Respuesta :

Answer:

the required temperature of uranium hexafluoride is 54156.25 K

Explanation:

Given the data in the question;

We know that average speed is;

u = [tex][ 3RT / MM ]^{1/2[/tex] ----------- let this be equation 1

where MM is the molar mass

T is temperature

R is universal gas constant and u is the average speed.

First we get the average speed of H₂

[tex]U_{H}[/tex]₂ =  [tex][ 3RT_H_2 / MM_H_2 ]^{1/2[/tex] ------ let this be equation 2

Next is the average speed of UF₆

[tex]U_{UF[/tex]₆ = [tex][ 3RT_{UF_6} / MM_{UF_6} ]^{1/2[/tex] ------ let this be equation 3

given that; both have the same average speed, equation 2 = equation 3;

[tex][ 3RT_H_2 / MM_H_2 ]^{1/2[/tex] = [tex][ 3RT_{UF_6} / MM_{UF_6} ]^{1/2[/tex]

we multiply both sides by 1/3R and also square both sides.

[tex][ T_H_2 / MM_H_2 ][/tex] = [tex][ T_{UF_6} / MM_{UF_6} ][/tex]

given that; temperature of hydrogen T[tex]_{H[/tex]₂ = 37°C = ( 37 + 273.15)K = 310.15 K

we know that Molar mass of H₂; MM[tex]_{H[/tex]₂ = 2.016 g/mol  

and molar mass of  UF₆; MM[tex]_{UF[/tex]₆ = 352.02 g/mol

so we substitute

[ 310.15 K / 2.016 g/mol  ] = [ T[tex]_{UF[/tex]₆ / 352.02 g/mol ]

T[tex]_{UF[/tex]₆ = [ 352.02 g/mol  × 310.15 K ] / 2.016 g/mol

T[tex]_{UF[/tex]₆ = 109179.003 K/ 2.016

T[tex]_{UF[/tex]₆ = 54156.25 K

Therefore, the required temperature of uranium hexafluoride is 54156.25 K

ACCESS MORE
EDU ACCESS