Chemistry - A Molecular Science

Chapter 9 Reaction Energetics

of translational freedom of motion as it flies through its container, but the translational motion of the same molecule in the solid is

constrained to an oscillation about its lattice

position. The constrained motion in the solid re

lative to the gas mean

s that the molecules

in the solid have far fewer ways in which to distribute their energy.

The number of ways in which the energy of

a system can be distributed is such an

important property of the system that a thermodynamic variable is defined to quantify it. The thermodynamic property is called

entropy

and given the symbol

S. Systems with high

entropies can distribute energy in more

ways than those with low entropies.

The motion of molecules in the gas phase is mu

ch less constrained than in the liquid or

solid states, and the number of ways a syst

em of molecules can distribute its energy

increases as constraints to molecular motion are removed. Therefore, the entropy of a system of molecules in the g

as phase is much greater than th

at of the same system in a

condensed state. Molecules in the liquid state

have slightly more freedom of motion than

those in the solid, so the entrop

y of a system of molecules in the liquid state is slightly

greater than in the solid state. We will

use the following relationship frequently:

Sgas

>> S

liquid

> S

solid

Constraints not only decrease the entropy of

a system, they also tend to order the

system. For example, motion is unconstrained in the gas phase, so the entropy of a gas is high. However, when intermolecular forces cons

train the molecules, the molecules align to

increase their interactions and, in so doi

ng, produce the short-range order found in the

liquid state. When the forces further constrain the system, the molecules align better so as to maximize their interacti

ons. The increased constraints produce the long-range order

found in the solid state. Thus, increasing the c

onstraints on a system decreases its entropy

and increases its order. We conclude that

Disordered systems have greater entropies than do ordered ones.

Indeed, entropy is commonly defined in terms of the order in a system. However, entropy is a measure of the number of ways in which the energy of a system can be distributed; the order in a system is simply a good predictive tool because ordered systems are more constrained and have lower entropies than disordered systems.

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