INTERMOLECULAR FORCES AND INTERACTION ENERGY 207 



— 5.76 X 10' volts/cm. This illustrates the very intense fields that occur in 

 the vicinity of ions, and the effects such ions have on neighboring molecules 

 must be considered in terms of these strong fields. 



The electrical field strength is the force that is exerted on a unit charge 

 at the point under consideration. Hence the force exerted on an electron 

 by another electron at a distance of 5 A would be — 1.92 X 10^ dynes/esu 

 X — 4.8 X 10-1" gg^^ = 92 X 10"^ dynes since: 



F„.ce^/^,^^Ml^igl ,6-2, 



The electrical potential in the neighborhood of a point charge is the work 

 required to bring a unit charge from infinity to the point at which the 

 potential is evaluated and is given by: 



a ze 



Electrical potential = V = -i— = — —- (6-3) 



dD dD 



The electrical potential 5 A from an electron would thus be — 4.8 X IQ-^^esu/ 

 5 X 10-8 cm = - 9.6 X 10-^ ergs/esu = - 2.88 volts. 



Finally, the most important quantity for our purposes, the mutual poten- 

 tial energy of two separated charges, is the work required to bring the char- 

 ges from infinite separation to the distance under consideration. This energy 

 can be evaluated by integration of the force between the charges from in- 

 finity to the separation distance d: 



d 

 Potential energy = (f = - \ fdx = — = (6-4) 



It is also the product of the electrical potential at the distance d from the 

 first charge (F^) by the magnitude of the second charge [q.^), since Fj 

 is the work involved in taking unit charge over the same path. The poten- 

 tial energy of two electrons at 5 A distance would then be — 9.6 X 10"^ 

 ergs/esu X - 4.8 X lO-^" esu = 4.6 X lO-^'^ ergs = 1.1 X IO-22 kcal. The po- 

 tential energy is positive if the charges are of the same sign (repulsion) 

 and negative if the charges are of opposite sign (attraction). A univalent 

 cation separated by 5 A from a univalent anion would possess — 1.1 X 10-^^ 

 kcal potential energy. In such cases it is most convenient to express the 

 energy in molar terms. Thus a mole of such ion-pairs would have a poten- 

 tial energy of — 1.1 xlO--^ kcal/ion pair X 6.024x10^3 ion pairs/mole = 



— 66.3 kcal/mole. In fact. Ec£. 6-4 may be rewritten in the convenient form: 



cp = 332 — — kcal/mole (6-5) 



