Mixtures of helium and oxygen are used in scuba diving tanks to help prevent ‘the bends’, a
condition caused by nitrogen bubbles forming in the bloodstream. If 95 L of oxygen and 25
L of helium at STP are pumped into a scuba tank with a volume of 8.0 L, what is the partial
pressure of each gas in the tank and what is the total pressure in the tank at 25 oC?
is the answer 12.96?
and 3.41
mols O2 = 95/22.4 = ?
mols He = 25/22.4 = ?
Use PV = nRT and substitute mols O2 fo pO2.
Do same for He for pHe.
Ptotal = pHe + pO2.
To determine the partial pressures of each gas and the total pressure in the tank, we need to use the ideal gas law.
The ideal gas law is given by the equation: PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's find the number of moles of oxygen and helium in the scuba tank using the ideal gas law.
For oxygen:
P1V1 = n1RT
Since the oxygen is at STP (standard temperature and pressure), which is 0 degrees Celsius or 273 Kelvin and 1 atm:
P1 = 1 atm
V1 = 95 L
T1 = 273 K
R = 0.0821 L·atm/(mol·K)
Now we can solve for n1:
(1 atm)(95 L) = n1(0.0821 L·atm/(mol·K))(273 K)
n1 ≈ 3.62 moles
For helium:
P2V2 = n2RT
Using the same reasoning, since the helium is at STP:
P2 = 1 atm
V2 = 25 L
T2 = 273 K
Now we can solve for n2:
(1 atm)(25 L) = n2(0.0821 L·atm/(mol·K))(273 K)
n2 ≈ 1.03 moles
Now that we have the number of moles of oxygen (n1) and helium (n2) in the tank, we can calculate their partial pressures using the formula:
Partial Pressure = (moles of gas / total moles of gas) * total pressure
Partial pressure of oxygen:
PO2 = (n1 / (n1 + n2)) * Ptotal
Substituting in the values:
PO2 = (3.62 / (3.62 + 1.03)) * Ptotal
PO2 ≈ 0.778 * Ptotal
Partial pressure of helium:
PHe = (n2 / (n1 + n2)) * Ptotal
Substituting in the values:
PHe = (1.03 / (3.62 + 1.03)) * Ptotal
PHe ≈ 0.222 * Ptotal
Since the total pressure in the tank is the sum of the partial pressures of each gas, we have:
Ptotal = PO2 + PHe
Ptotal ≈ 0.778 * Ptotal + 0.222 * Ptotal
1 * Ptotal ≈ Ptotal
Therefore, the total pressure in the tank is equal to Ptotal.
Now, to calculate the total pressure in the tank at 25 degrees Celsius (298 Kelvin), we need to apply the ideal gas law again:
Ptotal * Vtotal = (n1 + n2) * R * T3
Where:
Ptotal = total pressure
Vtotal = total volume
n1 + n2 = total number of moles
T3 = 298 K
Substituting in the values:
Ptotal * 8.0 L = (3.62 + 1.03) mol * (0.0821 L·atm/(mol·K)) * 298 K
Now solve for Ptotal:
Ptotal = [(3.62 + 1.03) * 0.0821 * 298] / 8.0
Ptotal ≈ 1.791 atm
Therefore, the partial pressure of oxygen in the tank is approximately 0.778 atm, the partial pressure of helium is approximately 0.222 atm, and the total pressure in the tank at 25 degrees Celsius is approximately 1.791 atm.