Question

The enthalpy of combustion of solid carbon to form carbon dioxide is \(-393.7 \mathrm{~kJ} / \mathrm{mol}\) carbon, and the enthalpy of combustion of carbon monoxide to form carbon dioxide is \(-283.3 \mathrm{~kJ} / \mathrm{mol}\) CO. Use these data to calculate \(\Delta H\) for the reaction $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) $$

Short answer

The enthalpy change for the reaction \(2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g)\) is \(\Delta H = -1354 \mathrm{~kJ/mol}\).

Step-by-step solution

Write down the given reactions and their enthalpy changes

The given reactions are: 1. Combustion of solid carbon to form carbon dioxide: $$ \mathrm{C}(s) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) \quad \Delta H_1=-393.7 \mathrm{~kJ/mol} $$ 2. Combustion of carbon monoxide to form carbon dioxide: $$ \mathrm{CO}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) \quad \Delta H_2=-283.3 \mathrm{~kJ/mol} $$ The enthalpy changes for these reactions, ∆H\(_1\) and ∆H\(_2\), are given.

Formulate the desired reaction

The desired reaction is: $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H_{x} $$ Our goal is to find the enthalpy change for this reaction, ∆H\(_x\).

Construct the Hess's Law cycle

Using the given reactions and the desired reaction, we can construct a Hess's Law cycle: 1. Multiply the first given reaction by 2 and reverse the direction: $$ 2\mathrm{CO}_2(g) \longrightarrow 2\mathrm{C}(s) + 2\mathrm{O}_{2}(g) \qquad 2\Delta H_1 $$ 2. Multiply the second given reaction by 2: $$ 2\mathrm{CO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2\mathrm{CO}_2(g) \qquad 2\Delta H_2 $$ Now, add these modified reactions to get the desired reaction: $$ 2\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H_x $$ The overall enthalpy change, ∆H\(_x\), will be equal to the sum of the enthalpy changes of the modified reactions.

Calculate the enthalpy change (∆H) for the desired reaction

Use the enthalpy changes to find ∆H\(_x\): $$ \Delta H_x = 2(\Delta H_1) + 2(\Delta H_2) $$ $$ \Delta H_x = 2(-393.7 \mathrm{~kJ/mol}) + 2(-283.3 \mathrm{~kJ/mol}) $$ $$ \Delta H_x = -787.4 \mathrm{~kJ/mol} - 566.6 \mathrm{~kJ/mol} $$ $$ \Delta H_x = -1354 \mathrm{~kJ/mol} $$ Therefore, the enthalpy change for the reaction 2 C(s) + O\(_2\)(g) → 2 CO(g) is -1354 kJ/mol.

Key concepts

Enthalpy of Combustion

The enthalpy of combustion is a vital concept in thermochemistry. It measures the energy released when a substance completely burns in oxygen. This process transforms reactants, typically a fuel and oxygen, into combustion products, primarily carbon dioxide and water. The combustion reactions provided in the exercise showcase the enthalpy of combustion for two substances:

• Solid carbon burning to form carbon dioxide, with an enthalpy change of \(\Delta H_1 = -393.7 \, \mathrm{kJ/mol}\).
• Carbon monoxide burning to form carbon dioxide, with an enthalpy change of \(\Delta H_2 = -283.3 \, \mathrm{kJ/mol}\).

In a chemical reaction, if the result is a negative enthalpy change, it signifies that the reaction is exothermic, releasing heat. The formula for combustion reactions is crucial for understanding how elements, such as carbon, transform during the process.
By using the enthalpy of combustion, chemists calculate the energy changes in reactions, playing a key role in designing energy-efficient systems.

Enthalpy Change

Enthalpy change, represented as \(\Delta H\), is a measure of heat absorbed or released during a chemical reaction at constant pressure. It indicates the energy difference between reactants and products in a reaction. In the exercise, the students are tasked with finding the enthalpy change for forming carbon monoxide from carbon. This calculation uses Hess's Law, which states that the total enthalpy change for a reaction is the same, regardless of the path taken, as long as initial and final conditions are constant. To apply Hess's Law:

• We compile the known reactions and their \(\Delta H\) values.
• Adjust the reactions to match the desired overall reaction.
• Sum the enthalpy changes, taking into account their stoichiometric coefficients.

The practice of using Hess's Law helps students understand how to manipulate chemical equations to find unknown enthalpy changes, developing critical problem-solving skills in thermochemistry.

Carbon Monoxide

Carbon monoxide (CO) is a colorless, odorless gas that is considered hazardous, as it binds with hemoglobin in blood more effectively than oxygen, depriving the body of essential oxygen. It is a byproduct of incomplete combustion, which occurs when insufficient oxygen is present to convert carbon completely to carbon dioxide. In the exercise, carbon monoxide plays a central role. Students calculate the enthalpy change for producing CO from carbon and oxygen using given combustion data. This calculation is crucial for understanding the energetics involved in CO formation, which is significant in combustion processes that occur, for instance, in car engines or industrial applications.
Ensuring complete combustion is important to minimize CO production, thereby reducing air pollution and health risks associated with carbon monoxide emissions.

Carbon Dioxide

Carbon dioxide (CO2) is a naturally occurring gas that is vital for life on Earth. It is a major product of combustion reactions and a significant greenhouse gas, contributing to the warming of the planet. In the context of the exercise, carbon dioxide is the final product of both combustion reactions provided:

• From solid carbon and oxygen, representing the complete oxidation process.
• From carbon monoxide and additional oxygen, illustrating intermediate oxidation stages.

Understanding the formation of CO2 in these reactions is important in various fields, including environmental science and industrial processes, as it influences air quality and climate change considerations.
The calculations from the exercise offer insights into how energy is transformed during these conversions, emphasizing the importance of CO2 management in maintaining ecological balance.