Question

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\); (b) \(\mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\) Explain.

Short answer

We would expect C2H6(g) to have a higher standard molar entropy than C2H2(g) due to its higher number of atoms and molecular complexity. Similarly, we would expect CO2(g) to have a higher standard molar entropy than CO(g) for the same reasons.

Step-by-step solution

(a) Comparing standard molar entropy of C2H2(g) and C2H6(g)

First, we need to analyse their molecular structure. C2H2, or ethyne, is a simple hydrocarbon with two carbon atoms triple-bonded together and one hydrogen atom bonded to each carbon atom. In contrast, C2H6, or ethane, is a more complex hydrocarbon in which two carbon atoms are bonded together and each carbon atom is bonded to three hydrogen atoms. Since C2H6 has more atoms and is more complex, its molecules can arrange themselves in more ways, leading to a higher degree of disorder. Therefore, we would expect C2H6(g) to have a higher standard molar entropy than C2H2(g).

(b) Comparing standard molar entropy of CO2(g) and CO(g)

Now, let's analyse the molecular structure of these two compounds. CO2, or carbon dioxide, is a linear molecule with a carbon atom double-bonded to two oxygen atoms, one on each side. On the other hand, CO, or carbon monoxide, is also a linear molecule but with a carbon atom triple-bonded to only one oxygen atom. Since CO2 has more atoms and is slightly more complex than CO, we would expect CO2(g) to have a higher standard molar entropy than CO(g).

Key concepts

Entropy and Molecular Complexity

Entropy is a fundamental concept in thermodynamics, relating to the measure of disorder or randomness in a system. The more ways in which the particles of a substance can be arranged without changing the overall state, the higher the entropy. When it comes to molecular complexity, this concept becomes particularly interesting. Complex molecules like those with multiple atoms and varied configurations can have more microstates - that is, different ways the molecules can be arranged. This multiplicity leads to increased entropy.

For instance, consider a complex hydrocarbon versus a simpler one; the complex one will typically have a greater number of molecular configurations and thus, a higher standard molar entropy. This relationship is critical when comparing the entropy values of substances, as it underpins the reason why molecules with a larger number of atoms and potential interactions generally have higher entropy values.

Comparison of Molar Entropy

When tasked with comparing the standard molar entropy between different substances, it's vital to consider both the number of particles and their structural complexity. Standard molar entropy is an intrinsic property of a substance that indicates how much energy per mole is dispersed at a standard temperature. The more complex the molecule, the greater the number of possible states it can have, which correlates with higher entropy.

Looking at hydrocarbons with equal numbers of carbon atoms, the one with greater molecular complexity, meaning more bonds or more varied types of bonds, will typically exhibit a higher standard molar entropy. Similarly, for molecules with the same number of atoms, variations in bonding and structure can lead to different entropies. This is why substances with larger or more complex molecular structures often have higher standard molar entropies than their simpler counterparts.

Molecular Structure and Entropy

Molecular structure has a profound effect on a substance's entropy. The geometry and bonding patterns of a molecule dictate the number of ways the molecule can exist in different energy states or spatial orientations. Linear molecules, for example, have fewer possible orientations than non-linear ones, and this constrains their possible microstates.

A molecule with double or triple bonds may have a different range of motion and interaction potential compared to one with only single bonds, impacting the entropy. Additionally, symmetry within a molecule can decrease the number of distinguishable microstates, thus affecting its entropy. As we delve into molecules of increasing size and complexity, the entropy considerations become more intricate. By breaking down the molecular structure, we can better understand and predict the entropy behavior of substances.