Concise Physical Chemistry

c08 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

122 A STATISTICAL APPROACH TO THERMODYNAMICS

When these two degrees of freedom and the Na multiplicity

(

22

)

are taken into

account, the equilibrium constant calculation at 1300 K is complete

Keq= 4

(

6. 95 × 104

)

[

1

3. 132 × 103 ·( 6. 254 )

]

= 14. 2

which, considering the magnitude of the numbers revalued is in good agreement with

the previous calculation.

Problem 8.1

Find the equilibrium constantKeqat 300 K for a simple nondegenerate two-level

system

A(g)→B(g)

where the energy of level B,εB,is1.25kJmol−^1 higher thanεA. What are the

percentage occupations of levels A and B? What is the probability of selecting a

molecule from the lower level if the selection process is completely random and does

not favor either level?

Problem 8.2

Calculate the thermal wavelength of Na 2 (g) molecules at 1000 K. Compare your

answer to the value 8.14 pm.

Problem 8.3

If we multiply the thermal wavelength of Na by 1/

√

2, we get the thermal wavelength

of Na 2. Why is that?

Problem 8.4

Why isν=cν ̃, whereνis the frequency of electromagnetic radiation,cis its speed

3. 0 × 108 ms−^1 , and ̃νis the “wavenumber in spectroscopist’s terminology with

units of reciprocal seconds (s−^1 )?

Problem 8.5

No doubt you have noticed that solid iodine I(s) produces a purple vapor upon heating

in a closed container. The vapor is diatomic I 2 (g) which enters into an equilibrium

with atoms I(g) in a way analogous to Na 2 (g) and Na(g) already discussed. Calculate

the thermal wavelength of molecular I 2 (g) and I(g) atoms confined to a molar volume

at 1000 K.