Question

At what temperature will a molecule of UF6 have the same average speed as a molecule of hydrogen at 37 degrees celsius?

Answer 1

We know,

Average speed is given by the formula Cav = 8RT/M where R = gas constant, T = temperature, M = molar mass of the gas and = other constant

Now, average speed of hydrogen at 370C will be as:

T = 370C = (37+273) K = 310 K

molar mass (M) for H2 = 2 g

So, Cav(H2) = 8RT/M = 8R*310/*2

Let average speed of UF6 at temperature T will have the same as of hydrogen at 370C.

So, Cav(UF6) =Cav(H2) = 8R*310/*2 ----(1)

molar mass of UF6 = 352 g

From the formula we get as:

Cav(UF6) =8RT/*352 ---(2)

From equation(1) and (2) we have,

8R*T/*352 = 8R*310/*2  

Remove square root on both the sides

=> 8R*T/*352 = 8R*310/*2

=> T/352 = 310/2

=> T = 54560 K