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1. 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掳C, but the temperature in Death Valley will reach a peak of 51掳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.)Please help with chemistry problem so lost?Use the gas equation
PV = nRT
Work out the moles N2 using the original conditions of Temp and Pressure...
P = pressure (249 kPa = 2.4574 atm)
V = 15.6 L
n = moles
T = Temp in Kelvin (21 deg C = 273.15 + 21 = 294.15 Kelvin)
R = gas constant = 0.0821 L atm mol^-1 K^-1
- (R varies accoring to your units of Pressure and Volume, to use 0.0821 L atm mol^-1 K^-1 you will need to convert pressure to atm - see link on Gas constant and pressure conversion)
n = PV / RT
n = (2.4574 atm x 15.6 L) / (294.15 K x 0.0821 L atm mol^-1 K^-1)
n = 38.33544 atm L / 24.149715 L atm mol^-1
n = 1.5874 moles N2
n = 1.59 mol (3 sig fig)
Now, the temp goes up to 51 deg C
So new temp = 273.15 + 51 = 324.15 K
T = 324.15 K
So now work out what pressure the number of moles of N2 will give at the new Temp
all other conditions are the same
PV = nRT
Therefore
P = nRT / V
P = (1.5874 mol x 0.0821 L atm mol^-1K^-1 x 324.15 K) / 15.6 L
P = 2.71 atm
The pressure goes up to 2.71 atm
2.71 atm = 274.59 kPa
SO yes, the tires will burst.
Now
You need to work out how many moles will give you a pressure of 269 kPa at 51 deg C, (because this is when the tyres will blow up. Then go back and work out what pressure this number of moles generates under the starting conditions of 21 deg C and 15.6 L
Again
PV=nRT
For tires to burst at 51 deg C
P = 269 kPa (= 2.6548 atm)
V = 15.6 L (question says assume no volume change)
T = 51 deg C = 324.15 K
R = 0.0821 L atm mol^-1K^-1
n = unknown
n = RV / RT
n = (2.6548 x 15.6) / (0.0821 x 324.15)
n = 1.5562 moles of N2
1.5562 moles of N2 in the tyres will give a pressure of 269 kPa at 51deg C, so this is the MINIMUM moles of N2 that will make the tires
blow up.
Now, enter this number of moles into the original starting conditions to tell you what pressure the tyres will be at if you start with this number of moles of N2.
P = ?
V = 15.6 L
n = 1.5562 mol
T = 21 deg C = 294.15 K
R = 0.0821 L atm mol^-1K^-1
P = nRT / V
P = (1.5562 mol x 0.0821 x 294.15 K) / 15.6 L
P = 2.4091 atm
P = 244.1 kPa
The starting pressure needs to be 244.1 kPa or just under in order for the tyres not to burst..
