# Question b3b27

May 9, 2016

$66.675$

#### Explanation:

Vapor density is simply the density of a gas compared with the density of hydrogen gas, ${\text{H}}_{2}$, 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

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {\text{vapor density" = "molar mass of a gas"/"molar mass of H}}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

Aluminium combines with chlorine, $\text{Cl}$, to form aluminium chloride, ${\text{AlCl}}_{3}$, and ionic compound that contains one aluminium cation, ${\text{Al}}^{3 +}$, and three chloride anions, ${\text{Cl}}^{-}$.

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 ${\text{35.45 g mol}}^{- 1}$.

The molar mass of the compound will be

$1 \times {\text{27 g mol"^(-1) + 3 xx "35.45 g mol"^(-1) = "133.35 g mol}}^{- 1}$

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 ${\text{35.5 g mol}}^{- 1}$, you will end up with

$\text{vapor density} = 66.75$