Question

4. On a summer day, you take a road trip through Chelan, WA, in a Tesla Model S. You start out at a temperature of 19°C in the morning, but the temperature in Chelan will reach a peak of 55°C. Each tire on your car holds 16.2 L of nitrogen gas at a starting pressure of 245 kPa. The tires will burst if the internal pressure exceeds 265 kPa. Answer the following questions and show your work. (no work = no credit) given R = 8.31. o How many moles of nitrogen gas are in each tire? o What would the maximum tire pressure be at 50 degrees C? o Will the tires burst in Chelan? Explain. o 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

Answer and Explanation:

Initial temperature before starting T = 19oC = 292.15 K

Initial volume = 16.2L

Tyre pressure = 245kPa = 2.418atm           [1atm=101.235kPa]

1. The number of mol (n)=PV/RT = (2.418 16.2) divided by (0.08205 292.15) = 1.634

2. At 55oC the pressure = (1.634 0.08205 328.15) divide by16.2 atm = 2.716 atm = 275kPa

3. The tyre will burst because the pressure exceed the tolerance limit

4.Max press = 265kPa = 2.615atm

V = 16.2L [given no significant change]

n = (2.615 16.2) divide by (0.08205 328.15) = 1.573

So, initial pressure will be = (1.573 0.08205 292.15) divide by16.2 = 2.328atm = 235.9kPa