1. 1.636 moles
2. 271.06 kPa pressure
3. Tires will be burst
4. 235.91 kPa
Explanation:
Step 1:
PV = nRT, is the equation to be used where
P represents pressure
V represents volume
n represents moles of gas
R is constant
T represents temperature in Kelvin
n=RT/PV
It is given that the pressure is 245 kPa at initial temperature 19 C and tire volume is 16.2 L. Temperature must be converted to Kelvin, 19 C equals 292K.
n=PV/RT ->245*16.2/(8.31*292) = 1.636
Number of moles of Nitrogen in the tire = 1.636
Step 2:
We need to find the maximum tire pressure at 50 C (323K)
P = nRT/V
Substituting the values P = (1.636 * 8.31 * 323)/16.2 = 271.06 kPa
The tire pressure at 50 C will be 271.06 kPa
Step 3
We need to figure out if the tires would burst in Chelan when the temperature is 55 C. It is given that the maximum pressure the tires can withstand is 265 kPA, so any pressure above this will cause the tire to burst. In Step-2 we calculated that the pressure is 271.06 kPA at 50 C which is more than the maximum pressure the tire can withstand. The pressure would increase further with temperature and at 55 C the pressure will be more than 271.06 kPa. So the tires are likely to burst in Chelan.
Step 4:
We need to find the pressure of Nitrogen at 19 C before the start of the trip so that tires will not burst. The pressure at 55 C is 265 kPa. Let us find the number of moles at this temperature and pressure.
n= PV/RT -> n=265*16.2/(8.31*328) = 1.575
Now let us find the pressure at 19 C.
P = nRT/V -> 1.575*8.31*292/16.2 = 235.91 kPa
