Problem 27 - Basic Principles of Organic Chemistry

Question

The entropy change \(\Delta S^{0}\) for the formation of chloroethane by chlorination of ethane is \(+0.5 \mathrm{e} . \mathrm{u}\), and for the formation of chloroethane by combination of hydrogen chloride with ethene \(\Delta S^{0}\) is \(-31\) e.u. Explain. $$ \begin{array}{ll} \mathrm{CH}_{3}-\mathrm{CH}_{3}+\mathrm{Cl}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{HCl} & \Delta S^{0}=+0.5 \mathrm{e.u} \\\ \mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{HCl} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl} & \Delta S^{0}=-31 \mathrm{e.u} \end{array} $$

Step-by-Step Solution

Answer

Reaction 1 has a slight increase in entropy; reaction 2 has a large decrease in entropy due to the change in the number of molecules.

Step 1: Understanding the Concept of Entropy

Entropy is a measure of the disorder or randomness in a system. When the number of molecules in a system increases, typically entropy increases. Conversely, when the number of molecules decreases, entropy tends to decrease.

Step 2: Identifying Reaction 1

The reaction \[ \mathrm{CH}_{3}-\mathrm{CH}_{3} + \mathrm{Cl}_{2} \rightarrow \mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{Cl} + \mathrm{HCl} \]has an entropy change \( \Delta S^{0} = +0.5 \mathrm{e.u} \). This slight positive entropy change suggests that the increase in disorder slightly outweighs any decrease in the system.

Step 3: Analyzing Reaction 1

In the first reaction, two molecules (ethane and chlorine) convert into two different molecules (chloroethane and HCl). Since the number of total molecules does not change and the nature of the products only slightly increases randomness, entropy change is slightly positive.

Step 4: Identifying Reaction 2

The reaction \[ \mathrm{CH}_{2}=\mathrm{CH}_{2} + \mathrm{HCl} \rightarrow \mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{Cl} \]has an entropy change \( \Delta S^{0} = -31 \mathrm{e.u} \). This negative entropy change indicates a decrease in the disorder of the system.

Step 5: Analyzing Reaction 2

In the second reaction, two reactant molecules (ethene and HCl) combine to form a single product molecule (chloroethane). This reduction in the number of gas molecules significantly decreases the entropy, resulting in a large negative change in entropy.

Step 6: Conclusion

Reaction 1 results in a slight overall increase in disorder (positive entropy change) due to forming two different molecules from two others. Reaction 2 results in a decrease in disorder (negative entropy change) because two reactants form one product, reducing gaseous molecules.

Key Concepts

Entropy Change

Entropy is a key concept in thermodynamics that refers to the disorder or randomness within a chemical system. It is represented by \( \Delta S \). In chemical reactions, the change in entropy reflects how the system's molecular arrangement becomes more or less ordered.
For example, reactions that result in more gaseous molecules generally show an increase in entropy due to increased possible arrangements. Conversely, when a reaction produces fewer molecules, it often leads to a decrease in entropy.
The value of \( \Delta S^{0}\) may be positive or negative depending on these changes. In the formation of chloroethane, different reactions show varying entropy changes, which are crucial for understanding how the molecular structure and behavior are affected.

Chlorination of Ethane

The chlorination of ethane involves the chemical reaction where ethane (\( \C_{2}H_{6} \)) reacts with chlorine (\( \Cl_{2} \)) to form chloroethane (\( \C_{2}H_{5}Cl \)) and hydrogen chloride (\( \HCl \)). This reaction is represented by:

• \( \C_{2}H_{6} + Cl_{2} ightarrow C_{2}H_{5}Cl + HCl \)

The entropy change (\( \\Delta S^{0} \)) for this reaction is \(+0.5 \) e.u. This small positive change suggests that the overall disorder of the system slightly increases.
Notably, the number of molecules remains constant, but the chemical alteration gives rise to new types of molecules, slightly boosting the system's randomness.

Chloroethane Formation

Chloroethane can be formed through different pathways, influencing the entropy change. In one alternative route, ethene (\( \CH_{2}=CH_{2} \)) reacts with hydrogen chloride:

• \( \CH_{2}=CH_{2} + HCl ightarrow C_{2}H_{5}Cl \)

This process entails a significant change in entropy, calculated as \( \\Delta S^{0} \ = -31 \) e.u. as opposed to other methods.
Here, two reactant molecules combine to form one product, decreasing the number of gas particles in the system. This substantial reduction in gaseous particles results in a large negative entropy change, indicating a significant decrease in disorder.

Chemical Reaction Analysis

Analyzing chemical reactions reveals how different processes and reactions impact entropy and disorder. In the reactions leading to the formation of chloroethane, we observe varied entropy changes:

• In chlorination of ethane, the slight positive entropy change indicates minor increase in molecular randomness.
• Conversely, the combination of ethene and HCl, leading to a significant negative entropy change, suggests a large decrease in molecular disorder due to fewer gas molecules formed.

This analysis helps students understand how the nature and number of molecules produced or consumed in reactions contribute to the system's overall energy and entropy. Crucially, accurate prediction of entropy changes assists in predicting reaction spontaneity and feasibility.