# Homework Help: Energies of interaction

1. Feb 24, 2015

### burns96

1. The problem statement, all variables and given/known data
Neglecting hydrogen-bonding, calculate the interaction energy between
(i) H3O+ and H2O and
(ii) H3O+ and H3O+,
if each pair is separated by 0.3 nm and assuming that the aqueous solvent can be treated as a medium with constant relative permittivity. Using your result, comment on the likelihood of ideal behaviour by H3O+ at high molality

2. Relevant equations
Ion-dipole interaction
V=−qμ/(4πϵ0)r2
r is the distance of separation.
q is the charge of the ion ( only the magnitude of the charge is shown here.)
μ is the permanent dipole moment of the polar molecule.

Ion-ion interaction
U(r)= (q1q2)/(4*π*E0)*(1/r)

3. The attempt at a solution
V=−qμ/(4πϵ0)r2
r is the distance of separation so 0.3nm
q is the charge of the ion so 1 here
μ is the permanent dipole moment of the polar molecule 6.2 x 10-30 C m
So if I can treat it as having constant relative permittivity then I just need the permittivity of a vacuum.
so
(-1 x 6.2 x 10-30)/(4π8.85 x 10-12x(0.3x10-9)2
And I got 0.619 from this which doesn't sound right?

U(r)= (q1q2)/(4*π*E0)*(1/r)
(1x1)/(4π8.85 x 10-12x(0.3x10-9) x (1/0.3x10-9)
=2.70 x 1018 which sounds ridiculous

2. Feb 25, 2015

### Staff: Mentor

You definitely need to put units in there.