Problem 67 - Chemistry An Atoms First Approach

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 $$2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g)$$

Step-by-Step Solution

Answer

The enthalpy change for the reaction \(2C(s) + O_{2}(g) \rightarrow 2CO(g)\) is \(\Delta H = 220.8 \mathrm{kJ/mol}\).

Step 1: Write the given reactions and enthalpy changes

We have the following reactions and the corresponding enthalpy changes: 1. C(s) + O2(g) → CO2(g) ΔH1 = -393.7 kJ/mol C 2. CO(g) + 1/2 O2(g) → CO2(g) ΔH2 = -283.3 kJ/mol CO Our goal is to find the enthalpy change (ΔH) for the reaction: 2C(s) + O2(g) → 2CO(g).

Step 2: Manipulate the given reactions to align with the target reaction

First, we need to determine how the given reactions can be combined or manipulated to match the target reaction. To get 2CO(g) as a product, we should modify the second reaction: Given Reaction: CO(g) + 1/2 O2(g) → CO2(g) ΔH2 = -283.3 kJ/mol CO Multiply the reaction by 2: New Reaction: 2CO(g) + O2(g) → 2CO2(g) ΔH2' = 2(-283.3 kJ/mol CO) = -566.6 kJ Now, we should manipulate the first reaction to have CO2(g) as a reactant: Given Reaction: C(s) + O2(g) → CO2(g) ΔH1 = -393.7 kJ/mol C Reverse the reaction: New Reaction: CO2(g) → C(s) + O2(g) ΔH1' = -(-393.7 kJ/mol C) = 393.7 kJ/mol C

Step 3: Use Hess's Law to calculate the enthalpy change of the target reaction

Now we can use Hess's Law, which states that the enthalpy change of a reaction is the sum of the enthalpy changes of the individual reactions. Add the modified reactions from Step 2 to get the target reaction: 2CO(g) + O2(g) → 2CO2(g) ΔH2' = -566.6 kJ 2CO2(g) → 2C(s) + 2O2(g) ΔH1' = 2(393.7 kJ/mol C) = 787.4 kJ/mol C Sum: 2C(s) + O2(g) → 2CO(g) ΔH = ΔH1' + ΔH2'

Step 4: Calculate the enthalpy change for the target reaction

Now we will add the enthalpy changes of the modified reactions: ΔH = ΔH1' + ΔH2' ΔH = 787.4 kJ + (-566.6 kJ) ΔH = 220.8 kJ/mol The enthalpy change for the reaction 2C(s) + O2(g) → 2CO(g) is ΔH = 220.8 kJ/mol.

Key Concepts

Hess's Law

Hess’s Law is a principle in chemistry that helps us calculate the enthalpy change of a chemical reaction, even when it might be difficult to measure directly. The law states that if a reaction can be expressed as the sum of two or more reactions, the total enthalpy change for the reaction is the sum of the enthalpy changes for each step. This property arises because enthalpy is a state function, meaning it depends only on the initial and final states of a system, not the path taken to get there.

To illustrate, think of Hess’s Law like a journey. Whether you travel directly or take several stops, the total change in your position is the same. In our example problem, we combined two known reactions involving carbon and carbon monoxide to determine the enthalpy change for forming carbon monoxide from carbon. By reversing and multiplying known reactions, we created a pathway to match our desired reaction and applied Hess's Law to find the overall enthalpy change.

This concept is extremely useful because it allows us to calculate changes in enthalpy (\( \Delta H \)) without needing to directly experiment with potentially dangerous or impractical reaction conditions.

Enthalpy of Combustion

Enthalpy of combustion is the heat change that occurs when one mole of a substance completely reacts with oxygen under standard conditions. It is typically expressed in kilojoules per mole (kJ/mol) and is always a negative value because combustion is an exothermic process, releasing energy to the surroundings.

In our exercise, we dealt with two combustion reactions: the combustion of carbon to form carbon dioxide and the combustion of carbon monoxide to form carbon dioxide. Knowing the enthalpy changes for these combustion reactions allowed us to use them in Hess's Law to find the enthalpy change for a different reaction.

Whenever you come across combustion reactions, remember that they play a crucial role in energy production, like burning fuels in engines or power plants. Understanding the energy changes involved helps us evaluate the efficiency and environmental impact of fuels.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to transform substances. They follow certain laws, which helps predict the outcome of reactions and the energy changes involved. In thermochemistry, we are often concerned with the enthalpy change (\( \Delta H \)) of a reaction - this tells us whether a reaction absorbs energy (endothermic) or releases energy (exothermic).

Our example highlights a specific case where we want to convert carbon and oxygen into carbon monoxide. To solve for the unknown enthalpy change, we used known reactions and manipulated them according to Hess's Law.

Understanding chemical reactions is crucial for fields like biochemistry, materials science, and environmental science. These processes are foundational to producing food, medicines, and sustainable energy sources.

Thermochemistry

Thermochemistry is a branch of chemistry that deals with the heat involved in chemical processes. It helps us understand how energy flows during chemical reactions, allowing us to predict how a reaction will behave or how much energy it will produce or require.

In thermochemistry, reactions are analyzed in terms of enthalpy, entropy, and free energy. However, in many beginner courses, the focus is predominantly on enthalpy. The exercise problem we tackled helps underline how theorized concepts such as enthalpy can be applied to calculate unknowns in real-world scenarios.

By interpreting energy changes in reactions, chemistry enables innovations in energy production, like developing better batteries or creating new materials with desired thermal properties. Practical applications of thermochemistry potentially improve the quality of life by increasing efficiencies and reducing environmental impacts.