An unknown gas at 130 degrees celsius has a rms speed that is 0.50 that of the rms speed of N2 molecules at 50 degrees celsius. What is the molecular weight of unknown gas?

The molecular weight of an unknown gas is 613.8 kg.

Explanation:

RMS or root mean square velocity is given by the formula,

RMS =

where R is the gas constant = 8.314 kgm²s⁻²K⁻¹mol⁻¹

T is the temperature in Kelvin = 50 + 273 = 323 K

Molar mass of the Nitrogen gas in kg is 0.028 kg/mol

So we can find the RMs of the nitrogen by plugin the above values in the above equation, we will get,  

RMS =

     = 536.4 m/s

Now we have to take half of RMS as 268.2 m/s

Now we have to rearrange the equation to get M as,

M =

Now the temperature is T = 130 + 273 = 403 K

Plugin the values as,

M =  

   = 613.8 kg/mol

So the molecular weight of an unknown gas is 613.8 kg.