Problem 25 - Chemistry: An Atoms-Focused Approach

Question

Rank the compounds in each of the following groups in order of increasing standard molar entropy \(\left(S^{\circ}\right):\). a. \(\mathrm{CH}_{4}(g), \mathrm{CF}_{4}(g),\) and \(\mathrm{CCl}_{4}(g)\) b. \(\mathrm{CH}_{2} \mathrm{O}(g), \mathrm{CH}_{3} \mathrm{CHO}(g),\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}(g)\) c. \(\mathrm{HF}(g), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{NH}_{3}(g)\)

Step-by-Step Solution

Answer

Question: Rank the following sets of compounds in terms of their standard molar entropy (S°): a. CH4(g), CF4(g), CCl4(g) b. CH2O(g), CH3CHO(g), CH3CH2CHO(g) c. HF(g), H2O(g), NH3(g) Answer: a. CH4(g) < CF4(g) < CCl4(g) b. CH2O(g) < CH3CHO(g) < CH3CH2CHO(g) c. HF(g) < H2O(g) < NH3(g)

Step 1: a. CH4(g), CF4(g), and CCl4(g)

To rank these compounds, we will consider factors such as molecular weight, molecular complexity, and atomic size. Generally, entropy increases with complexity and the number of atoms in the compound. In this case, we have CH4(g), CF4(g), and CCl4(g). They all have a central carbon atom, but the surrounding atoms vary, which leads to variation in molecular weight and complexity. We can see that: - CH4(g) has the lowest molecular weight with four hydrogen atoms around the carbon atom - CF4(g) has a higher molecular weight with four fluorine atoms - CCl4(g) has the highest molecular weight with four chlorine atoms. Since standard molar entropy increases with molecular weight and complexity, we can rank these compounds as follows: \(\mathrm{CH}_{4}(g) < \mathrm{CF}_{4}(g) < \mathrm{CCl}_{4}(g)\).

Step 2: b. CH2O(g), CH3CHO(g), and CH3CH2CHO(g)

As mentioned earlier, standard molar entropy (S°) increases with molecular complexity and the number of atoms in the compound. In this case, we have CH2O(g), CH3CHO(g), and CH3CH2CHO(g). The number of atoms increases from CH2O to CH3CH2CHO, which indicates an increase in molecular complexity. Therefore, we can rank these compounds based on their standard molar entropy: \(\mathrm{CH}_{2}\mathrm{O}(g) < \mathrm{CH}_{3}\mathrm{CHO}(g) < \mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{CHO}(g)\)

Step 3: c. HF(g), H2O(g), and NH3(g)

In this case, we have HF(g), H2O(g), and NH3(g). We can rank these based on their molecular complexity. While they all have three atoms, their atomic arrangements are different. Hydrogen bonding is also a factor to consider, as molecules with hydrogen bonding have lower entropy due to the higher level of organization. From these factors, we can rank the compounds based on their standard molar entropy: - HF(g) has the lowest entropy as it has a single hydrogen bond and lower complexity - H2O(g) has two hydrogen bonds and higher complexity, but the bonds reduce its entropy - NH3(g) has three hydrogen atoms and a nitrogen atom, which increases its complexity and leads to the highest entropy among the three compounds Thus, the ranking is: \(\mathrm{HF}(g) < \mathrm{H}_{2}\mathrm{O}(g) < \mathrm{NH}_{3}(g)\).

Key Concepts

Molecular Complexity

Molecular complexity refers to the structure and intricacy of molecules. As molecules become more complex, they generally have more atoms and bonds, allowing for a greater variety of movements and vibrations. This increase in potential energy states leads to higher entropy, a measure of disorder in a system.

When comparing compounds like \[ \text{CH}_4(g), \text{CF}_4(g), \text{and CCl}_4(g), \]all these have tetrahedral geometries but vary in complexity due to different atoms. **CH\(_4\)** is less complex with only hydrogen atoms. In contrast, **CCl\(_4\)** is more complex because chlorine is larger and can vibrate in more ways than hydrogen, contributing to higher entropy.

**Key points:**

• More atoms and types of atoms in a molecule often mean higher molecular complexity.
• Higher molecular complexity results in more vibrational modes.
• Increases in complexity typically lead to higher entropy because the molecule can assume more energetic states.

Molecular Weight

Molecular weight, or molar mass, is the sum of the atomic weights of all atoms in a molecule. Higher molecular weight often correlates with greater standard molar entropy due to the increased potential for atomic and molecular motion.

For the compounds: \[ \text{CH}_4(g), \text{CF}_4(g), \text{and CCl}_4(g), \]\( \text{CH}_4 \) has the lowest molecular weight, and \( \text{CCl}_4 \) has the highest. This is because chlorine atoms are heavier than fluorine and hydrogen atoms, thus contributing to an increased number of energy levels the molecule can access.

**Consider this:**

• More massive atoms add to a molecule's weight, affecting its entropy.
• As molecular weight increases, the entropy tends to increase because of higher density of vibrational states.
• A molecule with a very high molecular weight, like CCl\(_4\), generally shows higher entropy than lighter molecules.

Hydrogen Bonding

Hydrogen bonding is a special type of interaction that occurs when hydrogen is covalently bound to electronegative atoms like oxygen, nitrogen, or fluorine. It significantly affects the behavior of molecules, including their standard molar entropy.

In the group of molecules\[ \text{HF}(g), \text{H}_2\text{O}(g), \text{and NH}_3(g), \]hydrogen bonds play a key role in determining entropy. **HF** forms a strong hydrogen bond, leading to a more ordered, less entropic state. **H\(_2\)O** can form multiple hydrogen bonds, which again lower its entropy compared to simpler molecules with similar atomic counts, like **NH\(_3**. However, the hydrogen bonding also adds complexity, which can counterbalance the reduction of entropy to some extent.

**Remember:**

• Hydrogen bonds increase molecular stability and order, reducing entropy.
• Compounds capable of multiple hydrogen bonds have unique entropy characteristics.
• For example, H\)_2\(O’s hydrogen bonding makes it more ordered than NH\)_3$, affecting its entropy ranking.