Question

Rank each set of substances in order of increasing standard molar entro py \(\left(S^{\circ}\right) .\) Explain your reasoning. \begin{equation} \mathrm{NH}_{3}(g) ; \mathrm{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \mathrm{He}(g) \end{equation} \begin{equation} \begin{array}{l}{\text { b. } \mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(I) ; \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { c. } \mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)}\end{array} \end{equation}

Short answer

a. He(g) < Ne(g) < NH3(g) < SO2(g) < CH3CH2OH(g); b. H2O(s) < H2O(l) < H2O(g); c. CH4(g) < CF4(g) < CCl4(g).

Step-by-step solution

Understanding Standard Molar Entropy

Standard molar entropy \(S^\circ\) is a measure of the amount of disorder or randomness in a substance. A gas generally has more entropy than a liquid or solid because its particles are more dispersed and in higher energy states. Larger molecules have greater entropies because they possess more complex structures with more vibrations and rotational states. Additionally, more atoms mean more possible arrangements and motions.

Ranking for NH3(g), Ne(g), SO2(g), CH3CH2OH(g), He(g)

To rank these substances, consider the molecular complexity and atomicity. Helium (He) is a monoatomic gas and will have the lowest entropy. Neon (Ne) is also monoatomic, so it will have entropy higher than helium but lower than the molecular gases. Among the molecular gases, ammonia (NH3) with a simpler molecular structure and fewer atoms than sulfur dioxide (SO2) and ethanol (CH3CH2OH) will have lower entropy. Ethanol, being the largest and most complex molecule, will have the highest entropy.

Ranking for H2O(s), H2O(l), H2O(g)

For the different states of water, the order of entropy is based on the physical states. Ice \(H_2O(s)\) as a solid will have the lowest entropy. Liquid water \(H_2O(l)\) has higher entropy due to increased molecular motion, but it's less than water vapor \(H_2O(g)\), which as a gas will have the highest entropy.

Ranking for CH4(g), CF4(g), CCl4(g)

In considering entropy of similar molecular structures, compare the molecular mass and complexity. Methane \(CH_4\) as the simplest molecule will have the lowest entropy. Tetrafluoromethane \(CF_4\) is more complex due to the fluorine atoms, so it will have higher entropy. Tetrachloromethane \(CCl_4\), with the heaviest and most complex structure, will have the highest entropy among the three.

Key concepts

Entropy and Disorder

Entropy is a cornerstone concept in thermodynamics and is often perceived as a measure of disorder or randomness within a system. This idea plays a significant role in understanding how systems evolve over time and why certain processes occur naturally while others do not.

Imagine you have a box filled with colored balls, all neatly arranged by color. If you were to shake the box, the arrangement would likely become less ordered, with the colors mixed up. This is akin to an increase in entropy; the system becomes more disordered. In a thermodynamic sense, entropy is associated with the number of ways we can arrange the components of a system without changing its overall appearance or energy. The principle that entropy increases over time, known as the second law of thermodynamics, explains why energy spreads out if not restrained and why we observe phenomena such as diffusion or the melting of ice into water.

When applying this concept to substances such as Ne(g) or He(g) mentioned in the exercise, their entropy is relatively low due to their simplicity as monoatomic gases. They have fewer ways to be arranged and less internal motion compared to more complex molecules.

Physical States and Entropy

Entropy varies considerably with the physical state of a substance due to differences in molecular motion and arrangement. In solids, particles are closely packed in a regular array and have limited freedom of motion, resulting in lower entropy. As the state changes to liquid, the particles gain more movement, allowing for an intermediate level of entropy.

When the substance is in the gaseous state, as in the case of H2O(g) from the exercise, the molecules are far apart and move randomly at high speeds, leading to a much higher level of entropy compared to its solid or liquid counterparts. This illustrates why water vapor (H2O(g)) has higher entropy than liquid water (H2O(l)) and ice (H2O(s)). The increase in entropy as water transitions from solid to liquid to gas also reflects the increased energy and entropy associated with phase changes, providing insight into the amount of disorder present in different physical states of matter.

Molecular Complexity and Entropy

The complexity of a molecule plays a critical role in determining its standard molar entropy. Larger and more complex molecules, such as ethanol (CH3CH2OH(g)) from the problem set, can have a higher entropy due to the increased number of atoms and variety of possible vibrations, rotations, and translations. These motions contribute to the overall disorder of the system.

In contrast, smaller and simpler molecules like methane (CH4(g)) have fewer vibrational modes and possible configurations, leading to lower entropy values. As molecules grow in size and complexity, as seen with CF4(g) and CCl4(g), they exhibit greater entropies because there are substantially more ways to distribute energy within the molecule. This results in increased disorder and, consequently, higher entropy values. The rankings provided in the exercise solution appropriately reflect the molecular complexity, with the more complex molecules possessing higher entropy than their simpler counterparts.