Physical Chemistry , 1st ed.

its form in terms of number of moles of substance, gives us a way to determine
Sfor a process where temperature is changing:

SnCln 

T

T

f

i

 (3.18)

Just like evaluating Hat different temperatures, we have a scheme for deter-
mining Sat different temperatures:

1. Use equation 3.18 to evaluate the change in entropy for the reactants as they
   go from their initial temperature to a reference temperature, usually 298 K.


2. Use the entropies from the tabulated data to determine the entropy
   change of the reaction at the reference temperature.


3. Use equation 3.18 again to evaluate the change in entropy for the products
   as they go from the reference temperature to the original temperature.
   The entropy change at the specified temperature is the sum of these three
   entropy changes. We are taking advantage of the fact that entropy is a state
   function: the change is dictated by the change in the conditions, not how the
   system got there. Therefore, our three-step process, which is equivalent to per-
   forming the change in a single step at the stated temperature, has the same en-
   tropy change as the one-step process. (The assumption is that the heat capac-
   ity,C, does not vary with temperature. It does, but for small Tvalues this
   assumption is a very good approximation.)
   Gas-phase processes occurring under nonstandard pressures are also easily
   calculated in terms of either the changing pressures or volumes of the system.
   The following two equations were derived earlier in this chapter.

SnRln 

V

V

f

i

 (3.19)

SnRln p

p

f

i

 (3.20)

These equations can also be used in a stepwise fashion as described above for
nonstandard temperature.

Example 3.8

What is the entropy change of the reaction

2H 2 (g) O 2 (g) →2H 2 O ()

at 99°C and standard pressure? Treat the heat capacities of H 2 ,O 2 , and H 2 O

as constant at 28.8, 29.4, and 75.3 J/molK, respectively. Assume molar quan-

tities based on the balanced chemical reaction and ideal gas behavior.

Solution

1. The first step is to determine the change in entropy as the reactants, 2 moles
   of H 2 and 1 mole of O 2 , change temperature from 99°C to 25°C (which is
   372 K to 298 K). This is labeled S 1. It is, according to equation 3.18:
   S 1 

(2 mol)28.8 

mo

J

lK

ln 

2

3

9

7

8

2

K

K

+ (1 mol)29.4 

mo

J

lK

ln 

2

3

9

7

8

2

K

K



S 1 19.3 

K

J



3.7 Entropies of Chemical Reactions 83