# 16.9: Some Trends In Entropy Values

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A close inspection of the entropy values in the Table of Molar Entropies reveals several trends which can be explained in terms of the factors of molecular mass and restriction of movement.

Table $$\PageIndex{1}$$ Molar Entropy Values

 Compound Smo /J K-1mol-1 Compound Smo /J K-1mol-1 Solids Diatomic Gases C (diamond) 2.377 C (graphite) 5.74 H2 130.7 Si 18.8 D2 145.0 Ge 31.1 HCl 186.9 Sn (gray) 44.1 HBr 198.7 Pb 64.8 HI 206.6 Li 29.1 N2 191.6 Na 51.2 O2 205.1 K 64.2 F2 202.8 Rb 69.5 Cl2 223.1 Cs 85.2 Br2 245.5 NaF 51.5 I2 260.7 MgO 26.9 CO 197.7 AlN 20.2 Triatomic Gases NaCl 72.1 H2O 188.8 KCl 82.6 NO2 240.1 Mg 32.7 H2S 205.8 Ag 42.6 CO2 213.7 I2 116.1 SO2 248.2 MgH2 31.1 N2O 219.9 AgN3 99.2 O3 238.9 Liquids Polyatomic Gases( > 3) Hg 76.0 CH4 186.3 Br2 152.2 C2H6 229.6 H2O 69.9 C3H8 269.9 H2O2 109.6 C4H10 310.2 CH3OH 126.8 C5H12 348.9 C2H5OH 160.7 C2H4 219.6 C6H6 172.8 N2O4 304.3 BCl3 206.3 B2H6 232.0 Monatomic Gases BF3 254.0 He 126.0 NH3 192.5 Ne 146.2 Ar 154.8 Kr 164.0 Xe 169.6

Solids, Liquids, and Gases Perhaps the most obvious feature of the table of molecular entropies is a general increase in the molar entropy as we move from solids to liquids to gases. In a solid, the molecules are only capable of restricted vibrations around a fixed point, but when a solid melts, the molecules, though still hampered by their mutual attraction, are much freer to move around. Thus when a solid melts, the molar entropy of the substance increases. When a liquid vaporizes, the restrictions on the molecules’ ability to move around are relaxed almost completely and a further and larger increase in the entropy occurs. When 1 mol of ice melts, for example, its entropy increases by 22 J K–1, while on boiling the entropy increase is 110 J K–1.

Molecular Complexity A second clear trend in the table is the higher molar entropy of substances with more complex molecules. To some extent this is due to the mass since on the whole more complex molecules are heavier than simpler ones. However, we still find an increase of entropy with complexity when we compare molecules of very similar masses:
 Substance Ar(g) F2(g) CO2(g) C3H8(g) Sm°/J K–1 mol–1 155 202.7 213.6 269.9 Molar mass/g mol–1 40 38 44 44 Number of atoms 1 2 3 11

The more atoms there are in a molecule, the more ways the molecule can change its shape by vibrating. In consequence there are more ways in which the energy can be distributed among the molecules.

Strength of Bonding Another trend in entropy, most noticeable in the case of solids, is the decrease in the entropy as the forces between the atoms, molecules, or ions increases. A good example is the three solid compounds
 Substance NaF(s) MgO(s) AlN(s) Sm°(298 K)/J K–1 mol–1 51.5 26.8 20.2 Molar mass/g mol–1 42.0 40.3 41.0

which are isoelectronic with sodium fluoride. Since there is very little difference in the molar masses, the entropy decrease can only be attributed to the increase in the coulombic attraction between the ions as we move from the singly charged ions Na+ and F through the doubly charged ions Mg2+ and O2–, to the triply charged ions A13+ and N3–. (While it is true that there is a fair degree of covalent character to the bonding in AIN, the effect of this will be to increase the strength of the bonding.)

##### Example $$\PageIndex{1}$$: Molar Entropy

From each of the following pairs of compounds choose the one with the higher standard molar entropy at 25°C. Give brief reasons for your choice.

a) HBr(g), HCl(g) c) ND3(g), Ne(g) e) C2H6(g), C2H4(g) b) Cs(s), Cs(l) d) KCl(s), CaS(s)

Solution

a) HBr and HCl are very similar except for their mass. HBr will have a higher entropy because of its greater mass. b) At the same temperature, the liquid form of a substance always has a higher entropy than the solid. c) ND3 (D = deuterium) and Ne have almost identical molar masses (20 g mol–1) However, since ND3 is more complex, it can vibrate and rotate while Ne cannot. ND3 will have the higher entropy. d) KCl and CaS are isoelectronic. Because both anion and cation are doubly charged in CaS, the ions are more tightly held to each other and can vibrate less readily. Thus KCl must have the higher entropy. e) On all counts C2H6 must have a higher entropy than C2H4. C2H6 is heavier and more complex than C2H4. In addition there is free rotation about the C—C bond in C2H6 but hindered rotation about the C=C bond in C2H4.

This page titled 16.9: Some Trends In Entropy Values is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Ed Vitz, John W. Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, & Adam Hahn.