Answer to Question #219611 in Physical Chemistry for Along

Question

For a molecule of oxygen at 1atm pressure at 25degree Celsius
Find translational partition function

Answer 1

mass of O₂ is 2*16*1.6606*10^-27 kg, where 16 is weight of oxygen atom in a.m.u, 1.6606*10^-27 kg is 1 atomic mass unit.

2$\pi$mk_BT=2*3.1415*(2*16*1.6606*10^-27 kg)*1.3807*10^-23 J/K*300 K=1.3829*10^-45 J kg.

In the equation written above: k_B - Boltzmann constant, J/K.

We find the de Brogile thermal wavelength, $\Lambda$, m:

$\Lambda$=h/(2$\pi$mk_BT)^1/2=6.6262*10^-34 J s/(1.3829*10^-45)^1/2=1.7818*10^-11 m.

In the equation written above: h - Planck constant, J s.

We calculate the value of the translation partition function, q_tr:

q_tr=V/$\Lambda$³=1 m³/(1.7818*10^-11 m)³=1.7676*10³². This means that 1.7676*10³² quantum states are thermally accessible to the molecular system.

Answer: 1.8