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

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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.


Some additional examples.

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, 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!!


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