Question

A SCUBA tank, an air tank used for breathing under water, is initially filled with gas at a pressure of 2.8x107 Pa and 32 oC. The tank has a volume of 11.5 L. If the tank will continue to provide air until it reaches a pressure of 1.2x106 Pa, how many moles of gas will it provide to a diver diving in water at 10 oC? Give your answer in moles to at least three significant figures. Hint: There will be air left in the tank when the it reaches the lowest pressure the tank can deliver. The amount of air left might be useful in solving this problem.

Answer 1

Given

The pressure at initial situation P = 2.8 x 10⁷ Pa

The temperature at initial situation T = 32^o C = 32 + 273 K = 305 K

The pressure at the end P’ = 1.2 x 10⁶ pa

The temperature at final condition T’ = 10^oC = 10+273 = 283 K

Volume of the container V = 11.5 L = 0.0115 m³

Universal gas constant R = 8.314 m³ Pa/mol K

Solution

The Ideal Gas law states that PV=nRT

Where n is the number of moles

n = PV/RT

In the initial situation the number of moles in the container can be

n₁ = PV/RT

n₁ = 2.8 x 10⁷ x 0.0115 / 8.314 x 305

n₁ = 126.98 mol

The number of moles left in the container

n₂ = P’V/RT’

n₂ = 1.2 x 10⁶ x 0.0115 / 8.314 x 283

n₂ = 5.86 moles

to total number of moles provided by the tank to the diver is N = n₁ – n₂ = 126.98 - 5.86 = 121.12 moles