density of a gas mixture

alexmath

what's the formula for the density of a gas mixture? Thank you!
ρ1=m1/v1
ρ2=m2/v2
but the gas mixture isn't ρ1+ρ2.

nasu

The density of the mixture is ρ=(m1+m2)/(V1+V2).
From this basic definition you can find various expression, as a function of the given quantities. You need to know the ratio between the two components (in volume , mass, molar fractions etc).
For example, if the volume fractions are given,
V1=c (V1+V2)=c V
V2=(1-c) V

Then
ρ=(ρ1 V1+ρ2 V1)/(V1+V2)=[ρ1 c V+ρ2 (1-c) V]/V=ρ1 c + ρ2 (1-c)

alexmath

heeey, but volume is not additive. Should i assume it is?

nasu

Oh, you specified that you are interested in gases.
The example does not apply then but the general formula does.
Combined with the ideal gas law, should give you the result for any specific case.
In this case you have to decide in what conditions (pressure, temperature) do you take the densities of the components .
If we take the densities of the components at their partial pressures then you we can write
ρ=ρ1+ρ2 where ρ1=m1/V and ρ2=m2/V where V is the total volume of the mixture.
Is this what you need?

alexmath

ohhhh... if the gases are ideal, volumes are additive then, right?

nasu

No, I did not say that. I agreed that my example with additive volumes does not apply for gases. Sorry for not being clear enough.
If you have two gases in a container, each one occupies the volume of the container. They have the same volume and this is equal to the volume of the mixture too. Their pressures are additive (see partial pressures). And the densities, defined at the component's partial pressure, are additive too.