Coulomb's Law yields an expression for the energy of interaction for a pair of point charges.

 

V= 2.31 * 10^-19 (Q1)(Q2)/r

V is the energy (in J) required to bring the two charges from infinite distance separation to distance r (in nm).
Q1 and Q2 are the charges in terms of electrons.
(i.e. the constant in the above expression is 2.31×10-19 J nm electrons-2)

For a group of "point" charges (e.g. ions) the total energy of interaction is the sum of the interaction energies for the individual pairs.
Calculate the energy of interaction for the arrangement of ions shown in the diagram below.

 

d = 0.620 nm.

d                                         d

+2.     -2.                            +2.     -2very large distance

PROBLEM SET 2: INTERACTION ENERGIES AND PROPERTIES OF SOLUTIONS: Information you will need for these problems: Dielectric constant of H₂O is 80. Dielectric constant of n-pentane is 1.84. Avogadro constant = 6.022 x 10²³ mol^-1.Coulomb constant = 9 x 10⁹ Nm².C². Charge on an electron = 1.602 x 10^-19 C.

1. A chloride ion and a sodium ion are separated by a center-center distance of 0.5 nm. Calculate the interaction energy (the energy required to pull them infinitely apart) if the medium between them is (a) water, or (b) n-pentane. Express the energy in joules per mole of ion pairs.

(c) How far apart would the ions need to be for them to have the same interaction energy as that when they are separated by 0.5 nm in water (i.e. as calculated in part a) if the medium between them is n-pentane? Give your answer in nm.

what is the energy interaction between a sodium ion and one water molecule oxygen? assume a charge of -0.8 on the water molecule oxygen and a dielectric constant of 80.