compressed 02 carried

Question

Bottles of compressed O2 carried by climbers ascending Mt. Everest have an internal volume of 5.90 L. Assume that one such bottle has been filled with O2 to a pressure of 2025 psi at 25°C. Also assume that O2 behaves as an ideal gas. (a) How many moles of O2 are in the bottle? (b) What is the mass in grams of O2 in the bottle? (hint use Ideal Gas Law).           .

Answer 1

(a) 33.2 mol O₂  |  (b) 1.06 × 10³ g (about 1.06 kg)

Step 0 — get the units to match your R

This is where the problem is won or lost. Using R = 0.08206 L·atm/(mol·K) means pressure must be in atm, volume in L, and temperature in K.

P = 2025 psi ÷ 14.696 psi/atm = 137.8 atm
V = 5.90 L (already fine)
T = 25 + 273.15 = 298.15 K

(a) Solve PV = nRT for n

n = PV/RT = (137.8 atm)(5.90 L) / [(0.08206)(298.15)]

n = 813.0 / 24.47 = 33.2 mol O₂

(b) Moles to grams

O₂ is diatomic: 2 × 16.00 = 32.00 g/mol — not 16.00.

m = (33.2 mol)(32.00 g/mol) = 1063 g ≈ 1.06 kg

Is that believable?

Yes, and pleasingly so. Real Everest oxygen cylinders carry roughly 1–1.2 kg of O₂ and weigh about 3–4 kg full — so a bottle of gas weighing about a kilogram is exactly right, and it is a reminder that compressed gas has serious mass. That mass is the whole logistical problem of high-altitude climbing.

Another way to feel the number: 33.2 mol at STP would fill 744 L. Squeezing that into 5.90 L is about a 126-fold compression, which is what 138 atm means physically.

Three places this goes wrong

1. Leaving pressure in psi. It gives a number ~14.7× too large. If your answer is around 490 mol, this is why.
2. Using 25 instead of 298.15. Celsius in a gas law inflates n by roughly 12×.
3. Using 16 g/mol for oxygen. Halves part (b). Elemental oxygen gas is O₂.

If your course prefers SI, R = 8.314 J/(mol·K) works equally well — convert psi to pascals (2025 psi = 1.396 × 10⁷ Pa) and volume to cubic metres (5.90 × 10⁻³ m³). Same 33.2 mol. Pick the R whose units you are least likely to fumble.