Lecture 2
Quantization of Electric Charge
A. Avogadro’s Number
After Copernicus, Kepler, Galileo and Newton the equations of motions of point masses in
force fields were available to describe the equation of low pressure high temperature gases:
(a) Equation of state pV=NRT
(b) Chemical reactions like H + Cl
HCl
With two basis assumptions:
(a) Gasses consist of point particles
(b) At the same p, T in the same volumes (V) there are equal number of particles
What was not known how many particles there are N(p,T,V) = ?
The great progress was made when Avogadro discovered that for any element.
NA
in one molar mass of any element there are
6.02 1023 particles
Homework set 1
1. Calculate the molar masses of one mole of the following elements in grams
1 mole of H =
1 mole of C =
1 mole of Na=
1 mole of Cl =
1 mole of Cu=
1 mole of S =
1 mole of O =
1 mole of U 238
grams
grams
grams
grams
grams
grams
grams
grams
B. Electrolysis
Chemical changes occur when an electric current is passed
through a solution. This process is known as electrolysis.
Faraday studied the conduction of electricity in liquids (1833)
He passed a DC current through weakly conducting solutions
and observed a subsequent liberation of the components of the
solution at the electrodes.
Quantitatively Faraday discovered that the same quantity of
electricity “F”, called the “Faraday”, (and equal to about
96500 coulomb of charge) always decomposes 1 mole of mass
of monovalent ions
Homework set 1
2. Consider a solution of Na Cl. If F = 96500C passes through the solution.
How many grams of Na appears at the cathode and how many grams of Cl
at the anode?
3. Consider a solution of
CuSO4 . Knowing that Cu
and SO4
are
bivalent ions, calculate how many “F “ charge will be needed to
decompose one mole of Cu on the negative electrode ?
Faraday’s finding can be summarized mathematically as
M
Q
nJ
Where M is the total mass liberated in grams at the electrodes,
is the molar mass of the molecule in grams, Q is the total
electric charge passed through the solution, n is the valence of
the ions and F is the Faraday constant of J = 96500C
Fundamental Unit of Electric Charge
Assuming that the electrolyzes process takes place in three steps
1.) A and B atoms are bond by ionic bond into AB molecules
2.) AB A + +B dissociation takes place due to the electric
field and solution
3.) Drifts to the electrodes
_
+
A
B
_ +
Battery
4. Negative and positive charges are deposited on the electrodes
and become neutral atoms attached to the electrodes
From the assumptions of the above processes the fundamental
relation follows
F
N Ae
Homework set 1
4. From the knowledge of F and N calculate the magnitude of e
e=
coulombs
Fundamental Unit of Electric Charge
where NA is Avogadro’s number
Specifically, Faraday found that to decompose 1 mole of
monovalent ions requires a total charge of 96,487 C being
passed through the solution.
Therefore, we have
e
F
NA
96487
6.02 10 23
1.60 10
19
C