Question

A cylinder of medical oxygen has a volume of 35.4 L, and contains O2 at a pressure of 151 atm and a temperature of 25 °C. What volume of O2 does this correspond to at normal body conditions, that is, 1 atm and 37 °C?

a) 24.8 L
b) 26.5 L
c) 30.2 L
d) 35.4 L

Answer 1

The volume of medical oxygen at normal body conditions, when converted from the initial conditions of 151 atm and 25 °C, is approximately 5305 L based on the Combined Gas Law.

Step-by-step explanation:

To determine the volume of medical oxygen at normal body conditions from the given volume at high pressure and temperature, we must use the Combined Gas Law which is:

(P1 * V1) / T1 = (P2 * V2) / T2

where

P is pressure

V is volume

T is temperature (in Kelvin)

First, convert temperatures to Kelvin:
T1 = 25 °C + 273 = 298 K and T2 = 37 °C + 273 = 310 K.

Now plug our known values into the equation and solve for V2:
(151 atm * 35.4 L) / 298 K = (1 atm * V2) / 310 K.

Cross multiply and solve for V2:
(151 atm * 35.4 L) * 310 K = 298 K * 1 atm * V2,
which simplifies to V2 = (151 atm * 35.4 L * 310 K) / (298 K * 1 atm).

After calculation:
V2 ≈ 5305 L, which means the correct answer is: c) 5305 L.