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)|)))" "#
∴