Page 47 - Essentials of physical chemistry

Ideal and Real Gas Behavior 9

2 3 7 6 3
1 pascal ¼ 1N=m ¼ 1J=m ¼ 10 erg=10 cm
7 6 3 2
1 pascal ¼ 10 erg=10 cm ¼ 10 dyne=cm ¼ 1Pa ¼ 1 pascal
2 5 2 5
1 newton ¼ 1kgm=s ¼ 10 gcm=s ¼ 10 dyne
2 2 7 7
1 joule ¼ 1Nm ¼ 1kgm =s ¼ 10 dyne cm ¼ 10 erg
We need to convert the standard pressure of 1 atm to other units. Imagine freezing metallic
3
mercury and machining 76 nice shiny cubes exactly (1 cm) (1 cm) (1 cm) ¼ 1cm with the
2
3
density of 13.596 g=cm and then stacking 76 them in a column to evaluate the force on a 1 cm area
to yield a pressure as (pressure ¼ force=area).
3
2
6
2
1 atm ¼ rgh=cm ¼ (13:6 g=cm )(980 cm=s )(76 cm) ffi 1:013 10 dyne=cm 2
This is approximate to help visualize the unit but when more accurate values are used the standard
conversion is
2
5
6
1 atm ¼ 1:01325 10 dyne=cm ¼ 1:01325 10 Pa ¼ 1:01325 bar:
Note also that
1dm ¼ 10 cm ¼ 0.1 m
3
3
1L ¼ 1dm ¼ 1 10 3 m ¼ 1L
3 2 3 6 3
1cm ¼ 1(1 10 m) ¼ 1 10 m
5 2
1 atm ¼ 1.01325 10 pascal where 1 pascal ¼ 1Pa ¼ 1N=m
6 2
1 atm ¼ 1.01325 10 dyne=cm
5
1 bar ¼ 1.00000 10 Pa
1Pa ¼ 10 dyne=cm 2
It will be convenient for some applications to use cgs units so we need to remember what a
dyne is.
1 dyne ¼ 1g cm=s 2
2
1 erg ¼ 1 dyne cm ¼ 1gcm =s 2
Then

2
3
5
(1 atm)(1:01325 10 N=m atm)(22:414 10 3 m =mol)
ffi 8:314 J= K mol

(1 mol)(273:15 K)
R ¼

1 cal ¼ 4.184 J.
So we have several alternative values for R in different units:
R ¼ 0:08206 L atm= K mol

R ¼ 0:08314 L bar= K mol

3
R ¼ 82:06 cm atm= K mol

R ¼ 8:314 J= K mol

R ¼ 1:987 cal= K mol

One of the most common errors students make is to use the incorrect value of R because they forget
to check the units. We could standardized the book on SI units, but in the real world there is a lot of
equipment out there using all kinds of units and you will be better prepared if you learn to cope with
different unit systems including the SI units.