A bicycle tyre has a volume of 500 cm³. If this is inflated with nitrogen gas to a pressure of 6.0 atm at 300 K, the number of molecules in the inflated tyre is

The amount of gas in the tyre, $n=\frac{pV}{RT}=$$\frac{\left(6.0\mathrm{atm}\right)\left(500\times {10}^{-3} {\mathrm{dm}}^3\right)}{\left(0.082 {\mathrm{dm}}^3\text{ atm }{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}\right)(300 \mathrm{K})}$$=0.122\mathrm{mol}$.

The number of molecules is$N=n{N}_{\mathrm{A}}=(0.122 \mathrm{mol}) \left(6.022\times {10}^{23} {\mathrm{mol}}^{-1}\right)=7.34\times {10}^{22}$