Chemistry - Real Gas Question with Solution | TestHub

At very high pressure $Z=1+bP/RT$, so the slope = $b/RT$.

$b=0.0821\times 300\times 2.0\times 10^{-3}=0.0493\mathrm{L}/\mathrm{mol}$.

$b=4\times N_A$ x v, where v is the volume of one molecule, so $v=0.0493/(4\times 6.022\times 10^{23})=2.05\times 10^{-26}\mathrm{L}$.

Convert: $1\mathrm{L}=1000{\mathrm{cm}}^3$, so $v=2.05\times 10^{-23}{\mathrm{cm}}^3$.

Traps: leaving out the factor 4 gives $8.2\times 10^{-23}{\mathrm{cm}}^3$; forgetting the L to ${\mathrm{cm}}^3$ conversion gives $2.0\times 10^{-26}$; using $R=8.314$ gives $2.1\times 10^{-21}$.

Answer: (C).