Question

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

Short answer

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

Step-by-step solution

Understanding Standard Molar Entropy

Standard molar entropy is a measure of the amount of disorder or randomness in a substance when it is in its standard state. Generally, gases have higher entropy than liquids and solids, larger molecules have higher entropy than smaller molecules, and substances with complex structures have higher entropy than simpler substances.

Ranking Set (a)

First, consider that all substances in set (a) are gases. Among gases, monoatomic gases such as noble gases have the lowest entropy. Among polyatomic gases, linear and less complex molecules have lower entropy compared to larger, more complex molecules. Thus, the order of increasing standard molar entropy is He(g) < Ne(g) < NH3(g) < SO2(g) < CH3CH2OH(g).

Ranking Set (b)

For set (b), comparing the same substance in different states, the entropy increases from solid to liquid to gas. Therefore, the order of increasing standard molar entropy is H2O(s) < H2O(l) < H2O(g).

Ranking Set (c)

For set (c), all substances are gases, but they differ in molecular size and number of atoms. Increase in the number of heavier atoms and complexity generally leads to increased entropy. Thus, the order is CH4(g) < CCl4(g) < CF4(g), with CF4(g) having the highest entropy due to the high molar masses of the fluorine atoms and the symmetrical, tetrahedral shape of the molecule increasing its entropy.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In the context of our discussion, it primarily concerns the concept of entropy, which is a central theme in thermodynamics. Entropy, denoted as S, is the measure of the disorder or randomness within a system. The second law of thermodynamics states that in an isolated system, entropy will tend to increase over time, meaning that systems will naturally progress towards disorder. Standard molar entropy, S^°, refers to the entropy content of one mole of a substance under standard conditions (1 bar of pressure and a specified temperature, usually 298.15 K).

Understanding how entropy functions in reactions and substances helps us predict the spontaneity of chemical processes. As a system becomes more disorganized, the entropy increases. When we consider different states of matter or different molecular structures, we can predict how the standard molar entropy varies between them due to the intrinsic properties of molecules and intermolecular forces, leading to the very 'entropy ranking' seen in textbook problems.

Entropy Ranking

Entropy ranking involves putting multiple substances in order according to their standard molar entropies. Factors affecting entropy ranking include the state of matter, molecular size, molecular complexity, and the type of atoms within the molecule. Generally, as we've seen in the provided solution, gases have higher entropy than solids and liquids because particles in the gaseous state are more spread out, allowing for more possible arrangements (disorder). When comparing gases, those composed of single atoms (monatomic gases) have lower entropy than those composed of multiple atoms (polyatomic gases). Complexity and size further influence the ranking: larger molecules and those with complex structures possess higher entropies.

Furthermore, symmetry plays a role too. Molecules with symmetrical structures can have their atoms arranged in space in fewer distinct ways compared to more complicated or asymmetrical molecules, leading to different entropy levels. In exercises that ask students to rank substances in order of increasing standard molar entropy, it's essential to consider all these factors to determine the correct order. For example, helium gas (He(g)) has lower standard molar entropy than ethanol gas (CH₃CH₂OH(g)) because it is monatomic and much less complex in structure.

States of Matter

The three primary states of matter—solids, liquids, and gases—have distinctly different properties which affect their standard molar entropies. Solids have the lowest entropy because their particles are tightly packed in a highly ordered arrangement. Liquids have more entropy than solids as their particles are more spread out and can move around more freely, making the substance less ordered. Gases have the highest entropy of the three states because particles in a gas are well separated and free to move in all directions, leading to a high level of disorder.

Transitions between these states—known as phase changes—include processes like melting, boiling, and sublimation, and they are associated with changes in entropy. For instance, when ice (solid water) melts into liquid water, entropy increases because the orderly arrangement of water molecules in ice breaks down as they move into the liquid phase. This concept is key in problems like ranking the standard molar entropies of water in its different phases. Hence, H₂O(s) has a lower standard molar entropy than H₂O(l), which in turn is lower than H₂O(g).