Laughing gas, or nitrous oxide, is often shipped in roughly 50 L cylinders.

Calculate the pressure of 100.0 moles of ${N}_{2}O$ in a cylinder at STP using the van der Waals equation of state:

$$\left( P+\frac { { n }^{ 2 }a }{ { V }^{ 2 } } \right) \left( V-nb \right) =nRT$$

where $P$ is the pressure, $n$ is the number of moles, $V$ is the volume, $R$ is the gas constant, $T$ is the temperature, and $a$ and $b$ are the van der Waals constants specific to nitrous oxide.

${a}_{{N}_{2}O}=3.78\frac{{L}^{2}atm}{{mol}^{2}}, {b}_{{N}_{2}O}=4.42\times {10}^{-2}\frac{L}{mol},R=0.082\frac{L\times atm}{mole\times K}$