Physical Chemistry Third Edition

142 3 The Second and Third Laws of Thermodynamics: Entropy

are included in Table A.8 of Appendix A. These values can be used to calculate entropy

changes for chemical reactions. Consider a chemical reaction with a reaction equation

written as in Chapter 2:

0 

∑s

i 1

νiFi (3.5-6)

whereνiis the stoichiometric coefficient of substanceiandFiis an abbreviation for its

chemical formula. Since entropy is a state function,∆Sfor a reaction at temperature

T 1 must be equal to the sum of the entropy changes of the three processes: (1) The

reactants are cooled to 0 K; (2) the chemical reaction is carried out at 0 K; and (3) the

products are heated to temperatureT 1. The entropy change for process (1) is equal to

the negative of the sum of the absolute entropies of the reactants. The entropy change

for process (2) equals zero according to the third law. The entropy change for process

(3) is equal to the sum of the absolute entropies of the products. Therefore,∆Sfor the

reaction at temperatureT 1 is given by

∆S(T 1 )

∑s

i 1

νiSm,i(T 1 ) (3.5-7)

wheresis the number of substances involved in the reaction and whereSm,i(T 1 ) stands

for the absolute molar entropy of substance numberiat temperatureT 1. Remember

that the stoichiometric coefficients for products are positive and those for reactants are

negative, so that equation represents the absolute entropies of the products minus those

of the reactants. Compare this equation with Eq. (2.7-12), which contains enthalpy

changes of formation. In Eq. (2.7-12) elements in their most stable form can be omitted

from the formula for∆H◦, since their enthalpies of formation are equal to zero. The

formula for∆Smust include all substances sinceSm,i(T 1 ) does not vanish for elements

at nonzero temperature.

The Standard State for the Entropy

For a solid or liquid, the standard state is the actual substance at pressureP◦(exactly

1 bar). For a gas, the standard state is a hypothetical ideal gas state at the standard

pressureP◦(1 bar). That is, a correction must be made for the difference between the

entropy of the real gas at pressureP◦and the corresponding ideal gas at pressureP◦.

We will discuss how to make this correction in Chapter 4, but the correction is small for

ordinary pressures, and we can usually neglect it. These standard states are the same

as for the enthalpy.

EXAMPLE3.16

Compute the standard-state entropy change for 1 mol of the reaction

0 2CO 2 (g)−2 CO(g)−O 2 (g)

if the product and reactants are at 298.15 K.