Question

2. On a summer day, you take a road trip through Moses Lake, WA, in a sports car. You start out at a temperature of 21°C in the morning, but the temperature in Moses Lake will reach a peak of 55°C. Each tire on your car holds 15.2 L of nitrogen gas at a starting pressure of 247 kPa. The tires will burst if the internal pressure exceeds 270 kPa. Answer the following questions and show your work. (no work = no credit) 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 Moses Lake? 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:

1- 1.54 mol.

2- 271.9 kPa.

3- Yes, the tires will burst.

4- 235.67 kPa.

Explanation:

Q1- How many moles of nitrogen gas are in each tire?  

• To calculate the no. of moles of nitrogen gas in each tire, we can use the general law of ideal gas: PV = nRT.

where, P is the pressure of the nitrogen gas (P = 247.0 kPa/101.325 = 2.44 atm),

V is the volume of the nitrogen gas (V = 15.2 L),

n is the no. of moles of the nitrogen gas (n = ??? mole),

R is the general gas constant (R = 0.082 L.atm/mol.K),

T is the temperature of the nitrogen gas (T = 21 °C + 273 = 294 K).

∴ n = PV/RT = (2.44 atm)(15.2 L)/(0.082 L/atm/mol.K)(294.0 K) = 1.54 mol.

Q2: What would the maximum tire pressure be at 50 degrees C?  

• Now, the temperature is raised to be 50°C (T = 50°C + 273 = 323 K).

• The pressure can be calculated using the general gas law: PV = nRT.

∴ P = nRT/V = (1.54 atm)(0.082 L/atm/mol.K)(323.0 K)/(15.2 L) = 2.68 atm = 271.9 kPa.

Q3: Will the tires burst in Moses Lake? Explain.

• Yes, the tires will burst because the internal pressure be 271.9 kPa that exceeds 270 kPa, the pressure above which the tires will burst.

Q4: 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.)  

• To get the pressure that we must begin with:

• Firstly, we should calculate the no. of moles at:

T = 55°C + 273 = 328 K,

Pressure = 270 kPa (the pressure above which the tires will burst). (P =270 kPa/101.325 = 2.66 atm).

• V = 15.2 L, as there is no significant change in tire volume.

∴ n = PV/RT = (2.66 atm)(15.2 L)/(0.082 L.atm/mol.K)(328 K) = 1.5 mol.

• 1.5562 moles of N₂ in the tires will give a pressure of 270 kPa at 55°C, so this is the minimum moles of N₂ that will make the tires burst.

• Now, we can enter this number of moles into the original starting conditions to tell us what pressure the tires will be at if we start with this number of moles of N₂.

P = ???  

V = 15.6 L.

n = 1.5 mol

T = 21°C + 273 = 294.0 K  

R = 0.0821 L.atm/mol.K.

∴ P = nRT/V = (1.5 mol x 0.082 x 294.0 K) / (15.6 L) = 2.2325 atm = 235.67 kPa.

• So, the starting pressure needs to be 235.67 kPa or just under in order for the tires not to burst.