Problem: Cyclists sometimes use pressurized carbon dioxide inflators to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide.At 297 K , to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.51 L mountain bike tire? (Note: The gauge pressure  is the difference  between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.)

FREE Expert Solution

$$\begin{gathered} \boxed{\mathbf{PV}\mathbf{=}\mathbf{nRT}} \\ \mathrm{n}=\frac{\mathrm{m}}{\mathrm{M}} \\ \frac{\mathrm{P}\cancel{\mathrm{V}}}{\cancel{\mathrm{V}}}=\frac{{\displaystyle \frac{\mathrm{m}}{\mathrm{M}}}\mathrm{RT}}{\mathrm{V}} \\ \boxed{\mathbf{P}\mathbf{=}\frac{\mathbf{mRT}}{\mathbf{VM}}} \end{gathered}$$