# If 2.31 g of the vapor of a volatile liquid is able to fill a 498 ml flask at 100 degrees C and 775 mmHg, how do you calculate the molar mass of the liquid? Also, how do you calculate the density of the vapor under these conditions?

##### 1 Answer

The molar mass of the gas is 139 g/mol, and its density is 4.64 g/L.

#### Explanation:

We can use the **Ideal Gas Law** to solve both of these problems:

#color(blue)(|bar(ul(color(white)(a/a)PV = nRT color(white)(a/a)|)))" "#

**Molar mass**

Since

#color(blue)(|bar(ul(color(white)(a/a)PV = m/MRTcolor(white)(a/a)|)))" "#

We can rearrange this to get

#M = (mRT)/(PV)#

∴

∴ The molar mass is 139 g/mol.

**Density**

We have seen that .

#color(blue)(|bar(ul(color(white)(a/a)PV = m/MRTcolor(white)(a/a)|)))" "#

We can rearrange this to

#PM = m/VRT#

But

∴

#color(blue)(|bar(ul(color(white)(a/a)ρ = (PM)/(RT)color(white)(a/a)|)))" "#

∴