Problem 35 - Chemistry The Molecular Science

Question

Estimate \(\Delta_{1} H^{\circ}\) for the conversion of \(1 \mathrm{~mol}\) carbon monoxide to carbon dioxide by combination with molecular oxygen. Is this reaction exothermic or endothermic?

Step-by-Step Solution

Answer

The reaction is exothermic with \(\Delta_{1} H^{\circ} = -283 \text{ kJ/mol}\).

Step 1: Write Down the Reaction

The reaction for the conversion of carbon monoxide (CO) to carbon dioxide (CO₂) by combining with molecular oxygen (O₂) is:\[2 ext{ CO} (g) + ext{O}_2 (g) ightarrow 2 ext{ CO}_2 (g)\]

Step 2: Calculate the Standard Enthalpy Change

To find \(\Delta_{1} H^{\circ}\) for 1 mole of CO, we need the standard enthalpies of formation (∆H⁰ₙ) for CO and CO₂.- \(\Delta_f H^{\circ} ( ext{CO}) = -110.5 \text{ kJ/mol}\)- \(\Delta_f H^{\circ} ( ext{CO}_2) = -393.5 \text{ kJ/mol}\)Using the formula for the reaction's standard enthalpy change:\[\Delta_{r} H^{\circ} = \sum (\Delta_f H^{\circ} \text{ of products}) - \sum (\Delta_f H^{\circ} \text{ of reactants})\]Substitute the values:\[\Delta_{1} H^{\circ} = [2(-393.5)] - [2(-110.5)]\]\[= -787 + 221\]\[= -566 \text{ kJ for 2 moles}; \ -283 \text{ kJ for 1 mole of CO}\]

Step 3: Determine Exothermic or Endothermic

Since \(\Delta_{1} H^{\circ} = -283 \text{ kJ/mol}\) is negative, the reaction is exothermic.

Key Concepts

Enthalpy of Reaction

The enthalpy of reaction, denoted as \( \Delta_r H^{\circ} \), indicates the heat change during a chemical reaction at standard conditions. Standard conditions are often at a pressure of 1 atm and a temperature of 25°C (298 K). This value helps understand whether a reaction absorbs or releases heat. Enthalpy, represented by the symbol \( H \), is akin to measuring the total "heat content" in a system. In chemistry, we are often interested in the change in enthalpy, rather than the total enthalpy itself. Changes in enthalpy during chemical reactions can signal the energy transfers as bonds break and new bonds form. The enthalpy of reaction can be calculated using the formula:

• \( \Delta_{r} H^{\circ} = \sum (\Delta_f H^{\circ} \text{ of products}) - \sum (\Delta_f H^{\circ} \text{ of reactants}) \)

This formula implies that you sum up the standard enthalpy of formation values for all products and subtract the sum of the standard enthalpy of formation for all reactants. The resulting value quantifies the shift in energy, setting the stage for determining if the reaction is exothermic or endothermic.

Exothermic and Endothermic Reactions

Chemical reactions are often categorized by how they transfer energy, specifically heat. Two primary categories describe these energy changes: exothermic and endothermic reactions.

• Exothermic Reactions: These reactions release heat into the surroundings. They are commonly felt because they increase the temperature of the surroundings (e.g., burning wood). A negative value for \( \Delta_{1} H^{\circ} \) indicates an exothermic process, as energy is expelled.
• Endothermic Reactions: These reactions absorb heat from the surroundings, thus reducing the temperature of the environment (e.g., melting ice). For these reactions, \( \Delta_{1} H^{\circ} \) is positive, indicating an uptake of energy from the surrounding area.

Knowing whether a reaction is exothermic or endothermic can guide us in predicting the energy efficiency of energy conversion and further application in real-world processes.

Standard Enthalpy of Formation

The standard enthalpy of formation, \( \Delta_f H^{\circ} \), is a crucial concept used to compute the enthalpy of reaction. It represents the change in enthalpy during the formation of 1 mole of a substance from its elements in their standard states, measured at 1 atm and 25°C.

• Standard State: This refers to the most stable form of an element or compound at standard conditions.
• Reference Points: The standard enthalpy of formation for a pure element in its reference state (like O2, N2) is zero. This serves as the baseline. Values for compounds are typically based on experimental data and vary depending on the specific substance.

In the exercise, the standard enthalpies of formation for \( \text{CO} \) and \( \text{CO}_2 \) were used to calculate the enthalpy of reaction. Understanding \( \Delta_f H^{\circ} \) helps chemists predict the energy changes involved in reactions and assists in engineering processes that harness chemical reactions.