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

the required temperature of uranium hexafluoride is 54156.25 K

Explanation:

Given the data in the question;

We know that average speed is;

u = ----------- 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

₂ =   ------ let this be equation 2

Next is the average speed of UF₆

₆ = ------ let this be equation 3

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

=

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

=

given that; temperature of hydrogen T₂ = 37°C = ( 37 + 273.15)K = 310.15 K

we know that Molar mass of H₂; MM₂ = 2.016 g/mol  

and molar mass of  UF₆; MM₆ = 352.02 g/mol

so we substitute

[ 310.15 K / 2.016 g/mol  ] = [ T₆ / 352.02 g/mol ]

T₆ = [ 352.02 g/mol  × 310.15 K ] / 2.016 g/mol

T₆ = 109179.003 K/ 2.016

T₆ = 54156.25 K

Therefore, the required temperature of uranium hexafluoride is 54156.25 K