506
9 Chemical Equilibrium
dependence of k 2 is given by
k 2 (T ) =
6.62608 × 10 −34 2
4(2π)
3
2 (1.3807 × 10 −23 )
1
2
√
T (6.02214 × 10 23 )
(49.03 × 1.6605 × 10 −27 )
3
2
e −7025.4/T
0.0244
,
or
k 2 (T ) = 2.16 3 × 10
7 m
3 s
−1 mol
−1
√
T e
−7025.4/T
= 2.16 3 × 10
10 L s
−1 mol
−1
√
T e
7025.4/T .
Thus, for T = 650 K, k 2 = 1.115 × 10 7 L mol −1 s −1 , and for T = 1000 K, k 2 =
6.08 6 × 10 8 L mol −1 s −1 .
9.5 Problems for This Chapter
1. Sodium vapour exists in two forms, monatomic sodium, Na, and diatomic
sodium, Na 2 . These species are related via the dissociation reaction
Na 2 (g) 2Na(g) .
Given that vib ( 23 Na 2 ) = 228.56 K, rot ( 23 Na 2 ) = 0.2220 K, M =
0.02299 kg mol −1 , and that the electronic term symbols for Na and Na 2 are X 2 S 1
2
and X 1 +
g , respectively, obtain an expression for the equilibrium constant for
the dissociation of sodium and evaluate K eq = K P for sodium at temperatures
of 298 and 1163 K. Note that the boiling temperature for liquid Na metal is T b =
1163 K.
2. Tritium (the mass three isotopes of hydrogen) is important in the nuclear power
industry, as it is one of the by-products generated by some nuclear reactors.
Molecular tritium, T 2 , undergoes an isotopic exchange reaction with molecular
hydrogen, H 2 , to give the mixed isotopologue HT according to the equilibrium
reaction
H 2
1
+
g
+ T 2
1
+
g
2HT
1
+
.
Experimental data pertinent to the hydrogen isotopologues H 2 , T 2 , and HT are
given in the following table: