions and helps in understanding how energy flows between the surroundings and the system.

Combustion Reaction

A combustion reaction is a chemical process where a substance reacts with oxygen, resulting in the production of heat and, often, light. This type of reaction generally involves:

• A fuel (like carbon in various forms) and oxidant (oxygen)
• The formation of products such as carbon dioxide and water

In the context of forming carbon dioxide, the combustion of carbon is a primary example. Here, carbon reacts with oxygen to produce carbon dioxide and releases energy as heat. This particular reaction can be represented as:\[\mathrm{C(graphite)} + \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g)\]It's essential to note that the enthalpy change for this reaction matches the standard molar enthalpy of formation for carbon dioxide, as it involves forming the compound directly from its elements.

Carbon Dioxide Formation

Carbon dioxide formation is a straightforward chemical process where carbon reacts with oxygen. This reaction is significant for various reasons:

• It demonstrates a simple route to form a common gas
• It's an exothermic process, releasing energy in the form of heat

For the reaction under standard conditions, the process involves carbon in the form of graphite and gaseous oxygen to form gaseous carbon dioxide:
\[\mathrm{C(graphite)} + \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g)\]
The enthalpy change associated with this reaction is equivalent to the standard molar enthalpy of formation for carbon dioxide. Since this formation involves simple elemental reactants, it's a clear depiction of how compounds are constructed from elemental forms. Understanding this process makes clear the connection between chemical reactions like combustion and enthalpy changes in thermochemistry.