States of Matter question bank (Chemistry)

A certain quantity of real gas occupies a volume of $0.15 {\mathrm{dm}}^3$ at $100 \mathrm{atm}$ and $500 \mathrm{K}$ when its compressibility factor is $1.07.$ Its volume at $300 \mathrm{atm}$ and $300 \mathrm{K}$ (When its compressibility factor is $1.4$) is $\_\_\_\_\_\_\times {10}^{-4}{\mathrm{dm}}^3$(Nearest integer)

At $600 \mathrm{K}$, the root mean square $\left(\mathrm{rms}\right)$ speed of gas $\mathrm{X}$ (molar mass $=40$) is equal to the most probable speed of gas $\mathrm{Y}$ at $90 \mathrm{K}$. The molar mass of the gas $\mathrm{Y}$ is _____ $\mathrm{g} {\mathrm{mol}}^{–1}$. (Nearest integer)