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(D) Let the total volume of the cylinder be $V$. Let the volume occupied by the gas of mass $2m$ be $V_1$ and the volume occupied by the gas of mass $

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$0.67$

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(D) Let the total volume of the cylinder be $V$. Let the volume occupied by the gas of mass $2m$ be $V_1$ and the volume occupied by the gas of mass $m$ be $V_2 = V - V_1$.Since the piston is in equilibrium,the pressure $P$ on both sides is the same.Since the piston is conducting,the temperature $T$ is the same for both gases.Using the ideal gas equation $PV = nRT = \frac{m_{gas}}{M}RT$,where $M$ is the molar mass of the gas:For the gas with mass $m$: $P(V - V_1) = \frac{m}{M}RT$  $(i)$For the gas with mass $2m$: $P V_1 = \frac{2m}{M}RT$  $(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{P V_1}{P(V - V_1)} = \frac{\frac{2m}{M}RT}{\frac{m}{M}RT}$$\frac{V_1}{V - V_1} = 2$$V_1 = 2V - 2V_1$$3V_1 = 2V$$\frac{V_1}{V} = \frac{2}{3} \approx 0.67$Thus,the larger mass occupies $0.67$ of the total volume.

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