Question

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

Answers

GPT 3.5
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.

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