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)?

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Answer 1 · 2016-08-14T18:30:47

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

This appears to be a Boyle's Law problem.

Boyle's Law is

#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 = "?"#

We can rearrange Boyle's Law 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#