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(D) From the ideal gas equation,$PV = nRT$.Since $n = \frac{m}{M}$,where $m$ is the mass and $M$ is the molar mass,we have $PV = \frac{m}{M}RT$.Rearra

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$0.5$

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(D) From the ideal gas equation,$PV = nRT$.Since $n = \frac{m}{M}$,where $m$ is the mass and $M$ is the molar mass,we have $PV = \frac{m}{M}RT$.Rearranging for density $ho = \frac{m}{V}$,we get $P = \frac{ho RT}{M}$.This implies that $\frac{P}{ho T} = \frac{R}{M} = 	ext{constant}$.Therefore,$\frac{P_1}{ho_1 T_1} = \frac{P_2}{ho_2 T_2}$.Given: $P_2 = 2P_1$ and $T_2 = 4T_1$.Substituting these values: $\frac{P_1}{ho_1 T_1} = \frac{2P_1}{ho_2 (4T_1)}$.Simplifying,$1 = \frac{2}{4} \cdot \frac{ho_1}{ho_2}$,which gives $1 = \frac{1}{2} \cdot \frac{ho_1}{ho_2}$.Thus,$ho_2 = 0.5 ho_1$.The density becomes $0.5$ times the original density.

$O_2$ gas is filled in a vessel. If the pressure is doubled and the temperature becomes four times,how many times will its density become?

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