### Converting between Units of Pressure: atm., mmHg and kPa

Here is a repeat from the "Four Variables" file:

There are three different units of pressure used in chemistry. This is an unfortunate situation, but we cannot change it. You must be able to use all three. Here they are:

1. atmospheres (symbol = atm)
2. millimeters of mercury (symbol = mmHg)
3. Pascals (symbol = Pa) or, more commonly, kiloPascals (symbol = kPa)

I. Converting between atmospheres and millimeters of mercury.

One atm. equals 760.0 mm Hg, so there will be a multiplication or division based on the direction of the change.

Example #1: Convert 0.875 atm to mmHg.

Solution: multiply the atm value by 760.0 mmHg / atm.

 760.0 mmHg 0.875 atm x –––––––––– 1 atm

Notice that the atm values (one in the numerator and one in the denominator) cancel, leaving mmHg.

Example #2: Convert 745.0 mmHg to atm.

Solution: divide the mmHg value by 760.0 mmHg / atm

 745.0 mmHg ––––––––––––––– = 0.980 atm 760.0 mmHg / atm

Notice that the mmHg values cancel and the atm, in the denominator of the denominator, moves to the numerator. Note also that the answer of 0.980 atm has been rounded off to three significant figures.

II. Converting between atmospheres and kilopascals.

One atm equals 101.325 kPa, so there will be a multiplication or division based on the direction of the change.

Example #3: Convert 0.955 atm to kPa.

Solution: multiply the atm value by 101.325 kPa / atm.

 101.325 kPa 0.955 atm x –––––––––– = 96.8 atm (to three sig figs) 1 atm

Notice that the atm values( one in the numerator and one in the denominator) cancel, leaving kPa. Sometimes the 1 in front of atm is eliminated. In that case, think of the 1 as being understood to be there.

Example #4: Convert 98.35 kPa to atm.

Solution: divide the kPa value by 101.325 kPa / atm.

 98.35 kPa ––––––––––––––– = 0.9706 atm 101.325 kPa / atm

Notice that the kPa values cancel and the atm, in the denominator of the denominator, moves to the numerator. The answer is rounded to four significant figures.

III. Converting between millimeters of mercury and kilopascals.

760.0 mmHg equals 101.325 kPa, so both values will be involved. This situation is slighly unusual because most conversions involve a one, usually in the denominator. The conversion examples above are examples of a one being involved. For example, 760.0 mmHg / 1 atm in examples 1 and 2. The 1 was assumed to be present.

By the way, the 1 (as in 1 atm) has no influence on significant figures.

In this conversion, both 760.0 and 101.325 will be involved and the location of each (numerator or denominator) will depend on the conversion.

Example #5: Convert 740.0 mmHg to kPa.

 101.325 kPa 740.0 mmHg x –––––––––––– = 98.66 atm (to four sig figs) 760.0 mmHg

Notice that the mmHg will cancel, since one is in the numerator and one is in the denominator, leaving kPa as the unit on the answer.

Example #6: Convert 99.25 kPa to mmHg.

 760.0 mmHg 99.25 kPa x –––––––––––– = 744.4 mmHg (to four sig figs) 101.325 kPa

Notice that the kPa will cancel, since one is in the numerator and one is in the denominator, leaving mmHg as the unit on the answer.

Example #7: Convert 1.69 atm to torr

 760.0 torr 1.69 atm x –––––––– = 1280 torr (to three sig figs) 1 atm

torr is the same as mmHg. It was intended as a replacement for mmHg, however, mmHg did not fade away. You need to know what torr is. By the way, it is a lowercase t, not a capital, as in Torr.

If your instructor insists in using Torr, just follow his/her practice. Don't tell 'em some guy on the Internet (me!) said they were wrong.

Example #8: Convert 0.3587 atm to Pa

 101,325 Pa <--- note the comma, not decimal point 0.3587 atm x ––––––––– = 36340 Pa (to four sig figs) 1 atm

kPa (kilopascals) is the more commonly used unit, but Pa is used from time to time. 101.325 kPa = 101,325 Pa.

Example #9: Convert 820.1 torr to kPa

 101.325 kPa 820.1 torr x –––––––––– = 109.3 kPa (to four sig figs) 760.0 torr

Example #10: Convert 689 mmHg to Pa

 101,325 Pa 689 mmHg x –––––––––– = 91800 Pa (to three sig figs) 760.0 mmHg

Example #11: Convert 725.0 torr to mmHg

 760.0 mmHg 725.0 torr x ––––––––––– = 725.0 mmHg 760.0 torr

Ha!! A trick question!!

Example #12: A student reads a barometer in the laboratory and finds the prevailing atmospheric pressure to be 720.0 mmHg. Express this pressure in atmospheres, kilopascals, torrs, pounds per square inch, and pascals.

Hint: 1 atm = 101.325 kPa = 760.0 torr = 760 mmHg = 14.696 psi = 101,325 Pa

Solution:

(720.0 mmHg) (1 atm / 760 mmHg) = 0.9474 atm

(720.0 mmHg) (101.325 kPa / 760 mmHg) = 95.99 kPa

(720.0 mmHg) (760 torr / 760 mmHg) = 720.0 torr

(720.0 mmHg) (14.696 psi/ 760 mmHg) = 13.92 psi

(720.0 mmHg) (101,325 Pa / 760 mmHg) = 9.599 x 104 Pa

Comment: Pounds per square inch is not used in scientific circles. It's used in British and American society and that's about it. Since teachers like to think of themselves as sneaky, it might show up on your test!