Question

The vd for a certain gas is 70. If the molecular formula for this gas is `("CO")_x`, then what is `x`?

Answer 1

Thanks @michael-2 for clarifying what "vd" is.

The vapor density of a compound is:

`\mathbf(rho_"vap" = ("mass of n molecules of gas")/("mass of n molecules of H"_2(g)))`

Let's take `n = 6.0221413xx10^23`, i.e. the number of things in `"1 mol"`. Then what we have is:

`rho_"vap" = (M_(r,"gas"))/(M_(r,"H"_2))`

where `M_r` is the relative molar mass of the substance in `"g/mol"`.

So, since we know that `rho_"vap" = 70` and is unitless, that gives us:

`color(green)(M_(r,"gas") = M_(r,"H"_2) * rho_"vap")`

`= (2xx"1.0079 g/mol")xx70`

`=` `color(green)("141.106 g/mol")`

Based on that, and the molar mass of `"CO"` to be `12.011 + 15.999 = "28.01 g/mol"`, we have that:

`color(blue)(x) = (M_(r,"gas"))/(M_(r,"empirical formula"))`

`= ("141.106 g/mol")/("28.01 g/mol")`

`= 5.04 ~~ color(blue)(5)`