Problem 72 - Chemistry The Molecular Science

Question

These reaction enthalpies can be measured: \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) \(\Delta_{\mathrm{r}} H^{\circ}=-1411.1 \mathrm{~kJ} / \mathrm{mol}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)\) \(\Delta_{t} H^{\circ}=-1367.5 \mathrm{~kJ} / \mathrm{mol}\) Use these values and Hess's law to determine the reaction enthalpy for $$ \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) $$

Step-by-Step Solution

Answer

The reaction enthalpy is \(-43.6 \mathrm{~kJ/mol}\).

Step 1: Write the target reaction

The target reaction we need to find the enthalpy for is:\[ \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) \]

Step 2: Identify base reactions and their enthalpies

We are given two reactions with their enthalpies:1. \( \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \) with \( \Delta_{\mathrm{r}} H^{\circ} = -1411.1 \mathrm{~kJ/mol} \).2. \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \) with \( \Delta_{t} H^{\circ} = -1367.5 \mathrm{~kJ/mol} \).

Step 3: Reverse the ethanol reaction

To use Hess's law, we need to reverse the ethanol combustion reaction to form ethanol from its combustion products:\[ 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) +3 \mathrm{O}_{2}(\mathrm{~g}) \]The enthalpy change for this reversed reaction is the opposite of that given, so:\[ \Delta H = +1367.5 \mathrm{~kJ/mol} \]

Step 4: Apply Hess's Law

According to Hess's law, we can add reactions and their enthalpy changes to find the enthalpy for the target reaction. Adding the reversed ethanol reaction to the ethylene combustion reaction:\[(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)) + (2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) +3 \mathrm{O}_{2}(\mathrm{~g}))\]

Step 5: Cancel out common terms

After combining the reactions, cancel out the common products and reactants:- \( 2 \mathrm{CO}_{2}(\mathrm{~g}) \) and \( 3 \mathrm{O}_{2}(\mathrm{~g}) \) appear on both sides, so they can be eliminated.This simplifies to the target reaction:\[ \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g}) + \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) \]

Step 6: Compute net enthalpy change

We add the enthalpy changes:- \( \Delta_{\mathrm{r}} H^{\circ} = -1411.1 \mathrm{~kJ/mol} \) for ethylene combustion.- \( \Delta H = +1367.5 \mathrm{~kJ/mol} \) for reversed ethanol reaction. Using Hess's law: \[ \Delta H = (-1411.1) + 1367.5 = -43.6 \mathrm{~kJ/mol} \]

Step 7: Conclusion

The enthalpy change for the reaction \( \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g}) + \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) \) is \(-43.6 \mathrm{~kJ/mol}\).

Key Concepts

Reaction Enthalpy

The concept of reaction enthalpy is central to understanding energy changes in chemical reactions. Reaction enthalpy, also known as the enthalpy change, is the heat released or absorbed during a chemical reaction at constant pressure. It is denoted as \( \Delta_r H^\circ \) and is expressed in kilojoules per mole (kJ/mol).

In the context of the original exercise, we are given two reactions with their associated enthalpy changes. These values, \(-1411.1 \mathrm{~kJ/mol}\) for the combustion of ethylene and \(-1367.5 \mathrm{~kJ/mol}\) for ethanol, provide a quantifiable measure of the energy dynamics in the reaction.

Using these values and Hess's Law, one can determine the overall enthalpy change for a target reaction, which is a combination of the given reactions. Reaction enthalpy is an essential factor that influences reaction spontaneity and feasibility in thermodynamic processes.

Combustion Reactions

Combustion reactions play a fundamental role in energy exchange processes. A combustion reaction involves a substance (often a hydrocarbon like ethylene or ethanol) reacting with oxygen to produce carbon dioxide and water while releasing energy in the form of heat.

In the reactions given in the exercise, both ethylene and ethanol undergo combustion, highlighting their characteristics as exothermic reactions. This means they release energy, which is why their reaction enthalpies are negative.

Exothermic combustion reactions are vital in various applications, from engines to heating systems, due to their efficiency in converting chemical energy into thermal energy. The study of these reactions not only aids in understanding energy outputs but also has practical implications in designing processes that utilize the heat released.

Thermodynamics

Thermodynamics is the study of energy and its transformations. It is a broad field, but when discussing chemical reactions, thermodynamics helps us understand how energy is transferred within a system or between systems.

Hess's Law, a key principle in thermodynamics, asserts that the total enthalpy change of a reaction is independent of the pathway taken from reactants to products. This means that whether a reaction occurs in one step or several, the total enthalpy change remains the same.

This principle enables us to calculate the enthalpy change of complex reactions using simpler reaction steps with known values. By understanding these thermodynamic principles, students and scientists can predict reaction behaviors, efficiency, and energy requirements, essential for chemical innovation and environmental assessment.