Physical Chemistry Third Edition

10.5 Electrical Conduction in Electrolyte Solutions 475

10.48Poiseuille’s equation for the flow of a gas through a tube
is different from that of an incompressible liquid. If the
gas is assumed to be ideal, the equation for the molar rate
of flow is^10
dn
dt



πr^4

(

P 12 −P 22

)

16 ηLRT

where we now userfor the radius of the tube andRfor

the ideal gas constant, and wherenis the number of moles

of the gas that has passed through the tube. Find the time

required for 0.100 mol of carbon dioxide to flow through

a tube of length 40.0 cm and diameter 0.850 mm at

20.0◦C.

10.49Liquid water at 20.0◦C is flowing through a cylindrical

tube of length 1.00 m and radius 0.00200 m. The average

flow speed is 0.0500 m s−^1.

a.Find the volume rate of flow,dV/dt.

b.Find the difference in pressure at the ends of the tube.

c.Find the flow speed at the center of the tube.

d.Is the flow laminar?

10.5 Electrical Conduction in Electrolyte Solutions

Electric currents in metallic conductors and semiconductors are due to the motions of

electrons, whereas electric currents in electrolyte solutions are due to the motions of

ions.Ohm’s lawasserts that the current in a conducting system is proportional to the

voltage imposed on the system:

I

V

R

(10.5-1)

whereVis the voltage (the difference in electric potential between the ends of the

system),Iis the current (equal to the amount of charge passing a given location per

second), andRis the resistance of the conductor. (Do not confuse this use ofRwith

the ideal gas constant. There aren’t enough letters in the alphabet for us to use a letter

for only one variable.) The direction of an electric current is defined as the direction

of apparent motion of positive charges. This convention was proposed by Benjamin

Franklin. Ohm’s law with a constant resistance is obeyed very nearly exactly by metallic

conductors, to a good approximation by electrolyte solutions, and fairly accurately by

semiconductors.

Benjamin Franklin, 1706–1790, was a
self-trained physicist as well as a
printer, inventor, politician, and
diplomat. He also invented the
designation of the two kinds of electric
charge as positive and negative.

Ohm’s law is named for Georg Simon
Ohm, 1787–1854, a German physicist
who was a high-school teacher when he
discovered Ohm’s law by carrying out
experiments at home. He even made
his own wires for his early experiments.

Ohm found by painstaking experiments with homemade equipment that the resis-

tance of a conductor of uniform cross section is proportional to its length and inversely

proportional to its cross-sectional area. We define theresistivityrof a conducting object

shaped as in Figure 10.9 by

r

RA

d

(10.5-2)

whereAis the cross-sectional area anddis the length of the object. If Ohm’s law is

obeyed the resistivity is independent ofdandA, depending only on the composition

of the object, the temperature, and (very slightly) on the pressure.

The SI unit of resistivity is the ohm meter (ohm m). The reciprocal of the resistivity

is called theconductivityand denoted byσ:

σ

1

r

(10.5-3)

(^10) D. P. Shoemaker, C. W. Garland, and J. W. Nibler,Experiments in Physical Chemistry, 5th ed., McGraw-Hill, New York, 1989, p. 132ff.