At a given temperature,the pressure of an ide | vedclass

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(D) The ideal gas equation is given by $PV = nRT$,where $n$ is the number of moles.We know that $n = \frac{m}{M_w}$,where $m$ is the mass and $M_w$ is

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$\rho$

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(D) The ideal gas equation is given by $PV = nRT$,where $n$ is the number of moles.We know that $n = \frac{m}{M_w}$,where $m$ is the mass and $M_w$ is the molar mass.Substituting this into the equation,we get $PV = \frac{m}{M_w} RT$.Rearranging for pressure $P$,we have $P = \left(\frac{m}{V}\right) \frac{RT}{M_w}$.Since density $\rho = \frac{m}{V}$,the equation becomes $P = \frac{\rho RT}{M_w}$.At a constant temperature $T$ and for a specific gas (constant $M_w$),the pressure $P$ is directly proportional to the density $\rho$,i.e.,$P \propto \rho$.

At a given temperature,the pressure of an ideal gas of density $\rho$ is proportional to

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