Question

chemistry homework reviewScuba divers breath a specialized mixture of gases so the concentration of the dissolved oxygen in the blood stream does not reach toxic levels. A 12.5 L scuba diving tank contains a helium-oxygen(heliox) mixture of 24.2g of the He and 4.32 g of O2 at 25 degrees celsius What is the mole fraction of O2 in the tank?What is the partial pressure of O2 in the tank?

Answer 1

The mole fraction of O2 in the tank = 0.101

The partial pressure of O2 in the tank = 0.264 atm

Step-by-step explanation

Given:

Volume, V = 12.5 L

Temperature, T = 25 °C = (25 + 273.15 K) = 298.15 K

Mass of helium = 24.2 g

Mass of O2 = 4.32 g

Step-by-step solution:

The first step is to calculate the total pressure. The total pressure can be calculated using the ideal gas equation.

`PV=nRT`

n is the total moles in the container and can be calculated by converting the grams of helium and O2 to moles by taking their grams and dividing by their molar masses:

24.2 grams Neon x (1 mol Neon / 20.18 g Neon) = 1.199 mol Neon

4.32 grams Oxygen x (1 mol Oxygen / 31.998 g O2) = 0.135 mol Oxygen

Total moles = 1.199 + 0.135 = 1.334 mol

Now, we can solve for the total pressure using the equation above.

Putting V = 12.5 L; T = 298.15 K; n = 1.334 mol and R = 0.0821 L atm / mol K.

`\begin{gathered} P*12.5=1.334*0.0821*298.15 \\ \\ P=(32.65380541)/(12.5)=2.61\text{ }atm \end{gathered}`

The total pressure in the tank = 2.61 atm.

The mole fraction of O2 in the tank:

The mole fraction of O2 in the tank can be calculated using

`Mole\text{ }fraction\text{ }of\text{ }O_2=\frac{Mole\text{ }of\text{ }O_2}{Total\text{ }mole\text{ }in\text{ }the\text{ }tank}=(0.135)/(1.334)=0.101`

The mole fraction of O2 in the tank = 0.101

The partial pressure of O2 in the tank:

The partial pressure of O2 in the tank in the tank can be calculated using

Partial fraction of O2 = mole fraction of O2 x total pressure

Putting mole fraction of O2 = 0.101, and total pressure = 2.61 atm

Partial fraction of O2 = 0.101 x 2.61 atm = 0.264 atm

The partial pressure of O2 in the tank = 0.264 atm