Question

Calculate the height of a column of carbon tetrachloride, CCl4(l), with a density of 1.59 g/mL that exerts the same pressure as a 15.2 cm column of Mercury, Hg(l), that has a density of 13.6 g/ml. Express your answer in meters. Please only enter the numerical value of your answer.

Answer 1

P = F / A... pressure = force / area
F = m g... force = mass x acceleration due to gravity
? = m / V... density = mass / V... rearranging.. m = ?V
V = A x h... volume of the column of fluid = cross sectional area x height of the fluid

substituting...
P = F / A
P = (mg) / A
P = ((?V) x g) / A
P = ((?(Axh)) x g) / A
P = ? x A x h x g / A... cleaning it up
P = ? g h

*********
notice that Pressure is now independant of cross sectional area? and is a function of density, g and h only?

back to your problem
*********
there are a couple of different ways to do this.. you could say.. Pressure is pressure.. it's independant of the fluid we're using to measure it. 1 atm of pressure doesn't care if we measure it with a column of mercury or a column of CCl4 does it? acceleration due to gravity is the same way. "g" here on Earth doesn't care if we measure atmospheric pressure with a column of Hg or a column of CCl4. Why would it?

so.. because densities vary.. the height of the column must vary.

ie..
P-mmHg = P-mmCCl4.... pressure in mmHg = pressure in mm carbon tet... right?

so..
(? x g x h) Hg = (? x g x h) CCl4

canceling g
(? x h) Hg = (? x h) CCl4

rearranging...
h-CCl4 = h-Hg x (?-Hg / ?-CCl4)

solving.... assuming atmospheric pressure = 760.0 mmHg and density of Hg = 13.53 g/cm3
height CCl4 =152 mmHg x (13.53 g/cm / 1.594 c/cm3)
height CCl4 = 1290mmCCl4

ie.. the column would be about 1.290 meters tall