Air consits of 21% oxygen, 78% nitrogen and 1% argon by volume. Calculate the partial pressures in Pa if total pressure is 1 atm.

Question

My teacher just converted 1atm in pa and then did 21% of that for oxygen etc etc. Can you explain why she did this, is volume directly proportional to pressure? isnt it inversely proportional?

And for oxygen she just called it the oxygen mocule O2. But why? the question just said oxygen. Please someone shed some light.

Answer 1

Oxygen in the air is O2 like wise nitrogen is N2.

mole fraction = n (mole of 1 component) / N (total mole of all components)

Oxygen mole = 21 g /(32g/mol)=0.66 mole
Nitrogen mole = 78 g / (28g/mol) =2.78 mole
Argon mole = 1g / (40g/mol) =0.025

total mole =0.66 + 2.78 + 0.025 =3.465 mol

mole fraction oxygen = mole/total mole =0.19
mole fraction N =2.78/3.465 =0.8
mole fraction Ar =0.01

Partial pressure = mole fraction x pressure

oxygen partial pressure =0.19 x 1 atm = 0.19 atm. since 1 atm=101325 Pa; 0.19 atm =19251.75 Pa

and follow the same step for partial pressure of N2 and Ar. hope this helps.

Answer 2

since all the gases are in % (100 percent) you could easily convert those percentages to grams to find the moles of O2, N2, and Ar.

Answer 3

The atmosphere composition is % by volume, not by mass. If we take the gases as ideal gases then because the same volume of any gas contains the same number of moles the % by volume is also the % by mole, and hence fraction by mole.

0.21 mole
0.78 mole
0.1 mole

Thus because

Partial pressure = mole fraction x pressure

It is straightforward to calculate the partial pressure, so in atmospheres the partial pressure are

0.21 atm
0.78 atm
0.1 atm

which can be conveted to Pa by multiplying by 10^4

Oxygen exists in the atmosphere as O2, but you do not need to know this to answer the question.