Physical Chemistry , 1st ed.

In molar amounts, if we recognize that the total charge (positive or negative)

equals the magnitude of the charge times the fundamental unit of charge (e)

times the number of moles of ions, we can rewrite the above equations as

Iiezi

N

t

i (8.57)

where Nirepresents the number of ions of species i. The absolute value on the

charge of the ion ensures that the current will be positive.

Assuming that the ions are moving with some velocity vithrough the cross-

sectional area A, and expressing the concentration of the ion as N/V(that is,

amount divided by volume), we can write the change in amount per unit time,

Ni/ t, as the concentration times the area times the velocity, or



N

t

iN

V

iAv

i

Substituting into equation 8.57:

Iiezi

N

V

iAvi

Ions conducting current in solution are moving in response to an electro-

motive force acting across the solution. Recall from equation 8.5 that there is

a relationship between force Fand the electric field E:

FiqiE

which we can rewrite using eand the charge on the ion:

FieziE

Newton’s second law says that if a force is acting on an object, the object ac-

celerates and increases its velocity. If there is some ever-present force due to

the electric field, then an ion should accelerate forever (or until it physically

hits an electrode). However, in solution, there is also a force of friction due to

movement through the solvent (just like a swimmer feels a “drag” from the wa-

ter in a pool). This force of friction always works against the direction of mo-

tion, and is proportional to the velocity of the ion. Therefore, we can write

force of friction on ion fvi

where fis the proportionality constant. The force on the ion,Fi,becomes

FieziE fvi (8.58)

Because of the force of friction, at some velocity the net force on the ion will

drop to zero and the ion will no longer accelerate. Its velocity will remain

constant. According to equation 8.58, this terminal velocity can be derived as

follows:

0 eziE fvi

viez

f

iE (8.59)

But what is f, the frictional proportionality constant? According to Stokes’

law,the frictional constant of a spherical body with radius rimoving through

a fluid medium with a viscosity is

f 6 ri (8.60)

8.8 Ionic Transport and Conductance 235

Figure 8.10 Ionic current travels in two direc-
tions, and is measured in terms of how many ions
pass through some cross-sectional area Aper unit
time.

AreaA

I

I





Ionic
solution