Suppose that Daniel has a 3.00 3.00 L bottle that contains a mixture of O 2 O2 , N 2 N2 , and CO 2 CO2 under a total pressure of 4.80 4.80 atm. He knows that the mixture contains 0.230 0.230 mol N 2 N2 and that the partial pressure of CO 2 CO2 is 0.350 0.350 atm. If the temperature is 273 273 K, what is the partial pressure of O 2 O2

Partial pressure O₂ → 2.74 atm

Explanation:

Let's analyse the data given:

Volume → 3L

In the bottle there is a mixture of gases that contains, O₂, N₂ and CO₂.

Total pressure is 4.80 atm

Let's apply the Ideal Gases Law to determine the total moles of the mixture

P . V = n .  R. T

4.80 atm . 3L = n . 0.082 . 273K

n = 4.80 atm . 3L / 0.082 . 273K → 0.643 moles

We apply the concept of mole fraction:

Mole fraction of a gas X = moles of gas X / Total moles

Mole fraction of a gas X = Partial pressure X / Total pressure

In a mixture, sum of mole fraction of each gas = 1

We determine mole fraction of N₂ → 0.230 / 0.643 = 0.357

We determine mole fraction of CO₂ → 0.350 atm / 4.80 atm = 0.0729

1 - mole fraction N₂ - mole fraction CO₂ = mole fraction O₂

1 - 0.357 - 0.0729 = 0.5701 → mole fraction O₂

We replace in the formula: Mole fraction O₂ = Partial pressure O₂ / 4.80 atm

0.5701 . 4.80 atm = Partial pressure O₂ → 2.74 atm

The partial pressure of O2 is 2.73 atm

Explanation:

Step 1: Data given

Volume of the bottle = 3.00 L

Total pressure = 4.80 atm

Moles N2 = 0.230 moles

Partial pressure CO2 = 0.350 atm

Temperature = 273 K

Step 2: Calculate total number of moles

p*V = nRT

⇒ p= the pressure = 4.80 atm

⇒V = the volume = 3.00 L

⇒ n = the number of moles = TO BE DETERMINED

⇒ R = the gas constant = 0.08206 L*atm/K*mol

⇒ T = the temperature = 273 K

n = (pV)/(RT)

n = (4.80*3.00)/(0.08206*273)

n = 0.643 moles

Step 3: Calculate mol fraction CO2

Mol fraction CO2 = partial pressure/ total pressure

Mol fraction CO2 = 0.350 atm / 4.80 atm

Mol fraction CO2 = 0.0729

Step 4: Calculate moles CO2

Moles CO2 = mol fraction * total moles

Moles CO2 = 0.0729 * 0.643 moles

Moles CO2 = 0.0469 moles

Step 5: Calculate moles O2

moles O2 = total moles - moles N2 - moles CO2

moles O2 = 0.643 - 0.230 - 0.0469

moles O2 = 0.3661 moles

Step 6: Calculate mol fraction O2

Mol fraction O2 = 0.3661 / 0.643

mol fraction O2 = 0.569

Step 7: Calculate partial pressure O2

Partial pressure O2 = mol fraction * total pressure

Partial pressure O2 = 0.569 * 4.80 atm

Partial pressure O2 = 2.73 atm

The partial pressure of O2 is 2.73 atm