Concise Physical Chemistry

c06 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

90 THE GIBBS FREE ENERGY

PROBLEMS AND EXAMPLE

Example 6.1

Find the Gibbs free energy of formation for methane. The enthalpy of formation of

methane is
H^298 f,methane=− 74 .81 J mol−^1. Standard entropies of H 2 (g), C(graphite),

and methane CH 4 (g) are also known. They are 130.684, 5.74, and 186.26 J K−^1 mol−^1 ,

respectively.

Solution 6.1 For the reaction

C(graphite)+2H 2 (g)=CH 4 (g)

we have

Sr^298 ,CH 4 = 186. 26 −2(130.684)− 5. 74 =− 80 .848 J K−^1 mol−^1

At 298.15 K, we obtain

T
S=− 0 .080848(298.15)=− 24 .09 kJ mol−^1

and

G^298 f,CH 4 =− 74. 81 −(− 24 .093)=− 50 .72 kJ mol−^1

(Notice the conversion from J to kJ in the penultimate step.) In this way, we can build

up a table of Gibbs functions for as many compounds as time and money permit.

Problem 6.1

(a) Given that

G=H−TS

show that

dG=dH−TdS−SdT

(b) Given that

H=U+pV

show that

dH=dU+pdV+Vdp

forp=const.