Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent “the bends.”

Question

For a particular dive, 46 L He and 12 L O2 both at 25oC and 1.0 atm were pumped into a tank
with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the
tank at 25oC.

Answer 1

First, we need to calculate the moles of each gas that were pumped into the tank using the ideal gas law equation:

n_He = (P_He * V_He) / (R * T) = (1.0 atm * 46 L) / (0.0821 L.atm/mol.K * 298 K) = 1.83 mol He
n_O2 = (P_O2 * V_O2) / (R * T) = (1.0 atm * 12 L) / (0.0821 L.atm/mol.K * 298 K) = 0.48 mol O2

Next, we can calculate the mole fraction of each gas in the tank:

X_He = n_He / (n_He + n_O2) = 1.83 / (1.83 + 0.48) = 0.79
X_O2 = n_O2 / (n_He + n_O2) = 0.48 / (1.83 + 0.48) = 0.21

Now, we can use the mole fractions to calculate the partial pressure of each gas:

P_He = X_He * P_total = 0.79 * 1.0 atm = 0.79 atm
P_O2 = X_O2 * P_total = 0.21 * 1.0 atm = 0.21 atm

Finally, we can calculate the total pressure in the tank using the ideal gas law:

P_total = (n_total * R * T) / V_total = ((n_He + n_O2) * 0.0821 L.atm/mol.K * 298 K) / 5.0 L = 1.0 atm

Therefore, the partial pressure of helium is 0.79 atm, the partial pressure of oxygen is 0.21 atm, and the total pressure in the tank is 1.0 atm.