Question

Question #b3b27

Answer 1

`66.675`

Explanation:

Vapor density is simply the density of a gas compared with the density of hydrogen gas, `"H"_2`, kept under the same conditions for pressure and temperature.

In essence, vapor density tells you the ratio that exists between between the mass of a gas present in a given volume and the mass of hydrogen gas present in the same volume.

You can thus say that vapor density is equal to

`color(blue)(|bar(ul(color(white)(a/a)"vapor density" = "molar mass of a gas"/"molar mass of H"_2color(white)(a/a)|)))`

Now, your unknown element is said to have a molar mass of `"27 g mol"^(-1)` and a valency of `3`. A quick look in the periodic table wil reveal that you're dealing with aluminium, `"Al"`.

Aluminium combines with chlorine, `"Cl"`, to form aluminium chloride, `"AlCl"_3`, and ionic compound that contains one aluminium cation, `"Al"^(3+)`, and three chloride anions, `"Cl"^(-)`.

Notice that the cation has a charge of `3+`, which is why the element's valency was said to be equal to `3`.

In order to find the vapor density of aluminium chloride, you must first calculate its molar mass. Another look in the periodic table will show that chlorine has a molar mass of approximately `"35.45 g mol"^(-1)`.

The molar mass of the compound will be

`1 xx "27 g mol"^(-1) + 3 xx "35.45 g mol"^(-1) = "133.35 g mol"^(-1)`

You can take the molar mass of hydrogen gas to be approximately `2 g mol"^(-1)`, which means that the vapor density of the aluminium chloride will be

`"vapor density" = (133.35 color(red)(cancel(color(black)("g mol"^(-1)))))/(2 color(red)(cancel(color(black)("g mol"^(-1))))) = color(green)(|bar(ul(color(white)(a/a)66.675color(white)(a/a)|)))`

SIDE NOTE The actual answer will probably vary a bit depending on the value you pick for the molar mass of chlorine. For example, if you take `"35.5 g mol"^(-1)`, you will end up with

`"vapor density" = 66.75`