Question

The translational partition function of a molecule is given by:

qT=(2 π m k T)3/2 (V/h3).
(Note: m in the equation is the mass of the individual molecule).

If V=1 L and T=300 K answer the following question:

a) qT for HI at T = 300 K, and V = 1 L.

b) qT for HI at T = 2000 K, and V = 1 L.

Answer 1

Mass of I2 is 128 X 1.6606 X 10^-27 kg

a) 2πmkBT = 2 X 3.1415 X (128 X 1.6606 X 10^-27 kg) X 1.3807 X 10^-23 J/K X 300 K = 5.5 X 10^-45 J kg

Λ = h / (2 π m kB T)^1/2 = 6.6262 X 10^-34 J s / (5.5 X 10^-45 J kg)^1/2 = 8.93 X 10^-12m

qT = V / Λ^3 = 1000 X 10^-6 m3 / (8.93 X 10^-12 m )^3 = 1.4 X 10^30

b) 2πmkBT = 2 X 3.1415 X (128 X 1.6606 X 10^-27 kg) X 1.3807 X 10^-23 J/K X 2000 K = 3.67 X 10^-44 J kg

Λ = h / (2 π m kB T)^1/2 = 6.6262 X 10^-34 J s / (3.67 X 10^-44 J kg)^1/2 = 3.45 X 10^-12m

qT = V / Λ^3 = 1000 X 10^-6 m3 / (3.45 X 10^-12 m )^3 = 2.43 X 10^31