Chemistry - A Molecular Science

Example 9.4

Predict which system of molecules in each pair has the greater entropy.

(a)

(b)

Four atoms can distribute energy in more ways than two atoms, so system (b) has the greater entropy.

(a)

(b)

The order of the 12 atoms in (a) indicates that they are being constrained more than those with the random distribution in (b). Therefore, system (b) has the greater entropy

(a)

(b)

Each of the four molecules in (a) has 3(3) = 9 degrees of freedom, but each molecule in (b) has only 2(3) = 6 degrees. Therefore, the molecules in (a) can distribute their energy in more ways and have the higher entropy.

The two driving forces behind a process are the tendencies for systems to minimize

their potential energy (

H < 0) and to maximize the number of ways in which they can Δ

distribute their energy (

S > 0). However, unless the entropy change is large, the tendency Δ

to minimize enthalpy is the dominant driv

ing force. We have seen how to estimate

enthalpy changes from bond energies, and we now show how to predict whether the entropy change is large and positive, large and

negative, or negligible. The entropy change

of a reaction is given as

ΔS = S

products

• S

reactants

, so

ΔS > 0 when the entropy of the

products is greater than that of the reactants

. At this point, we need only predict whether

ΔS is large, and, if so, what is its

sign.* To do this, we recall that S

gas

S

liquid

S

solid

to

conclude that

entropy changes are large only in reacti

ons in which the number of moles of

gas changes

. We will ignore the effect of entr

opy changes that are not large because

enthalpy changes almost always dominate su

ch processes, and the sign of large entropy

changes can be estimated with the following:

*

ΔS can be calculated and the procedure is covered in Chapter 4 of Chemistry - A Q

uantitative Science.

ΔS > 0 for reactions that produce gas;

ΔS < 0 for reactions that consume gas; but

ΔS ~ 0 (negligibly small) for reactions that do not involve a

change

in the number of moles of gas.

Chapter 9 Reaction Energetics

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Carolina

State

University