Question

A cylinder of medical oxygen has a volume of 38.6L, and contains O2 at a pressure of 144 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?

Answer 1

To determine the volume of oxygen (O2) at normal body conditions, we can use the ideal gas law, which states:

PV = nRT

where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature in Kelvin

First, let's convert the given temperature and the target temperature to Kelvin: Given temperature (T1) = 25 °C + 273.15 = 298.15 K Target temperature (T2) = 37 °C + 273.15 = 310.15 K

Next, we'll calculate the number of moles of oxygen in the cylinder at the given conditions using the ideal gas law: P1V1 = nRT1

n = (P1V1) / (RT1)

where: P1 = pressure at given conditions = 144 ATM V1 = volume at given conditions = 38.6 L R = ideal gas constant = 0.0821 L·atm/(mol·K)

n = (144 ATM * 38.6 L) / (0.0821 L·atm/(mol·K) * 298.15 K)

n ≈ 200.34 moles

Now, we can use the number of moles and the target conditions to calculate the volume of oxygen at normal body conditions: P2V2 = nRT2

V2 = (nRT2) / P2

where: P2 = pressure at normal body conditions = 1 ATM

V2 = (200.34 moles * 0.0821 L·atm/(mol·K) * 310.15 K) / (1 ATM)

V2 ≈ 5060.36 L

Therefore, the volume of oxygen in the cylinder at normal body conditions (1 ATM and 37 °C) is approximately 5060.36 liters.