Question

Calculate the value of the translational partition function of O2 at 1000 K for a volume of 1 m3. Submit your answer multiplied by 10^−32 (i.e. if you calculate 4.2e33, input 42).​

Answer 1

The value of the function is
`q__(t )} = 1.878 *10^(35)`

Step-by-step explanation:

From the question we are told that

The temperature is
`T = 1000 \ K`

The volume is
`V = 1 m^3`

Generally the transnational partition function is mathematically represented as

`q__(t )} = [(2 * \pi * m * k * T )/( N_a * h) ]^{(3)/(2) } * V`

Where m is the molar mass of oxygen with a constant value of
`m = 32 *10^(-3) \ kg/mol`

k is the Boltzmann constant with a value of
`k = 1.38 *10^(-23 ) \ J/K`

`N_a` is the Avogadro Number with a constant value of
`N_a = 6.022 *10^(23) \ atoms`

h is the Planck's constant with value
`h = 6.626 *10^(-34 ) \ J\cdot s`

Substituting values

`q__(t )} = [(2 * 3.142 * 32*10^(-3) * 1.38 *10^(-23) * 1000 )/( 6.022 *10^(23) * [6.626 *10^(-34)] ^2 )]^{(3)/(2) } * 1`

`q__(t )} = 1.878 *10^(35)`