This is the energy released when 1 mol of gaseous ion pairs is formed, not when 1 mol of positive and negative ions condenses to form a crystalline lattice. This distance is the same as the experimentally measured bond distance.Įquation 8.3 E = ( − 9.79 × 10 − 19 J/ ion pair ) ( 6.022 × 10 − 23 ion pair /mol ) = − 589 kJ/mol ![]() The purple curve in Figure 8.1 "A Plot of Potential Energy versus Internuclear Distance for the Interaction between a Gaseous Na" shows that the total energy of the system reaches a minimum at r 0, the point where the electrostatic repulsions and attractions are exactly balanced. The total energy of the system is a balance between the attractive and repulsive interactions. At very short distances, repulsive electron–electron interactions between electrons on adjacent ions become stronger than the attractive interactions between ions with opposite charges, as shown by the red curve in the upper half of Figure 8.1 "A Plot of Potential Energy versus Internuclear Distance for the Interaction between a Gaseous Na". Because ions occupy space, however, they cannot be infinitely close together. As shown by the green curve in the lower half of Figure 8.1 "A Plot of Potential Energy versus Internuclear Distance for the Interaction between a Gaseous Na", Equation 8.1 predicts that the maximum energy is released when the ions are infinitely close to each other, at r = 0. If Q 1 and Q 2 have opposite signs (as in NaCl, for example, where Q 1 is +1 for Na + and Q 2 is −1 for Cl −), then E is negative, which means that energy is released when oppositely charged ions are brought together from an infinite distance to form an isolated ion pair. In this case, the proportionality constant, k, equals 8.999 × 109 J The equation can also be written using the charge of each ion, expressed in coulombs (C), incorporated in the constant. This value of k includes the charge of a single electron (1.6022 × 10 −19 C) for each ion. ![]() The proportionality constant k is equal to 2.31 × 10 −28 J Where each ion’s charge is represented by the symbol Q. Equation 8.1 E ∝ Q 1 Q 2 r E = k Q 1 Q 2 r
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