Deducing Number of Molecules in a Scuba Tank

[aerograce]

Homework Statement

A scuba tank has a volume of 2800cm3. For very deep dives, the tank is lled with 50%
(by volume) pure oxygen (O2) and 50% pure helium (He). The molar mass of helium
is 4 g mol/1, and for oxygen is 32 g mol/1.
How many molecules are there of each type in the tank if it is lled at 20 C to a
total pressure of 10 atmospheres? [Correct answer: N(He) = N(O2) = 3:55  1023]

Homework Equations

PV=nRT

The Attempt at a Solution

Correct answer given: The number of He molecules and O2 molecules are the same, since they occupy 50% by volume,
they have the same number of moles.
Each gas will contribute 5 atm in the gas cylinder. Using pV = NkT,
NO2 = NHe =3.51*10^23

My question is, how can we deduce N and P for two kinds of gases are the same. Because according to PV=nRT, we can only deduce that P(He)/N(He)=P(O2)/V(O2)

 

[Dick]

Homework Statement

A scuba tank has a volume of 2800cm3. For very deep dives, the tank is lled with 50%
(by volume) pure oxygen (O2) and 50% pure helium (He). The molar mass of helium
is 4 g mol/1, and for oxygen is 32 g mol/1.
How many molecules are there of each type in the tank if it is lled at 20 C to a
total pressure of 10 atmospheres? [Correct answer: N(He) = N(O2) = 3:55  1023]

Homework Equations

PV=nRT

The Attempt at a Solution

Correct answer given: The number of He molecules and O2 molecules are the same, since they occupy 50% by volume,
they have the same number of moles.
Each gas will contribute 5 atm in the gas cylinder. Using pV = NkT,
NO2 = NHe =3.51*10^23

My question is, how can we deduce N and P for two kinds of gases are the same. Because according to PV=nRT, we can only deduce that P(He)/N(He)=P(O2)/V(O2)

The pressure P is the same because both gases are in the same tank. A tank has only one pressure, same for temperature. Since each gas occupies the same volume, the N's must also be the same.

 

[Borek]

Have you heard about Avogadro's hypothesis? If not - google.