[zerality]

Hi,

I need help converting 745 torr to meters H20. (was given that the density of Hg is 13.6 g/ml and that water is .997g/ml).

I can obviously use a conversion calculator to work this out, but would like to try obtain the answer via dimensional analysis. I know that 745 torr = 745 mmHg = .745 meters Hg.

I'm not sure where to proceed from here. I think the proportion of the densities are involved.
.745 x (13.6/.997) = 10.16 m H20

[enahs]

Correct.

[zerality]

The reason why I am unsure about whether this is correct or not is that the units do no cancel appropriately to leave me with mH20.

[enahs]

The reason why I am unsure about whether this is correct or not is that the units do no cancel appropriately to leave me with mH20.

Sure they do.

745 torr - 745mm Hg = 0.745 m Hg

(0.745 m Hg )  ( 13.6 g  )  ( 1mL H₂O)     =  X m H₂O
                         1mL Hg      0.997 g       


The following are mathematically equivalent.

13.6g Hg     =   13.6g           =      (13.6g ) *  Hg
   1mL                 1mL Hg                ( 1mL )


The Hg is not really a unit, though you treat it like one in dimensional analysis. As a result, you can move it to the numerator or denominator in cases like this.

Be careful though, it can get tricky, because it is not always moveable. And remember in mathematics you can do anything you want to a number or unit as long as you do it to everything else (as you see in the example for how they cancle properly the same change was applied to the density of water).


Edit:

To clarify, the Hg (or H₂O, etc) in this case IS a unit for dimensional analysis and Chemistry but it is not a unit in mathematics. It is just a identifier.

[zerality]

Thanks for your help. I kept leaving ml - Hg as a "unit"  and thus it did not cancel out with ml- H20.

[Yggdrasil]

A good formula to remember is that, for a column of fluid with density d and height h, the pressure P exerted by the fluid at the base of the column is given by:

P = dgh

where g is the gravitational constant (9.80m/s²).