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So the value of x is…

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The compressibility factor for a gas is the ratio of the observed molar volume of a gas to the calculated molar volume (using ideal gas equation) of the gas at the same pressure and temperature. It can also be defined as the ratio of the product and pressure and volume of the gas to the product of the number of moles, the gas constant and the temperature of the gas. The equations are given below:

$ Z=\cfrac { PV }{ nRT } $ (Where Z is the compressibility factor)

$ \Rightarrow Z=\cfrac { P{ V }_{ real } }{ nRT } $...(1)

Since according to the ideal gas equation: $ PV=nRT$

$ \Rightarrow { V }_{ real }=\cfrac { nRT }{ P } $

Putting the above equation in equation (1),

$ Z=\cfrac { { V }_{ real } }{ { V }_{ ideal } } $

We will use equation (1) to solve this question. Putting the value of n=0.2 mole, Z=0.2005, P=100 atm, R=0.0821 L atm ${ K }^{ -1 }{ mol }^{ -1 }$ and T=273 K, we get:

$0.2005=\cfrac { 1000\quad atm\times V }{ 0.2\quad mol\times 0.0821\quad L\quad atm\quad { K }^{ -1 }{ mol }^{ -1 }\times 273\quad K } $

$\Rightarrow V=8.89\times { 10 }^{ -3 }\quad L$

Hence the value of x is 3.