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

The heat of formation of CO is \(-110.5 \text{ kJ/mol}\) per mole. The answer is (c).

Step 1: Understanding the Heat of Formation

The heat of formation can be calculated using the available data on the heats of combustion. We use the fact that the formation of carbon monoxide from carbon and oxygen can be analyzed in terms of their combustion reactions.

Step 2: Setting Up the Combustion Reactions

1. The combustion of carbon: \[ \text{C} + \text{O}_2 \rightarrow \text{CO}_2 \] with a heat of combustion of \(-393.5 \text{ kJ/mol}\).2. The combustion of carbon monoxide: \[ \text{2 CO} + \text{O}_2 \rightarrow \text{2 CO}_2 \] with a heat of combustion of \(-283.5 \text{ kJ/mol}\).

Step 3: Using Hess's Law

We apply Hess's law to express the heat of formation of \(\text{CO}\) from the given heats of combustion. The process is: 1. Form \(\text{CO}\) from \(\text{C}\) and \(\text{O}_2\).2. Make sure this agrees with the known combustion reactions.

Step 4: Calculating Heat of Formation of CO

We apply the concept: \(\text{C}_{(s)} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO} \).Using Hess's Law: \(\Delta H_f (\text{CO}) = \Delta H_c (\text{C}) - \Delta H_c (\text{CO})\). Plugging in data: \(-393.5 \text{ kJ/mol} - \left(-2 \times 283.5 \text{ kJ/mol}/2\right)\).Which simplifies to \(-393.5 \text{ kJ/mol} - (-283.5 \text{ kJ/mol}) = -110.5 \text{ kJ/mol}\).

Step 5: Conclusion

We found that the heat of formation for carbon monoxide per mole is \(-110.5 \text{ kJ/mol}\).

Key Concepts

Heats of Combustion

The heat of combustion is a crucial concept in thermodynamics and chemistry. It represents the energy released when a substance undergoes complete combustion with oxygen under standard conditions. This reaction is exothermic, meaning it releases energy, often in the form of heat or light. For example, the combustion of carbon to form carbon dioxide is given by the reaction:

• \[ \text{C} + \text{O}_2 \rightarrow \text{CO}_2 \]

This process releases \(-393.5 \text{ kJ/mol}\) of energy. Similarly, the combustion of carbon monoxide is represented by:

• \[ \text{2 CO} + \text{O}_2 \rightarrow \text{2 CO}_2 \]

which releases \(-283.5 \text{ kJ/mol}\) of energy per mole of carbon monoxide combusted. By knowing the heats of combustion for various reactions, we can derive other important thermochemical data, such as heats of formation, using tools like Hess’s Law. Understanding heats of combustion allows chemists to analyze energy changes in reactions, thus guiding the design of processes and materials for better efficiency.

Hess's Law

Hess's Law is a fundamental principle that provides a way to predict the heat of a reaction by breaking it down into a series of steps that have known changes in enthalpy. This law states that the total enthalpy change for a chemical reaction is the same, regardless of whether it occurs in a single step or through multiple stages. Therefore, we can rearrange known reactions to deduce unknown heats of formation or combustion.In the context of the formation of carbon monoxide \((\Delta H_f (\text{CO}))\), we used Hess's Law to combine the heat of combustion of carbon and the heat of combustion of carbon monoxide:

• The reaction forming \( \text{CO}_{(g)} \) from \( \text{C}_{(s)} \) and \( \frac{1}{2}\text{O}_2 \) is not directly measurable.
• Using Hess's Law, these known combustion reactions can be manipulated to find this formation enthalpy, effectively by adding or subtracting their energy values.

By calculating this using data from combustion reactions, we found that \(\Delta H_f (\text{CO}_{(g)}) = -110.5 \text{ kJ/mol}\).Hess's Law is invaluable for providing insights into the thermodynamics of reactions and processes.

Carbon Monoxide Formation

The formation of carbon monoxide \( (\text{CO}) \) from elemental carbon and oxygen is an important chemical process that relates directly to environmental and industrial contexts. Carbon monoxide is formed through the reaction:

• \[ \text{C}_{(s)} + \frac{1}{2} \text{O}_2 \rightarrow \text{CO}_{(g)} \]

This is an exothermic process, though less exothermic than the formation of carbon dioxide directly from carbon.
In practical scenarios, carbon monoxide is an intermediate product in industrial processes such as the production of tungsten via the reduction of tungsten oxide. It is also a byproduct of incomplete combustion in engines, which is why understanding its formation is key to reducing harmful emissions.
The heat of formation for \(\text{CO}_{(g)}\) calculated as \(-110.5 \text{ kJ/mol}\) reflects the energy associated with its formation from carbon and oxygen. Monitoring and managing the formation of carbon monoxide is crucial due to its toxic nature when inhaled by humans. Therefore, vehicles and industrial plants are usually equipped with technology to minimize \(\text{CO}\) emissions.