16.9: Some Trends In Entropy Values

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	Sm^o /J K^-1mol^-1	Compound	Sm^o /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 O^2–, to the triply charged ions A1³⁺ and N^3–. (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.