Answer to Question #124575 in Physical Chemistry for Oluwakolade James

Question

Calculate the value of the translational partition function of O_2
2
​
at 1000 K for a volume of 1 m^3
3
. Submit your answer multiplied by 10^{-32}
−32
(i.e. if you calculate 4.2e33, input 42).

Answer 1

Answer

Mass of O₂ is 2 x 32 x 1.6606 x 10^-27 kg

2πmkBT = 2 x 3.1415 x (2 x 32 x 1.6606 x 10^-27kg) x 1.3807 x 10^-23 J/K x 1000 K = 9.2196 x 10^-45 J kg

Λ = h/(2πmkBT)^1/2 = 6.6262 x 10^-34 JS/(9.2196 x 10^-45 J kg)^1/2 = 6.90 x 10^-12 m

The value of translational partition function = v/ Λ³ = 1m³/(6.90 x 10^-12 m)³ = 30.4 x 10³²

Multiplied by 10^-32  the answer is 30.4 (Ans.)