Question

At what temperature will uranium hexafluoride , the densest gas known have the same average speed as a molecule of the lightest gas, hydrogen at 37 degree celcius

Answer 1

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 = $[ 3RT / MM ]^{1/2$ ----------- 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

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

Next is the average speed of UF₆

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

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

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

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

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

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

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

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

so we substitute

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

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

T$_{UF$₆ = 109179.003 K/ 2.016

T$_{UF$₆ = 54156.25 K

Therefore, the required temperature of uranium hexafluoride is 54156.25 K