**copyright 2003**
**Gary L. Bertrand**
**University of Missouri-Rolla**

**When a mild electric field (Volts,
E)
is applied across a pair of electrodes immersed in a solution, there is
a tendency for current (Amperes,
I)
to flow. This current is carried through the metal wires by electrons,
but electrons are not able to move through the solution. The current
through the solution must be carried by ions. Part of the current
is carried by negatively-charged anions
moving in the same direction as the electrons. The rest of the current
is carried by positively-charged cations
moving in the opposite direction.**

**The amount of current that is
observed depends on a number of factors:**

** 1. The current
(I) is directly
proportional to the voltage (E).**

** 2. The current
(I) is directly
proportional to the area of the electrodes (A).**

** 3. The current
(I) is inversely
proportional to the distance between the electrodes (d).**

** 4. The current
(I) is roughly
proportional to the concentrations of the ions (C).**

**This suggests an equation relating
these terms:**

**
I = constant
xExAxC/d
,**

**in which the constant depends
on the solvent,**
**the nature of the ions, and
the temperature.**

**The ratio of voltage to current
is defined as the electrical resistance (E/I
= R), so the
ratio of current to voltage is the reciprocal of the resistance:**

** I/E
= 1/R
= constant x C
x (A/d)
.**

**The quantity A/d
is determined by the construction of the electrodes, and is called the
cell constant (K _{cell},
cm) with dimensions of cm^{2}/cm.**

**Conductivity is defined as 1/R.
It has the units of ohms ^{-1}, and was originally called mhos,
but is now defined as Siemens
(S).**

**The specific conductivity ( K,
kappa)
is defined as the conductivity between electrodes of 1 cm^{2} area
and 1 cm apart:**

**with dimension S/cm , and**

**
K = constant
x
C .**

**When the concentration of the
ions is given in moles/cm ^{3}, the constant is called the molar
conductivity and has the dimension of S-cm^{2}/mole.**

**It is more common to use a term
called the equivalent conductivity (L
, lambda
, S-cm^{2}/equivalent)**

**
K = L
x C x
N ,**

**in which N
is a simple factor for converting from moles to equivalents:**

**
N = 1
for 1:1 electrolytes such as HCl, KBr, NaNO _{3}, etc.**

**
N = 2
for H _{2}SO_{4}, BaCl_{2}, PbSO_{4}**

**
N = 3
for Al(OH) _{3}, H_{3}PO_{4}**

**
N = 6
for Al _{2}(SO_{4})_{3}**

**Precise measurements show that
the equivalent conductivity varies slightly with concentration, approaching
a limiting value at infinite dilution (L _{o}),
and increases with increasing temperature. The concentration
of ions is equal to the equivalent concentration for an ionic compounds
which ionizes completely (strong electrolyte), but for a partially-ionized
compound (weak electrolyte) the concentration of ions may be much smaller
than the equivalent concentration of the compound.**

**The value of L
provides a measure of how easily the ions move through the solution.
A simpler comparison can be made by measuring the conductivities of solutions
of different ionic compounds at the same equivalent concentration.
This comparison can be made at any concentration, but with most commercial
instruments with a cell constant of unity (K _{cell
}=
1) a convenient concentration is 0.001
moles/Liter for 1:1 electrolytes and 0.0005
moles/Liter for divalent electrolytes (sulfates and barium or calcium salts).**