Question

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?

Answer 1

The molecular weight of an unknown gas is 613.8 kg.

Step-by-step explanation:

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

RMS =
`$\sqrt{(3RT)/(M) }`

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 =
`$\sqrt{(3* 8.314* 323)/(0.028) }`

= 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 =
`$(3RT)/(√(RMS) )`

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

Plugin the values as,

M =
`$(3* 8.314* 403)/(√(268.2) )`

= 613.8 kg/mol

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