At 300, K,the density of a certain gaseous mo | vedclass

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(C) The density $(\rho)$ of a gas is given by the formula $\rho = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and $

Vedclass · Accepted Answer

$112$

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(C) The density $(ho)$ of a gas is given by the formula $ho = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and $T$ is temperature.Given that the temperature $T$ is constant for both gases.For $N_2$ gas: $ho_{N_2} = \frac{P_{N_2} 	imes M_{N_2}}{RT} = \frac{4 	imes 28}{RT}$.For the unknown gas: $ho_{gas} = \frac{P_{gas} 	imes M_{gas}}{RT} = \frac{2 	imes M_{gas}}{RT}$.According to the problem,$ho_{gas} = 2 	imes ho_{N_2}$.Substituting the expressions: $\frac{2 	imes M_{gas}}{RT} = 2 	imes \left( \frac{4 	imes 28}{RT} ight)$.Canceling $RT$ from both sides: $2 	imes M_{gas} = 8 	imes 28$.$M_{gas} = 4 	imes 28 = 112\, g\, mol^{-1}$.

At $300\, K$,the density of a certain gaseous molecule at $2\, bar$ is double that of dinitrogen $(N_2)$ at $4\, bar$. The molar mass of the gaseous molecule is ............... $g\, mol^{-1}$.

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