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.

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

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3