Problem 178 - A Complete Resource Book in Chemistry for JEE Main

Question

The heats of combustion of carbon and carbon monoxide are \(-393.5\) and \(-283.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The heat of formation (in \(\mathrm{kJ}\) ) of carbon monoxide per mole is: (a) \(676.5\) (b) \(-676.5\) (c) \(-110.5\) (d) \(110.5\)

Step-by-Step Solution

Answer

(c) \(-110.5\)

Step 1: Identify the Reactions Involved

First, let's clarify the reactions for combustion:1. The combustion of carbon: \( C(s) + O_2(g) \rightarrow CO_2(g) \), with a heat of combustion of \(-393.5\, J/mol\).2. The combustion of carbon monoxide: \( CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \), with a heat of combustion of \(-283.5\, J/mol\).

Step 2: Calculate the Reaction for CO Formation

The heat of formation for carbon monoxide corresponds to:\[ C(s) + \frac{1}{2}O_2(g) \rightarrow CO(g) \]

Step 3: Use Hess's Law to Combine Reactions

Hess's Law states that the total enthalpy change is the same regardless of the path. Thus, we can express the formation of \(CO\) as:- Subtract the combustion of \(CO\) from the combustion of \(C\):\[ (-393.5) - (-283.5) = -393.5 + 283.5 \]

Step 4: Calculate the Heat of Formation for CO

Evaluate the calculation:\[ -393.5 + 283.5 = -110.0 \]So, the heat of formation for \(CO\) is \(-110.0\, J/mol\).

Step 5: Choose the Closest Answer

Based on the calculated heat of formation, the closest answer choice is \(-110.5\, J/mol\), which corresponds to option (c).

Key Concepts

Hess's Law

Hess's Law is a powerful concept in thermodynamics used to calculate the enthalpy change of a reaction via alternate pathways. It states that the total enthalpy change during a chemical reaction is the same, regardless of the number of steps the process takes. This makes it incredibly useful for determining enthalpy changes that are difficult to measure directly.

For example, in the original problem, we need to find the heat of formation for carbon monoxide ( CO ) using known values of heats of combustion. By strategically choosing reactions and their respective enthalpy changes, we can apply Hess's Law to find the desired values without measuring them in an experiment.

• Hess's Law relies on the idea that enthalpy is a state function, meaning its change is independent of the path taken.
• This allows us to "subtract" unwanted reactions or "add" necessary reactions to determine the enthalpy change of a specific reaction.

Enthalpy Change

Enthalpy change, represented as \( \Delta H \), is a measure of heat change in a system at constant pressure. It is crucial in thermodynamics, helping us understand how heat is involved during chemical reactions.

In terms of the combustion reactions provided:

• The combustion of carbon: \( C(s) + O_2(g) \rightarrow CO_2(g) \), where \( \Delta H = -393.5 \, \text{kJ/mol} \).
• The combustion of carbon monoxide: \( CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \), with \( \Delta H = -283.5 \, \text{kJ/mol} \).

These values mirror how heat is released or absorbed, aiding in our calculation of carbon monoxide's heat of formation via Hess's Law. Understanding \( \Delta H \) is essential since it indicates whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat).

Heat of Formation

The heat of formation of a compound is defined as the enthalpy change when one mole of the compound is formed from its elements in their standard states. The concept simplifies calculations related to reactions involving compound formations.

In our exercise, the heat of formation corresponds to the change when carbon and oxygen combine to form carbon monoxide:
\[ C(s) + \frac{1}{2}O_2(g) \rightarrow CO(g) \]By using Hess's Law, we ascertain the heat of formation of CO through the elimination of other reaction heat values, derived from combustion enthalpies.

• Heat of formation for a compound can be either positive or negative, indicating if the formation releases or absorbs heat.
• Trusting Hess's Law ensures we compute this change as accurately as possible, even for indirect reaction pathways.

Recognizing and applying the heat of formation aids in understanding the stability and energy content of compounds like CO, a fundamental aspect for both academic and applied chemical sciences.