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

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Answer 1 · 2016-06-06T21:46:33

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:

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

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

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

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