Question

7. An oxygen tank in a laboratory has an internal pressure of 12 atm at 25°C. If the pressure inside the tank exceeds 25 atm, the tank will explode. A fire breaks out in the laboratory raising the temperature of the gas cylinder to 398 "C. Show how to determine and then calculate the final internal pressure of the tank and indicate if the tank will explode or is safe may assume that the volume of the tank and the number of moles of oxygen gas inside the tank remain unchanged). 8. A nitrogen gas bubble begins to form in the left knee joint of a deep sea diver just before they begin their ascent to the surface. The nitrogen gas bubble in the knee has a volume of 0.0125 mL when the diver begins to ascend from a depth of 105 feet where the pressure is 4.15 atm and the temperature is 10.5 °C. Show how to determine (and then calculate) the volume of this nitrogen gas bubble (in mL) at the surface where the pressure is 0.998 atm and the temperature is 29.5 °C (you may assume that the number of moles of nitrogen gas in the bubble is constant).
#8 please

Answer 1

Sol 8.

As the number of moles of nitrogen gas in the bubble is constant , so ,

P1 × V1 / T1 = P2 × V2 / T2  

where P1 = Pressure at depth of 105 feet = 4.15 atm

V1 = Volume of nitrogen gas bubble in the knee

= 0.0125 mL

T1 = Temperature at depth of 105 feet

= 10.5°C = 283.65 K

P2 = Pressure at surface = 0.998 atm

T2 = Temperature at surface = 29.5°C = 302.65 K

Therefore ,  

Volume of nitrogen gas bubble at the surface  

= V2

= P1 × V1 × T2 / ( P2 × T1 )

= 4.15 × 0.0125 × 302.65 / ( 0.998 × 283.65 )

= 0.0555 mL