Textbook Question
Cyclopropane and propylene are isomers that both have the formula C3H6. Based on the molecular structures shown, which of these isomers would you expect to have the higher standard molar entropy at 25 °C?
Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 49
The standard entropies at 298 K for certain group 4A elements are: C(s, diamond) = 2.43 J>mol@K, Si1s2 = 18.81 J>mol@K, Ge1s2 = 31.09 J>mol@K, and Sn1s2 = 51.818 J>mol@K. All but Sn have the same (diamond) structure. How do you account for the trend in the S° values?
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Identify the physical state and structure of each element mentioned: Carbon (diamond), Silicon, Germanium, and Tin all in solid state. Note that Carbon, Silicon, and Germanium have the same diamond crystal structure, while Tin has a different structure.
Understand that standard entropy (S°) is a measure of the randomness or disorder in a system. Elements in the same physical state but with different crystal structures can have different levels of disorder.
Recognize that as you move down the group in the periodic table (from C to Sn), the atomic size and mass increase. This generally leads to an increase in entropy because larger atoms can have more complex vibrations and more disordered arrangements.
Consider the impact of crystal structure on entropy. The diamond structure, shared by C, Si, and Ge, is highly ordered, which tends to lower entropy. Sn, however, does not have this structure, which might contribute to its higher entropy.
Conclude that the trend in the S° values from C to Sn can be explained by both the increasing atomic size and mass, and the change in crystal structure, which contribute to the overall increase in disorder and thus entropy.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy
Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. The standard entropy values provided for the group 4A elements reflect their molecular complexity and structural arrangements, influencing their thermal energy distribution.
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Allotropes
Allotropes are different structural forms of the same element, where atoms are bonded together in different ways. For example, carbon exists as diamond and graphite, each with distinct properties and entropies. The presence of different allotropes, such as diamond for C and the more complex structures for Sn, affects the entropy values due to variations in atomic arrangement and bonding.
Trends in Group 4A Elements
In group 4A of the periodic table, elements exhibit trends in properties such as atomic size, electronegativity, and entropy. As you move down the group from carbon to tin, the atomic size increases, leading to more complex structures and higher entropy values. This trend is influenced by the increasing number of electrons and the resulting increase in possible microstates, contributing to the observed differences in standard entropy.
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Related Practice
Textbook Question
Three of the forms of elemental carbon are graphite, diamond,and buckminsterfullerene. The entropies at 298 Kfor graphite and diamond are listed in Appendix C.(b) What would you expect for the S° value of buckminsterfullerene(Figure 12.49, p. 509) relative to the valuesfor graphite and diamond? Explain.
Textbook Question
Using S° values from Appendix C, calculate ΔS° values for the following reactions. In each case, account for the sign of ΔS°.
(a) C2H4(g) + H2(g) → C2H6(g)
(b) N2O4(g) → 2 NO2(g)
(c) Be(OH)2(s) → BeO(s) + H2O(g)
(d) 2 CH3OH(g) + 3 O2(g) ⟶ 2 CO2(g) + 4 H2O(g)