Problem 25
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
Verified Answer
Question: Arrange the following compounds in order of increasing standard molar entropy (S°) in their respective groups:
Group a: CH4(g), CF4(g), CCl4(g)
Group b: CH2O(g), CH3CHO(g), CH3CH2CHO(g)
Group c: HF(g), H2O(g), NH3(g)
Answer:
Group a: CH4(g) < CCl4(g) < CF4(g)
Group b: CH2O(g) < CH3CHO(g) < CH3CH2CHO(g)
Group c: HF(g) < H2O(g) < NH3(g)
1Step 1: Group a: Ranking of CH4(g), CF4(g), and CCl4(g)
1. Compare molecular masses: CH4 < CCl4 < CF4
2. Compare the number of atoms: All have the same number of atoms.
3. Compare the phases: All are gases.
With these comparisons, the ranking of increasing standard molar entropy is:
CH4(g) < CCl4(g) < CF4(g)
2Step 2: Group b: Ranking of CH2O(g), CH3CHO(g), and CH3CH2CHO(g)
1. Compare molecular masses: CH2O < CH3CHO < CH3CH2CHO
2. Compare the number of atoms and complexity: CH2O < CH3CHO < CH3CH2CHO
3. Compare the phases: All are gases.
With these comparisons, the ranking of increasing standard molar entropy is:
CH2O(g) < CH3CHO(g) < CH3CH2CHO(g)
3Step 3: Group c: Ranking of HF(g), H2O(g), and NH3(g)
1. Compare molecular masses: HF ≈ H2O ≈ NH3 (all are very close)
2. Compare the number of atoms: All have the same number of atoms.
3. Compare the phases: All are gases.
In this case, there is no clear answer based on these factors. However, considering the molecular structure, HF molecules can't form hydrogen bonding in gas phase as it can in liquid phase. The NH3 molecule is more complex than the H2O molecule, and also forms more complex H-bond.
With these comparisons, the ranking of increasing standard molar entropy is:
HF(g) < H2O(g) < NH3(g)
Key Concepts
Molecular Mass ComparisonComplexity of MoleculesEntropy Ranking
Molecular Mass Comparison
The concept of molecular mass is fundamental when determining the standard molar entropy of a substance. Molecular mass refers to the total mass of all the atoms in a single molecule. An important step in calculating the standard molar entropy involves comparing these masses.
In general, substances with higher molecular masses tend to have greater standard molar entropy. This is because molecules with larger masses have more atoms that can move in different ways, contributing to the overall entropy. For instance, in group (a) of the exercise, comparing the molecular masses of
Similarly, in group (b), molecules like \( \text{CH}_3\text{CH}_2\text{CHO} \) have larger molecular masses, adding more atomic motions and increasing their entropy compared to lighter molecules such as \( \text{CH}_2\text{O} \). Therefore, comparing molecular masses is a crucial first step in discerning entropy differences.
In general, substances with higher molecular masses tend to have greater standard molar entropy. This is because molecules with larger masses have more atoms that can move in different ways, contributing to the overall entropy. For instance, in group (a) of the exercise, comparing the molecular masses of
- \( \text{CH}_4 \) (methane)
- \( \text{CF}_4 \) (carbon tetrafluoride)
- \( \text{CCl}_4 \) (carbon tetrachloride)
Similarly, in group (b), molecules like \( \text{CH}_3\text{CH}_2\text{CHO} \) have larger molecular masses, adding more atomic motions and increasing their entropy compared to lighter molecules such as \( \text{CH}_2\text{O} \). Therefore, comparing molecular masses is a crucial first step in discerning entropy differences.
Complexity of Molecules
Molecular complexity significantly influences a molecule's standard molar entropy. Complexity refers to the number and arrangement of atoms, which can lead to different types of rotational and vibrational motions. These contribute to the overall randomness and dispersal of energy, increasing entropy.
For example, in the exercise, consider the structure of molecules in group (b), where
In group (c), although molecular masses are similar across \( \text{HF} \), \( \text{H}_2\text{O} \), and \( \text{NH}_3 \), \( \text{NH}_3 \) is more complex as a molecule due to its trigonal pyramidal shape and ability to form multiple hydrogen bonds. This adds to the entropy by increasing the variety of spatial orientations and molecular interactions.
For example, in the exercise, consider the structure of molecules in group (b), where
- \( \text{CH}_2\text{O} \) is a relatively simple molecule with limited internal movement.
- \( \text{CH}_3\text{CHO} \) and \( \text{CH}_3\text{CH}_2\text{CHO} \) are progressively more complex due to additional carbon and hydrogen atoms that can introduce new motions.
In group (c), although molecular masses are similar across \( \text{HF} \), \( \text{H}_2\text{O} \), and \( \text{NH}_3 \), \( \text{NH}_3 \) is more complex as a molecule due to its trigonal pyramidal shape and ability to form multiple hydrogen bonds. This adds to the entropy by increasing the variety of spatial orientations and molecular interactions.
Entropy Ranking
Ranking substances by their standard molar entropy can be achieved by considering factors like molecular mass, complexity, and the phase of the substance.
In this exercise, while phases are consistent (all gases), we relied on molecular mass and complexity. For groups (a) and (b), heavier and more complex molecules like \( \text{CF}_4 \) and \( \text{CH}_3\text{CH}_2\text{CHO} \) were ranked higher in entropy because they feature more intricate arrangements, providing greater potential energy states.
Meanwhile, group (c) illustrates an interesting ranking phenomenon. Here, the size similarity demands deeper consideration. Hydrogen bonding potential and molecular geometry also influence the results. \( \text{NH}_3 \) outranks \( \text{H}_2\text{O} \) in entropy due to its ability to engage in multiple complex interactions, illustrating how sometimes structural and interactional considerations override simple mass or atom count.
Thus, entropy ranking is about evaluating complex interplays of mass, molecular structure, and interaction potentials to predict how different substances might behave under similar conditions.
In this exercise, while phases are consistent (all gases), we relied on molecular mass and complexity. For groups (a) and (b), heavier and more complex molecules like \( \text{CF}_4 \) and \( \text{CH}_3\text{CH}_2\text{CHO} \) were ranked higher in entropy because they feature more intricate arrangements, providing greater potential energy states.
Meanwhile, group (c) illustrates an interesting ranking phenomenon. Here, the size similarity demands deeper consideration. Hydrogen bonding potential and molecular geometry also influence the results. \( \text{NH}_3 \) outranks \( \text{H}_2\text{O} \) in entropy due to its ability to engage in multiple complex interactions, illustrating how sometimes structural and interactional considerations override simple mass or atom count.
Thus, entropy ranking is about evaluating complex interplays of mass, molecular structure, and interaction potentials to predict how different substances might behave under similar conditions.
Other exercises in this chapter
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