Question

Professional divers sometimes use heliox, consisting of 79% helium and 21% oxygen by mole. Suppose a perfectly rigid scuba tank with a volume of 11 L contains heliox at an absolute pressure of 2.1×10⁷Pa at a temperature of 31°C.

(a) How many moles of helium and how many moles of oxygen are in the tank?
(i) 4.72 mol He, 1.28 mol O₂
(ii) 3.81 mol He, 1.19 mol O₂
(iii) 2.95 mol He, 1.37 mol O₂
(iv) 5.64 mol He, 0.76 mol O₂

Answer 1

To determine the number of moles of helium and oxygen in the tank, use the ideal gas law equation: PV = nRT. Calculate the moles of helium and oxygen using the mole fraction of each gas and the total moles in the tank.

Step-by-step explanation:

To determine the number of moles of helium and oxygen in the tank, we can use the ideal gas law equation:

PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15.

The molar mass of helium is approximately 4 g/mol, and the molar mass of oxygen is approximately 32 g/mol.

We can calculate the moles of helium and oxygen using the mole fraction of each gas and the total moles in the tank.

The mole fraction of helium is given as 79%, which means it has a mole fraction of 0.79.

Thus, the moles of helium can be calculated as: 0.79 * total moles.

Similarly, the moles of oxygen can be calculated as: 0.21 * total moles.