Page 226 - Essentials of physical chemistry

188 Essentials of Physical Chemistry

Note that we now have not only a formula for the quantized energy E(n, Z) but a formula for the
radius of each quantized orbit. It is quite desirable to investigate the formulas to obtain meaningful
units for the energy and radius. At this point, we need to grapple with a few non-SI units. First, the
definition of an ‘‘electron volt’’ is the energy gained by an electron when accelerated through a
potential of 1 V.

1V ¼ 1J=C (1 Volt ¼ 1 joule per coulomb)
1C ¼ 1 A s (1 Coulomb ¼ 1 Ampere second)
1F ¼ 96,485.3383 C ffi 96,485 C ¼ 1 mol of electrons ¼ 1 Faraday ¼ 1F
1 F is the amount of A s that will electroplate 1 g atom of Ag þ e ! Ag 0
þ

23
1 electron charge ¼ (96,485.3383 C=6.0221415 10 ) ¼ 1.60217653 10 19 C
ffi 1.602 10 19 C
1eV ¼ 1(J=C)(1.60217653 10 19 C) ¼ 1.60217653 10 19 J ¼ 1.60217653 10 12 erg
ffi 1.602 10 19 J
The mass of an electron ¼ m e ¼ 9.1093826 10 31 kg ¼ 9.1093826 10 28 g ffi 9.11 10 28 g
The mass of a proton ¼ m p ¼ 1.67262171 10 27 kg ¼ 1.67262171 10 24 g ffi 1.67 10 24 g
23
1 mol of electron volts ¼ (6.0221415 10 =mol)(1.60217653 10 19 J)
¼ 96.485 kJ=mol ¼ 23.061 kcal=mol

In the 1930s, electrochemistry was a major part of physical chemistry and laboratory measure-
ments were related to easily reproducible experiments. Thus plating out 1 mole of silver metal
from a solution of AgNO 3 was an easy way to measure coulombs with an ammeter to measure
current and a clock measuring seconds. The Faraday constant then requires further definitions of
an ampere etc., but those constants can be obtained through measurements and calculations from
electroplating silver. Today, the modern values are all subjected to a least squares fit of all the
known constants with the best experimental data except, as mentioned above, the value of ‘‘c’’ is
now fixed and not subject to further measurement. The value of ‘‘c’’ is the kingpin of most of all
the other constants.
The units mentioned so far are either SI or accepted for use with SI units but we need
an additional value from the electrostatic unit system. In that system, charge is measured in
‘‘statcoulombs’’ as related to the cgs system where Coulomb’s law can be written as a force between
two charged particles separated by a distance.

qq
Force ¼ ma ¼ 2
r
so the charge

r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ffiffiffiffiffiffiffiffiffiffi (g cm)(cm ) g 1=2 cm 3=2
p
2 statcoulomb
q / mar 2
s s
The numerical conversion from statcoulombs to coulombs is 3.335641 10 10 , so we can convert
the electrochemical coulombs to statcoulombs in cgs units.

(1:60217653 10 19 C) 10
¼ 4:803204 10 statcoulomb
q e ¼ 10
(3:335641 10 )