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Isomersare moleculesthat havethesamechemical formula but different arrangements of atoms, as shown here for two isomers of pentane, \(\mathrm{C}_{5} \mathrm{H}_{12} .\) (a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain. (b) Which isomer do you expect to have the higher standard molar entropy? Explain. \([\) Section 19.4\(]\)

Short Answer

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(a) The difference in the enthalpy of combustion between the two isomers would not be significant because they have similar bond energies in their structures. (b) The linear isomer (n-pentane) is expected to have a higher standard molar entropy than the branched isomer (2,2-dimethylpropane) due to its flexible structure, which allows for more conformational possibilities and contributes to higher disorder in the system.

Step by step solution

01

Understanding Enthalpy of Combustion #

Enthalpy of combustion is the heat released when one mole of a substance undergoes complete combustion with oxygen at constant pressure. In this case, the combustion reaction for pentane isomers will be: \(C_5H_{12} + \frac{15}{2} O_2 \rightarrow 5 CO_2 + 6 H_2O\) Both isomers have the same formula (C5H12), so they will have the same number of moles of reactants and products. Therefore, we will analyze the bond energy to find the difference between their enthalpy of combustion.
02

Analyzing Bond Energy #

The enthalpy change in a chemical reaction depends mainly on the difference in bond energies between the reactants and the products. The combustion of both isomers will lead to the formation of CO2 and H2O, which have the same bond energies. Since both isomers have the same chemical formula, they will have similar bond energies in terms of carbon-carbon and carbon-hydrogen bonds.
03

Answer for Part (a) #

Based on the analysis of bond energies, we can expect that the difference in the enthalpy of combustion between the two isomers would not be significant because they have similar bond energies in their structures.
04

Understanding Entropy #

Entropy is a thermodynamic property that represents the randomness or disorder of a system. In the context of isomers, entropy is influenced by the number and nature of atoms, molecular geometry, and molecular flexibility. The higher the entropy, the higher the disorder in the system.
05

Analyzing Isomers' Structure #

We are given two isomers of pentane that have different arrangements of atoms: 1. n-pentane (linear chain): CH3-CH2-CH2-CH2-CH3 2. 2,2-dimethylpropane (branched chain): (CH3)3C-CH3 Isomer 1 has a linear structure, which can rotate around carbon-carbon single bonds, resulting in more conformational possibilities. On the other hand, isomer 2 has a more static structure due to the central carbon being bonded to three identical methyl groups.
06

Answer for Part (b) #

The linear isomer (n-pentane) is expected to have a higher standard molar entropy than the branched isomer (2,2-dimethylpropane) because of its flexible structure, which allows for more conformational possibilities and therefore contributes to higher disorder in the system.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Enthalpy of Combustion
Enthalpy of combustion refers to the amount of energy released as heat when one mole of a substance combusts completely in the presence of oxygen at constant pressure. This process results in the formation of common combustion products such as carbon dioxide and water. The reaction for pentane isomers combusting in excess oxygen follows the equation:\[C_5H_{12} + \frac{15}{2} O_2 \rightarrow 5 CO_2 + 6 H_2O\]In the context of isomers, like the ones you're familiar with, pentane isomers will have similar enthalpy values because they share the same molecular formula. - Since the reaction products are the same, the overall difference in energy released is minimal.- Because bond energies for both the reactant isomers are similar, there's no significant difference in the enthalpy of combustion.Thus, despite different arrangements, the heat released in the combustion of these isomers remains almost the same.
Standard Molar Entropy
Entropy, a thermodynamic property, measures the degree of randomness or disorder within a system. Standard molar entropy refers to this property quantified for one mole of a substance under standard conditions. When you look at isomers, differences in molecular arrangements can significantly influence their entropy. Let's delve into the isomers of pentane: - n-Pentane has a linear structure, promoting greater rotational freedom and flexibility. Its molecules can adopt various conformations, which enhances disorder. - On the other hand, 2,2-dimethylpropane is branched and compact, limiting its conformational variability. Due to its more flexible structure, n-pentane possesses higher standard molar entropy than 2,2-dimethylpropane. A more disordered state means higher entropy for n-pentane.
Bond Energy
Bond energy is key to understanding reaction processes, such as combustion. It refers to the energy required to break one mole of a specifc bond in molecules. For isomers, the focus lies in the nature of bonds rather than the arrangement. - Isomers have identical types of bonds, such as carbon-carbon and carbon-hydrogen bonds, so their bond energies are similar. - During combustion, the critical bonds in both pentane isomers break to form carbon dioxide and water. This similarity in bond energies for both isomers contributes to their comparable enthalpy of combustion, as noted in previous sections. The rearrangement of atoms does not result in significant bond energy difference, retaining similar energy release during reactions.
Molecular Structure
The molecular structure of isomers is key to their distinct properties, even though they share molecular formulas. It illustrates how atoms are arranged spatially, affecting various parameters such as entropy. Consider the two isomers of pentane: - **n-Pentane:** Features a linear molecular structure, allowing for more motion within its bonds, leading to potential increased conformational changes. - **2,2-Dimethylpropane:** Exhibits a branched and more compact form, restricting its movement and flexibility. The arrangement impacts entropy by enabling or disabling molecular vibrations and rotations. Structures that allow more rotational freedom often result in more disordered systems. Thus, the linear setup of n-pentane's carbon atoms grants its molecules higher uniformity and entropy as opposed to its branched counterpart.

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Most popular questions from this chapter

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