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