Physical Chemistry , 1st ed.

This equation is known as Coulomb’s law.In order to get the correct unit of

force, newtons, from equation 8.2, an additional expression is included in the

denominator of the equation. The complete SI form of Coulomb’s law is

F

4 

q 1

 0





q 2

r^2

 (8.3)

where q 1 and q 2 are in units of C and ris in units of m. The term 4in the de-

nominator is due to the three-dimensionality of space.* The term  0 (“epsilon

naught”) is called the permittivity of free space.Its value is 8.854    10

12 C^2 /(Jm),

and its units allow for the proper algebraic conversion from units of charge and

distance to units of force. Because the q’s can be positive or negative, by conven-

tion Fis positive for forces of repulsion and negative for forces of attraction.

Example 8.1

Calculate the force between charges in the following cases.

a. 1.6  10

18 C and 3.3    10

19 C at a distance of 1.00  10

9 m

b. 4.83     10

19 C and 3.22   10

19 C at a distance of 5.83 Å

Solution

a.Using equation 8.3, we substitute:

F

The coulomb units cancel, as does one of the meter units. The joule unit is

in the denominator of the denominator, which ultimately places it in the nu-

merator. Evaluating the numerical expression, we find that

F4.7  10

9 

m

J

4.7 10

9 N

In the final step, we have used the fact that 1 J 1 Nm. The positive value

for the force indicates that it is a force of repulsion. This is a very small

force for macroscopic objects, but a very large force for atom-sized systems,

like ions.

b.A similar substitution yields

F

where the distance of 5.83 Å has been converted to standard units of meters.

Solving:

F

4.1     10

9 N

In this case, because the force is negative, it represents a force of attraction

between the two charged bodies.

( 4.83 10

19 C)( 3.22 10
19 C)



4 8.854   10

12 

J

C

m

2

(5.83     10

10 m)^2

( 1.6 10

18 C)( 3.3 10
19 C)



4 8.854   10

12 

J

C

m

2

(1.00     10

9 m)^2

208 CHAPTER 8 Electrochemistry and Ionic Solutions

*Actually, 4is related to the three-dimensional coordinate system used to define space,

and the fact that the force is spherically symmetric and depends only on the distance be-

tween particles. This factor will appear again in our discussion of spherical polar coordi-

nates in Chapter 11.