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

1 Answer
Jul 18, 2016

Answer:

#"565 mmHg"#

Explanation:

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

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

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

#"1 atm " = " 101325 Pa"#

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

#"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.