Question

How high in meters must a column of glycerol be to exert a pressure equal to that of a 760-mm column of mercury? The density of glycerol is 1.26g/mL, whereas that of mercury is 13.6g/mL.

Answer 1

The gage pressure at the bottom f a column of liquid is
p = ρgh
where
ρ = density
g = acceleration due to gravity = 9.8 m/s²
h = height of the column of liquid

Note that
1 g/mL = 1000 kg/m³

With mercury,
h = 760 mm = 0.76 m
ρ = 13.6 g/mL = 13600 kg/m³
The pressure is
p = (13600 kg/m³)*(9.8 m/s²)*(0.76 m) = 1.0129 x 10⁵ Pa

With glycerol,
ρ = 1.26 g/mL = 1260 kg/m³
In order for the pressure to be the same, the height required, h, is
(1260 kg/m³)*(9.8 m/s²)*(h m) = 1.0129 x 10⁵ Pa
12348 h = 1.0129 x 10⁵
h = 8.2032 m

Answer: 8.203 m

Answer 2

If you know PV=nRT formula it should be clear that the pressure inversely proportional to the volume. Density is directly proportional to volume, so it also inversely proportional to the pressure (assuming the same mass of substance used).
The calculation for this question would be: 760mm*13.6 / 1.26= 8203.17 mm * 1000 meter/mm= 8.2 meter