# How to calculate the vapour density of a mixture?

I have a gaseous mixture of $$\ce{H2}$$ and $$\ce{CO2}$$ which contains $$66\%$$ by mass of $$\ce{CO2}$$. I have to figure out the vapour density of the mixture (defined as mass of a certain volume of a substance divided by mass of same volume of hydrogen).

My approach: let's assume $$\pu{100 g}$$ of mixture contains $$\pu{66 g}$$ of $$\ce{CO2}$$ and $$\pu{34 g}$$ of $$\ce{H2}$$. Hence, the amount of substance of $$\ce{CO2} = \pu{1.5 mol}$$ and the amount of substance of $$\ce{H2} = \pu{17 mol}$$. The total amount of substance $$= \pu{18.5 mol}$$.

The mass of $$\pu{1 mol}$$ of mixture is 5.4 g (mass of 18.5 mol is 100 g), and the vapour density $$\text{VD} = 2.7$$.

I got my answer right, but now I am doubtful of my approach. Was it safe to assume that the amount of substance of mixture equals that of the amount of substance of both the gases?

• And where does that value come from? Confusing. – Karl Jul 16 '17 at 14:15
• as VD= M/2 M(= molecular mass – user8167818 Jul 16 '17 at 14:18
• Vapour density is molar mass divided by two? That sounds strange. Shouldn't it have units of gramm per liter? – Karl Jul 16 '17 at 14:25
• @Karl The OP is right (vapour density). I wasn't sure whether it's $2$ or $29$. – andselisk Jul 16 '17 at 14:50
• @andselisk Thanks. I have never heard of this measure before, and hope I will never again. ;-) – Karl Jul 16 '17 at 15:15

## 1 Answer

Was it safe to assume that the amount of substance of mixture equals that of the amount of substance of both the gases?

Amount of substance is additive, just like mass. You have to be careful with volume, though. So yes, it is safe to make that assumption.

I have to figure out the vapour density of the mixture

I'm not sure you are starting with a safe question, i.e. if the vapour density quantity was intended to describe mixtures. Wikipedia has "vapour density = molar mass of gas / molar mass of H2", and I'm not sure whether a mixture has a defined molar mass. The same source states that vapour density is sometimes based on the density of air rather than dihydrogen gas (to assess whether certain gases collect on the floor or ceiling of a room when released).