c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come
PROBLEMS AND EXAMPLES 303Problem 18.7
The rotational partition function at 298 can be written as an integral:qrot(T)= 2 (J+ 1 )e−^ rotJ(J+^1 )/TdJwhere (^) rotis a parameter called the rotational temperature, Show thatqrot=T/
rot.
Problem 18.8
The fraction of molecules in a rotational state is given by the ratio of the partition
function for that state relative to the total partition function. But we know that
qrot=T/
rotfrom the previous problem, so
QJ
Qtotal=
2 (J+ 1 )e−^ rotJ(J+^1 )/TdJ
T/
rot=
2 (J+ 1 ) (^) rote−^ rotJ(J+^1 )/TdJ
T
PlotQJ/Qtotalas a function of J for NO which has (^) rot= 2 .34 atT=298 K.
Problem 18.9
The dipole momentμis a twisting moment in an electrical field between particles of
chargeqseparated by a distancer:
μ=qr
The unit ofqris coulomb meters. The unit charge in atomic problems is the charge
on a proton, 1. 6019 × 10 −^19 C. The Br–F bond length is 176 pm. What would the
dipole moment for the molecule BrF be if it were completely ionic Br+F−?
Problem 18.10
If the actual dipole moment of Br–F is only 1.42 D, what is the percent ionic character
of the bond? Is the bond predominantly ionic or covalent?
Problem 18.11
The molar polarization of bromoethane was measured at five different temperatures
with the following results:
T 205 225 245 265 285
PT 104.2 99.1 94.5 90.5 80.8
What are the polarizability and dipole moment of bromoethane?