What is the equivalent pressure of 0.743 atm in units of mm Hg?

1 Answer
Jul 18, 2016

"565 mmHg"565 mmHg

Explanation:

The problem wants you to use a known conversion factor to go from pressure expressed in atmospheres, "atm"atm, to pressure expressed in millimeter of mercury, "mmHg"mmHg.

Now, you can find the conversion factor that takes you from atmospheres to millimeter of mercury by using the pascals, "Pa"Pa, the SI unit of pressure.

In terms of pascals, an atmosphere is defined as a pressure of

"1 atm " = " 101325 Pa"1 atm = 101325 Pa

Similarly, a millimeter of mercury, which is simply the pressure exerted by a "1-mm"1-mm high column of mercury, is defined as a pressure of approximately

"1 mmHg " ~~ " 133.32239 Pa"1 mmHg 133.32239 Pa.

Your goal now is to find how many milliliters of mercury are needed to get to the equivalent of one atmosphere. You can say that you have

overbrace(101325 color(red)(cancel(color(black)("Pa"))))^(color(blue)("= 1 atm")) * "1 mmHg"/(133.32239color(red)(cancel(color(black)("Pa")))) ~~ "760 mmHg"

This tells you that a column of mercury "760 mm" high creates a pressure equal to "1 atm".

http://wps.prenhall.com/wps/media/objects/4678/4790892/ch09_01.htm

You can thus say that your conversion factor looks like this

color(purple)(|bar(ul(color(white)(a/a)color(black)("1 atm " = " 760 mmHg")color(white)(a/a)|)))

Use this conversion factor to find the equivalent pressure of "0.743 atm" in units of "mmHg"

0.743 color(red)(cancel(color(black)("atm"))) * "760 mmHg"/(1color(red)(cancel(color(black)("atm")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("565 mmHg")color(white)(a/a)|)))

The answer is rounded to three sig figs.