An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.60 ft3 of O2 gas at a pressure of 2300 lb/in2.
What volume would the oxygen occupy at atmospheric pressure (and the same temperature)?

Question

An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.60 ft3 of O2 gas at a pressure of 2300 lb/in2. 
What volume would the oxygen occupy at atmospheric pressure (and the same temperature)?

Josiah Austin · Accepted Answer

The volume of oxygen would be #"94 ft"^3#.

It looks like there is a Boyle's Law issue here. Boyle's Law states #color(blue)(|bar(ul(color(white)(a/a) P_1V_1 = P_2V_2color(white)(a/a)|)))" "# #P_1 = 2300color(white)(m) "lb/in"^2; V_1 = "0.60 ft"^3# #P_2 =color(white)(m) "14.7 lb/in"^2; V_2 = "?"# Boyle's Law can be rearranged to get #V_2 = V_1 × P_1/P_2# ∴ #V_2 = "0.60 ft"^3 × (2300 color(red)(cancel(color(black)("lb/in"^2))))/(14.7 color(red)(cancel(color(black)("lb/in"^2)))) = "94 ft"^3#

Josiah Austin · Answer

undefined To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature and the amount of gas are constant.

P1 * V1 = P2 * V2

Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume

We are given:
P1 = 2300 lb/in^2
V1 = 0.60 ft^3
P2 = 14.7 lb/in^2 (atmospheric pressure)

Rearranging the equation for V2, we get:

V2 = (P1 * V1) / P2

Plugging in the values:

V2 = (2300 lb/in^2 * 0.60 ft^3) / 14.7 lb/in^2

V2 ≈ 93.88 ft^3

So the volume of oxygen at atmospheric pressure would be approximately 93.88 ft^3.

An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.60 ft3 of O2 gas at a pressure of 2300 lb/in2. What volume would the oxygen occupy at atmospheric pressure (and the same temperature)?