Respuesta :
The molecular weight of an unknown gas is 613.8 kg.
Explanation:
RMS or root mean square velocity is given by the formula,
RMS = [tex]$\sqrt{\frac{3RT}{M} }[/tex]
where R is the gas constant = 8.314 kgm²s⁻²K⁻¹mol⁻¹
T is the temperature in Kelvin = 50 + 273 = 323 K
Molar mass of the Nitrogen gas in kg is 0.028 kg/mol
So we can find the RMs of the nitrogen by plugin the above values in the above equation, we will get,
RMS = [tex]$\sqrt{\frac{3\times 8.314\times 323}{0.028} }[/tex]
= 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 = [tex]$\frac{3RT}{\sqrt{RMS} }[/tex]
Now the temperature is T = 130 + 273 = 403 K
Plugin the values as,
M = [tex]$\frac{3\times 8.314\times 403}{\sqrt{268.2} }[/tex]
= 613.8 kg/mol
So the molecular weight of an unknown gas is 613.8 kg.
