Question

On a summer day, you take a road trip through Death Valley, California, in an antique car. You start out at a temperature of 21°C, but the temperature in Death Valley will reach a peak of 51°C. The tires on your car hold 15.6 L of nitrogen gas at a starting pressure of 249 kPa. The tires will burst when the internal pressure (Pb) reaches 269 kPa. Answer the following questions and show your work.
How many moles of nitrogen gas are in each tire?
• What will the tire pressure be at peak temperature in Death Valley?
• Will the tires burst in Death Valley? Explain.
• If you must let nitrogen gas out of the tire before you go, to what pressure must you reduce the tires before you start your trip? (Assume no significant change in tire volume.)

Answer 1

There is only one formula to use and we should assume ideal gas. This equation is: PV=nRT. For the following questions manipulate this equation to get the answer.
 1. n = PV/RT = (249*1000 Pa)(15.6 L)(1 m^3/1000 L)/(8.314 Pa-m^3/mol-K))(21+273) = 1.59 mol
 2. P = nRT/V = (1.59)(8.314)(51+273)/(15.6/1000)(1000) = 274.55 kPa
 3. Since the answer in #2 is more than 269 kPa, then the tires will likely burst. 4. Reduce pressure way below the limit 269 kPa.